THE PHENOMENOLOGY OF HARMONIC PROGRESSION

Michael Lance Russell

Dissertation Prepared for the Degree of

DOCTOR OF PHILOSOPHY

UNIVERSITY OF NORTH TEXAS

May 2020

APPROVED: Frank Heidlberger, Committee Chair Andrew Chung, Committee Member Stephen Austin, Committee Member Benjamin Brand, Chair of the Division of

Music History, Theory, and Ethnomusicology

Felix Olschofka, Director of Graduate Studies in the College of Music

John Richmond, Dean of the College of Music Victor Prybutok, Dean of the Toulouse

Graduate School

Russell, Michael Lance. The Phenomenology of Harmonic Progression. Doctor of

Philosophy (Music), May 2020, 156 pp., 58 examples, bibliography, 11 primary sources, 43

secondary sources.

This dissertation explores a method of music analysis that is designed to reflect the

phenomenology of the listening experience, specifically in regards to harmony. It is primarily

inspired by the theoretical approaches of the music theorist Moritz Hauptmann and by the

writings of philosopher Edmund Husserl.

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Copyright 2020

By

Michael Lance Russell

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ACKNOWLEDGEMENTS

There are many people I wish to thank for their encouragement and support throughout

my dissertation-writing process. First, thank you to my dissertation committee, whose insights

and criticisms were invaluable to my progress and development. I would also like to thank the

rest of the University of North Texas Music History, Theory, and Ethnomusicology department

for its high-caliber programs, resources, and people, which continue to foster my passion for

music theory. Thank you to my colleagues and friends in the UNT Theory department and

elsewhere for your encouragement and feedback through this process, with special thanks to

Kaja Lil, Yiyi Gao, and Andrew Vagts, each of whom have helped to edit my work and develop the

ideas.

Thank you to my life-long friends, particularly Taylor Katcher and Becky Bryan, for

showing continued enthusiasm and encouragement throughout the years. Thank you to my

family, whose financial and emotional support helped me complete this project when I was facing

doubt and concern over my ability and willingness to finish. Thank you to Brennan Harmon,

whose unflinching support carried me through to the end. And finally, thank you to my beloved

grandmother, Shirley Klein, who taught me the value of education, and showed me the true

meaning and practice of unrelenting, unconditional love and belief in my potential.

Rest in Peace, Nana.

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TABLE OF CONTENTS

Page ACKNOWLEDGEMENTS ................................................................................................................... iii INTRODUCTION ............................................................................................................................... 1 CHAPTER I: PHENOMENOLOGICAL ACCOUNTING OF MUSICAL MEANING ................................. 12

Musical Meaning and Phenomenology ............................................................................ 12

Applied Phenomenology in Music-Theoretical Discourse ................................................ 18

Phenomenological Thinking in the 19th Century Music Theory ...................................... 26 CHAPTER II: NEO-HAUPTMANNIAN TRANSFORMATIONS ............................................................ 38

Reimagining Transformational Theory ............................................................................. 38

Triadic Transformations .................................................................................................... 41

“Harmonic” Successions Where There Are No Common Tones ...................................... 55

The Indirectly Intelligible Intervals ................................................................................... 59

S-Transformations ............................................................................................................. 64

Lines of Communication ................................................................................................... 71 CHAPTER III: THE PROCESS OF HARMONIC SUCCESSION ............................................................. 78

Objects of Perception ....................................................................................................... 78

Perceptual Hierarchies ...................................................................................................... 84

Changes in Harmonic Process and Subverting Expectations ............................................ 90 CHAPTER IV: ANALYTICAL APPLICATIONS ................................................................................... 104

G.F. Handel, “Thus Saith The Lord” from Messiah ......................................................... 104

J.S. Bach, E-Major French Suite, BWV 817, Minuet ........................................................ 113

Arnold Schoenberg, “Erwartung” Op.2 No. 1 ................................................................. 126 SUMMARY AND CONCLUSIONS .................................................................................................. 150 BIBLIOGRAPHY ............................................................................................................................ 153

“Man is a creature that can get accustomed to anything, and I think that is the best definition of him.”

~Fyodor Dostoyevsky, The House of the Dead, 1861

The first sentence of Hugo Riemann’s Harmony Simplified states, “The Theory of Harmony

is that of the logically rational and technically correct connection of chords.” That is the premise

on which transformational theory is based. Since the revival of Riemannian theory spearheaded

by David Lewin, Brian Hyer, Jack Douthett, Peter Steinbach and others, transformational theory

has largely focused on parsimonious voice-leading with regards to the compositional process. A

transformation indicates a melodic motion that “transforms” one chord into another, i.e., Chord

A (Transformation X) = Chord B. The theory often seeks to illustrate these “logical” connections

with geometric modeling. In this way, transformational theory, as do most music theories, uses a

language which conceptualizes chords as discrete objects that exist in an abstract harmonic

“space.” This allows theorists to describe relationships between these discrete objects in terms of

their relative positions in that space.

However, what is missing from this approach is a thorough investigation into how the

listening person interacts with those discrete objects. After all, if a chord changes and no one is

there to hear it, does it make a sound? As Robin Attas notes, transformational theory often runs

contrary to a “phenomenological position” on music, where music is conceptualized and

investigated through the lens of subjective experience.1 Dmitri Tymoczko also notes the distinction

between theoretical positions. He observes that the cognitive structures for those who are

involved in making music are not necessarily the same as those involved in perceiving it, and as

1 Attas 2009, 2

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INTRODUCTION

such there are “at least two separate projects that music theorists can engage in: modeling what

composers actually do, and modeling what listeners actually experience.”2 Transformational

theory is an analytical model that is designed for the former project. In other words,

transformationalists study the motions of tones, but not how the meanings of those tones are

interpreted by the listener.

The purpose of this project is to introduce a new conceptualization of transformational

theory, one that attempts to model the listener’s phenomenological experience of harmony. In

order to do so, one must engage with musical meaning. The first chapter of this work reviews

current and historical literature on musical meaning, and how theorists have engaged musical

meaning through applied phenomenological models. Within the study of musical meaning, I am

referring specifically to absolute meaning – meaning determined from melodic, harmonic, and

rhythmic relations within a work itself. This position is called “musical formalism,” and it is in

contrast to extramusical meaning, where meaning is found in music through its perceived relation

with another lived experience. That kind of meaning is called “musical referentialism.”3 Although

both positions can and should be considered carefully in order to fully appreciate the totality of a

musical experience, it is absolute meaning with which this project is primarily concerned.

One of the central premises of this project is the notion that determining absolute meaning

represents temporal process in itself. This concept has been explored most notably in Christopher

Hasty’s book, Meter as Rhythm, in which he devises a uniquely phenomenological rhythmic theory

which he calls his “Theory of Projection.” Hasty’s theory, as is the theory serving as the foundation

2 Tymoczko 2011, 55 3 Meyer 1956, 2-3

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for this project, is grounded in a conception of temporal experience devised by Edmund Husserl.

In the Phenomenology of Internal Time-Consciousness, Husserl argues that the memory of an

event holds within it a more or less definite expectation of a future event, something he calls a

“protention.” Hasty incorporates this notion of protention into his rhythmic theory, or perhaps

more accurately, his theory of the perception of rhythm. Hasty argues that when a complete

rhythmic event is perceived, so too is an expected time of arrival (or “realization”) of a successive

rhythmic event. That expectation is the “projection,” or the Husserlian “protention.”

Hasty cites Moritz Hauptmann’s work, The Nature of Harmony and Meter, as one of two

primary precedents for his Theory of Projection.4 Hasty writes that his account of projection

resembles Hauptmann’s investigation into the absolute meaning of duple meter. Hauptmann

observes that the beginning of a successive event both determines meaning for itself and for the

first event by establishing a marked duration between the two events (Bestimmende) and

generates potential for a third event (Bestimmte):

If one impulse cannot determine a space of time or a definite length of time, but rather only a beginning without end, we do obtain a temporally determinate whole with two immediately successive impulses, in which the interval enclosed by the two impulses is the half. The first metrical determination is not simple but duple, a repeated time-interval.

These two impulses comprise only one extent of time. But with these two impulses we obtain not one but two determinate beats. With the second impulse, with the end of the enclosed space of time, there is given at the same time the beginning of a second which is equal in duration to the first. At the end of this beat we can expect a new impulse which, if it is not to give rise to an interruption, a cutting short of time that is determined by the two impulses, may not follow earlier than this end-point.

A simple duration is not a metrical unity and cannot emerge as a metrical whole. A simple duration has meaning for a metrical determination only as part of the whole, as a first for a second; for the metrical whole is from its determination an

4 The other being Fredrich Neumann’s 1959 book, Die Zeitgestalt: Eine Lehre vom musikalischen Rhythmus.

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inseparable double, a unity of two [eine Zwei-Einheit]. (Hauptmann 1853, pp. 211-212)

Here the absolute meaning of the two successive musical events that create duple meter

is the determination of the temporal relationship between them, “a first for a second,” and the

expectation (or potential) of a third impulse of equal measure. The temporal relationship between

impulses rests on the conscious experience of duration and the expectation of repetition. In this

project, I argue that one perceives the succession of harmonic events in a similar manner.

However, in successive harmonic events, determining what “projects” is quite a different task. The

perception of duration does not address the relationship between two differing chords; further,

expectation does not come about through repetition if the chords have different tones. If two

chords had the exact same tones, their relationship would be a metrical one, not harmonic. So

how then, is absolute harmonic meaning determined? To use Hasty’s terminology, how does a

chord or succession of chords generate a definite projective potential?

A harmonic entity is by definition a musical utterance in which multiple impulses occur

simultaneously, and so its absolute meaning must be determined by the relationships between

those impulses. With this in mind, we too can turn to Hauptmann’s work for guidance. Hauptmann

sought to determine the absolute meaning (the nature) of harmony through a study of the

intervallic relationships found within it. In his study he determined that there were three “directly

intelligible” intervals upon which the foundation of harmonic meaning is laid: The Octave, which

he believed expresses the notion of unity, the Fifth, which expresses opposition, and the Third,

which expresses the union of unity and opposition.5

5 Hauptmann 1853, 5-6

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Setting aside the distinctly Hegelian dialectical overlay of thesis, antithesis, and synthesis

for which Hauptmann is so well-known, the perspective of understanding the meaning of tones

through their relationships with other tones is a useful framework for determining how those

relationships transform in the succession of one harmony to the next. For Hauptmann, proper

voice-leading is not defined by a conservation of motion between the parts, but rather by the

listener’s capacity to identify a reference to a “common element which changes meaning during

the passage.”6

Consider the C-major triad followed by the F-major triad in Example I.1a. In tonal harmony,

this would likely be perceived as a tonic-predominant (I – IV) relationship. Generally accepted

theories of the harmonic phrase model would suggest that a G-major dominant V chord would be

most likely to follow, with a motion to another predominant or back to tonic being less likely but

possible alternatives. Leonard Meyer notes this in his discussion of probability, borrowing a “Table

of Usual Root Progressions” from Walter Piston.7 So then, one could argue that the predominant

chord creates an expectation for a dominant chord (hence, the term predominant). But such an

argument would be based on a statistical study of stylistic phenomena that occur over a large body

of musical works, rather than an observation of a repeated harmonic phenomenon within the

6 Hauptmann 1853, 43 7 Meyer 1956, 54

Example I.1: Harmonic Expectations

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context of a single composition. If a listener had never heard a tonal piece of classical music before,

they could not have been prepared to expect a tonic-predominant-dominant (I – IV – V) harmonic

pattern. While stylistic norms can and do play a role in generating expectation, they are ultimately

an externally imposed cultural expectation rather than one derived from the specific musical

experience itself.

While it is certainly true that all stylistic norms, understandings of them, and

understandings based on them come from musical experiences, in this project I seek to focus more

narrowly on the harmonic experiences that occur within the context of a single work; I wish to

discuss what harmonic transformations occur in this piece, at this time. Although one can (and

should) adjust their expectations when they have strong evidence to suggest a stylistically

informed option, it can also be useful to consider how harmonies can generate expectational

states for the listener absent any stylistic context. For example, we can focus on how the meanings

of common tones change as harmonies progress from one chord to another. For the progression

shown in the example, the tone which means Root in the C-major chord changes meaning and

becomes Fifth in the F-major chord. I annotate this transformation, which I call an R5, in Example

I.1b. I would argue that this change in meaning generates a projective potential for a repetition of

the transformation (in this case to a B° chord). I propose that this transformation of meaning is

what separates the two harmonies in the mind (“a first for a second”) and generates an

expectation for the next chord. The second chapter details new transformational types and

discusses the implications of the theory, which I call “Neo-Hauptmannian” transformational

theory, how it can fit into functional and non-functional harmonic models, and how it compares

and contrasts to other transformational theories.

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Neo-Hauptmannian harmonic transformations differ from Neo-Riemannian

transformations in important ways. First, Neo-Hauptmannian transformations redirect attention

away from the melodic activities that transform one chord into another and toward the changes

in meaning that one can interpret from those activities. In this way, Neo-Hauptmannian analysis

is not used as a method for studying compositional practices. Instead, it sets a framework for how

tones could move, and what expectational states a relationship between two chords can generate

for the listener; within that framework, there is some room for flexibility. Consider Example I.2a

and I.2b. If one identifies the R5-transformation as a perceptual action with projective potential,

there is an equal probability that it’s potential could be realized by an F-major chord or an F-minor

chord, because the change of meaning for the tone C is the same either way. If a composer were

to engage with this perspective in their compositional process, it would allow them to choose

either option while maintaining logical consistency. This is in contrast to David Lewin’s “tonic-

directed” transformational type SUBD, for example, which would definitively take a C-major chord

to F-major.8

From an analytical perspective, Neo-Riemannian transformations encounter a special

problem in their application – the connection of triads and tetrachords. There has been significant

8 Lewin 1982, 175-80

Example I.2 : Potential R5 Outcomes

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research concerning how triads can move from one to another, and how tetrachords can move

from one to another, but there is limited research on how to connect the independent systems.

Richard Bass called this problem an “absence of lines-of-communication.”9 Since Bass’s claim,

Julian Hook has proposed a way to bridge that gap in the form of what he calls “cross-type

transformations,” which, under certain conditions, can connect triads to tetrachords.10 But those

conditions are dependent upon specific types of voice-leading motions between certain

specifically major or minor triads and dominant or half-diminished tetrachords.

Obviously, additional tones greatly expand the possible types of chordal motion, since

there is a new axis of transformation on which to move. Douthett and Steinbach, Adrian Childs,

Edward Gollin, and Richard Cohn, to name a few, all have developed complex three-dimensional

voice-leading models to illustrate possible connections between tetrachords.11 Because Neo-

Riemannian transformations describe specific voice-leading motions, all of these models exist in a

closed, interconnected geometric space. Using these geometric spaces, the analysis of a musical

work is a matter of tracking the harmonic progression as it travels along the roads of

transformation laid before it, noting in which neighborhoods it stops, how direct its path, and to

where it returns. However, since these geometric spaces are closed networks, moving among

tetrachords that are of different types and not of the same pitch-class set (such as a motion from

a minor-minor seventh-chord to a major-major seventh-chord, for example), becomes

problematic.

9 Bass 2001, 41 10 Hook 2007, 4 11 Douthett and Steinbach 1998, Childs 1998, Gollin 1998, and Cohn 2003

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The Neo-Hauptmannian transformational language proposed here side-steps these issues.

Regarding the lines-of-communication problem – while the addition or subtraction of tones may

change the absolute meaning of held tones, the mental process by which the listener comes to

understand those meanings remains the same. As shown in Example I.2c, an R5-transformation

from a C-major triad would still be an accurate descriptor if the succeeding chord is an F7

tetrachord. The process of determining the meanings of intervals within a harmonic entity remains

the same regardless of whether a chordal seventh is added to a triad. Neo-Hauptmannian

transformations describe changes in interval-meaning, not voice-leading operations. The

transformational type is defined by the way the listener reorganizes their perception of what notes

are recognized as Root, Third, Fifth, or beyond. The subject of study is not the parsimonious

connections between chords, but rather the manner in which the interval-meanings of tones are

reinterpreted over time. If we are conceptualizing transformations in this way, then we cannot

model those transformations three-dimensionally; the experience is temporal, not spatial, and

listeners experience time linearly. Instead, an abstract model might look more like a root structure,

where each new chord projects new branches of possible musical expectations. The analyst could

then follow the progression of the work through the most likely of expectational states, noting

when and how those expectations are generated and when they are confirmed or denied.

The third chapter will turn to analytical applications of this meaning-focused Neo-

Hauptmannian transformational methodology. As a method of phenomenological analysis, it is

concerned with uncovering how harmonic motion generates expectation, if or how those

expectations might be denied or realized, and with describing how those realizations reinforce or

degrade past perceptions. It also allows us to imagine alternative unfoldings of a musical

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experience, lets us compare what the harmony actually does to what it could have done, and

allows us to speculate as to whether our understanding of what could have been informs our

perception of what is. This last concept is the one that David Lewin famously explored in his

analysis of Schubert’s “Morgengruß.”

The fourth chapter will offer detailed analysis of three musical examples using this Neo-

Hauptmannian transformational methodology. It will begin with the opening segment of Handel’s

“Thus Saith The Lord” from Messiah. Following that will be a complete analysis of Bach’s E-Major

French Suite, BWV 817, Minuet. This analysis will be accompanied by a critique and comparison of

Peter Smith’s perspective on the phenomenology of the minuet. In his 1995 article, “Structural

Tonic or Apparent Tonic? Parametric Conflict, Temporal Perspective, and a Continuum of

Articulative Possibilities,” Smith engages with David Lewin’s perception model to study an

apparent contradiction in the Minuet’s musical form. Contrasting our readings will demonstrate

how Neo-Hauptmannian methodology engages Lewin’s perception model, and showcase how it

can offer the analyst a unique perspective to a phenomenological reading. The final analysis will

be of one of Schoenberg’s earliest art songs, his Op. 2, No. 1, “Erwartung.” Although it is

significantly removed from the Handel and Bach pieces in the musical canon, “Erwartung”

encounters some of the same phenomenological issues as the earlier works. Analyzing it will

demonstrate the flexibility of Neo-Hauptmannian transformations, and offer a fresh artistic

interpretation of the poem based on the specific ways that Schoenberg challenges a listener’s

harmonic expectations.

The goal of this dissertation is to offer a unique phenomenological approach to harmonic

analysis. As I stated at the beginning of this introduction, most music theories use a language which

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conceptualizes chords in terms of discrete objects existing in a harmonic space, and that this often

runs contrary to a phenomenological analysis, which considers the time-experience of the listener.

Neo-Riemannian methods give us a means to describe logical chord connections in functional or

non-functional triadic and tetrachordal music. However, because the methods often focus on

voice-leading operations rather than the listener’s capacity to perceive changes in the contextual

meanings of those voices, their capacity to articulate phenomenological experience is limited.

With this Neo-Hauptmannian method, I believe an analyst can discern the phenomenology of

harmonic progression more precisely, both within the context of tonal harmony and other non-

functional contexts, and offer fresh insight into the listening experience.

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Generally speaking, there are two avenues of exploration in the study of musical meaning,

depending on one’s position on what constitutes meaning. In the opening chapter of Emotion and

Meaning in Music, Leonard Meyer frames the discussion as such:

The first main difference of opinion exists between those who insist that musical meaning lies exclusively within the context of the work itself, in the perception of the relationships set forth within the musical work of art, and those who contend that, in addition to these abstract, intellectual meanings, music also communicates meanings which in some way refer to the extramusical world of concepts, actions, emotional states, and character. Let us call the former group the “absolutists” and the latter group the “referentialists.”12

The process by which we attempt to interpret musical meaning draws a further distinction

between these two aesthetic positions. The first is musical formalism, which is the theory that

musical meaning is innate, self-evident, able to be systematically deduced, and rational. The

principle has existed throughout history as far back as Aristoxenus of Tarentum, as Amanda Staufer

has recently noted.13 However, Leonard Meyer was one of the first philosophers, as Staufer has

called him, to promote formalism in the realm of musical aesthetics. Formalism is the aesthetic

position that I take for this project and for the development of Neo-Hauptmannian theory. The

second is musical expressionism, which is the theory that musical meaning is externally imposed,

subjective, and can be inferred from the feelings and emotions that the music incites in the

listener.14

12 Meyer 1956, 1 13 Staufer 2018, 32 14 Meyer 1956, 2 – 3

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CHAPTER I

PHENOMENOLOGICAL ACCOUNTING OF MUSICAL MEANING

Musical Meaning and Phenomenology

Within a formalist approach, Meyer identifies two separate tasks that are required to

determine musical meaning: to become aware of the qualities of musical objects (or succession

thereof) that constitute meaning, and then to interpret those meanings. In other words, there is

the attempt to determine what is meaning and there is the attempt to determine what something

means. Meyer then criticizes absolutism, which would suggest that meaning is found in the

constituent elements of the stimulus itself, observing two fallacies in that kind of theoretical

position; 1.) there is a tendency to locate meaning in “one aspect of the communicative process,”

and 2.) there is a propensity to regard meanings as “designative” and “involving symbolism of

some sort.”15 To address these issues, Meyer begins by borrowing a definition of meaning from

Morris R. Cohen’s A Preface to Logic which states, “… anything acquires meaning if it is connected

with, or indicates, or refers to, something beyond itself, so that its full nature points to and is

revealed in that connection.”16 From this definition, Meyer determines that investigating the

intrinsic meaning of a harmonic entity is pointless – that meaning is not a property of things and

therefore meaning cannot be located in them or what they imply. Within this framework, true

meaning arises from a relationship between a stimulus, that to which the stimulus points, and a

conscious observer.17

For my formalist purposes, when I am considering the way that a stimulus points to

something, I am considering the phenomena of expectation.18 Expectation plays a critical role in

15 Meyer 1956, 33 16 Cohen 1944, 47, quoted in Meyer 1956, 34 17 Meyer 1956, 33 18 The idea of a stimulus “pointing to” something can be applied in multiple contexts, depending on the experience of the listener. A stimulus could function in terms of a musical topic as defined within a repertoire for those who are familiar with the style of the work. A musical stimulus could also function like a leitmotif in the context of a single work. Of course, this kind of recognition of what the music points to only applies if the listener has heard the stimulus before. Or, if one were to take an expressionist position, a stimulus could point to certain emotional,

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determining the meaning of a musical passage. Since music is a fundamentally temporal

experience, a listener’s cognitive perception of musical relationships depends on their ability not

only to interpret the meaning of the tones themselves, but also the way in which successive tones

relate to each other as a unified temporal object.19 With each new tone, the previous one passes

into memory, and that memory provides the context necessary to generate expectation. Edmund

Husserl, on the phenomenon of expectation in temporal experience, writes that in order to

understand the effect that memory has on meaning, one must accept that “every act of memory

contains intentions of expectation whose fulfillment leads to the present.”20 Husserl’s insight was

picked up by Meyer, who emphasizes the critical role expectation plays in determining embodied

musical meaning:

Embodied musical meaning is, in short, a product of expectation. If on the basis of past experience, a present stimulus leads us to expect a more or less definite consequent musical event, then that stimulus has meaning.21

Meyer goes on to say that the meaning of a work as a total experience is constituted in

three types; “hypothetical” meaning, meanings that arise during the act of expectation, “evident”

meaning, which are meanings that are attributed to antecedent stimulus once consequent ones

are physically sounded, and “determinate” meanings, which arise from the relationship between

hypothetical and evident meanings once a passage has ended.22

affective, or imaginative states. However, since our focus is on developing a harmonic formalism independent of style, the generation of expectational states by the listener based on specific harmonic relationships is of primary concern. 19 This idea is implicit in Riemann’s criticism of Hauptmann, which I noted above. 20 Husserl 1966, 76 21 Meyer 1956, 35 22 Meyer 1956, 37-38

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It should be remembered that meaning is something that is derived from that objective

“what” by the observing subject. Meaning does not exist independent of the one who perceives

it. This was articulated in reference to melody by Mikel Dufrenne in Phenomenology of Aesthetic

Experience, whom Thomas Clifton summarizes by stating, “The unifying bond between melody and

me is not a physical proximity, but a meaning which is constituted in me by the melody.”23 As I

noted in the introduction, there are two separate but related aspects of musical phenomena which

a musical analyst could explore: the musical objects themselves and the human experience of

those objects. The search for musical meaning falls into the latter category and is therefore an

ultimately phenomenological study.

Narrowly defining phenomenology has been a particularly elusive goal, even in the

literature that most directly engages with it. Clifton, for example, begins the preface of his book

Music as Heard the following:

One is tempted to pose the rhetorical question, What is Phenomenology? But this question was asked by Merleau-Ponty in 1945 in the preface to his Phenomenology of Perception, when Husserlian phenomenology was already about forty years old. If it has not been answered by either Husserl himself or subsequent phenomenologists, then I myself respectfully decline to answer it, at least in formal terms.24

Clifton goes on to say that he would instead choose to emphasize a discussion of how one

thinks phenomenologically, and on how phenomenological thought can be communicated. But

despite this early reservation, Clifton does offer general definitions of phenomenology, including,

“Phenomenology is a description of the self-evident as given in experience,”25 and

23 Clifton 1983, 47, referencing Dufrenne, The Phenomenology of Aesthetic Experience, pp. 231-32. 24 Clifton 1983, vii 25 Clifton 1983, 37

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“Phenomenology is, in brief, the logic of experience.”26 Lewin echoes this general definition of

phenomenology in “Phenomenology, Music Theory, and Mode of Perception” when he writes,

“The subject matter of Husserlian phenomenology is our conscious experience.”27 The Stanford

Encyclopedia of Philosophy defines phenomenology as the study of “the structure of various types

of experience ranging from perception, thought, memory, imagination, emotion, desire, and

volition to bodily awareness, embodied action, and social activity, including linguistic activity.”28 I

would offer my own understanding of the definition of phenomenology as the study of a subject’s

perception of an object and the logical structures of that perception. What each of these

definitions have in common is a focus on the experiencing subject rather than the object being

experienced. In these cases a phenomenon would be, as Clifton defines it, “a nonempirical,

intuitively grasped essence whose meaning is 1.) validated by a consciousness absorbed in the

experience of living-through that meaning, and 2.) independent of any particular actualization of

it.”29

Izchak Miller’s research in Husserl, Perception, and Temporal Awareness perhaps most

clearly represents phenomenological thought in terms of a “logic of experience.” In this work

Miller offers a detailed accounting of Husserl’s theory of perception, and in particular, his

perception of processes. Following a discussion of Husserl’s theory of intentionality, which refers

to “the property peculiar to our conscious experiences, namely, their being always directed at

putative objects,”30 i.e., the consciousness of something, Miller offers a series of logical formulae

26 Clifton 1983, 50 27 Lewin 1986, 75 28 SEP, Phenomenology 29 Clifton 1983, 38 30 Miller 1984, 7

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describing the act of perceiving, of which Miller calls the following a “fairly close” representation

of all the relevant details of the structure of the act of perceiving:

I perceivee x̅{n(tj)}[꓿x̅{p(ti)}[a, b, …],

꓿x̅{f(tk)}[a, b, …], a, b, …]

In this formula, the act “I perceive” includes the object of perception, which Miller

concludes is what Husserl means by the “Determinable-X (x̅).31 That object is perceived at a now-

point in time {n(tj)}. That perception is taken-in by the perceiver with the context of that

Determinable-X having been perceived at a past-point in time that is still held in the mind [꓿x̅{p(ti)},

which has definable qualities [a, b, …]. This perception held in the mind is what Husserl calls a

“retention,” a passively held memory that contextualizes the perception of an object at a now-

point. Together with the object at a now-point and the retention of that object from a past-point,

the perceiver also perceives an intention, or direction, of that object toward a future-point in time

꓿x̅{f(tk)}, which will have the definable qualities of [a, b, …]. Husserl calls this part of the perceptual

act a “protention,” an intention of expectation found in the act of memory (retention) whose

fulfillment leads to the present.32

The formula as it is shown here illustrates a series of time-points for a single, enduring

perceptual object, or Determinable-X. For example, the perceptual object could be a single long

tone that a listener is hearing and is aware that they are hearing it over several seconds. However,

the formula could be applied to a progression of phenomenological moments in which different

perceptual objects are introduced. As an example, let us examine a I – V7 harmonic relation at time

points A (ta) and B (tb), respectively. When I perceive the dominant-seventh chord at (tb), I also

31 Miller 1984, 94 32 Husserl 1966, 76

17

perceive the retained memory of the perception of the preceding tonic triad (ta) and an

expectation of a future tonic at (tc). Such application is explored in the music-theoretical discourse,

particularly in the work of Miller’s contemporaries.

Leonard Meyer was ahead of his time in the world of music theory for his application of

Gestalt Laws in his music analysis, most notably in his book Emotion and Meaning in Music, which

was published in 1956. Although he did not engage directly with Husserlian phenomenology, his

contribution to the psychology of music, a closely-related field, serves as a foundation for formalist

theoretical models, particularly in the areas of rhythm and meter. A distinctly Husserlian

phenomenological approach to the perceptual act is picked up in the music-theoretical discourse

during the 1980s and early 1990s. In Music as Heard, Clifton explores the phenomenological

concepts of temporal horizon, retention, and protention using musical examples throughout the

canon, although he does not establish a systematic theoretical construct through which he would

apply his analysis. In contrast, Eugene Narmour applies the phenomenological conception of

expectation to his theory of melodic implication and realization, which he summarizes as such:

Three basic theoretical constants constitute the implication-realization model: that A+A implies A (i.e., that sameness or similarity causes the subconscious expectation of more sameness or similarity, all other things being equal); that A+B implies C (i.e., that differentiation causes the expectation of further differentiation); and that the definition and evaluation of these two hypotheses in both cognition and musical analysis depend on syntactic parametric scales.33

It is notable that in Narmour’s theory, expectation is self-generated, meaning that the

implication is derived from the perception of the musical effect itself rather than the observation

33 Narmour 1992, 1

18

Applied Phenomenology in Music-Theoretical Discourse

of a general rule of style or common practice. Following Miller’s formula, the implication is the

protention, or future-point in time (꓿x̅{f(tk)}[a, b, …],[a, b, …]) of the perceived object, which is

presently at a now-point in time and informed by the retained context of a past-point in time

(x̅{n(tj)}[꓿x̅{p(ti)}[a, b, …]). Narmour writes, correctly in my view, that style structures are “an

extremely problematic source from which to divine the constants of a cognitive theory…for the

definition of style’s domain is too variable to enable the discovery of consistent cognitive rules of

analysis.”34 In order to develop an internally consistent analytical approach, Narmour focuses on

melodic patterns that are observable independent from any particular style. In other words,

Narmour’s theory starts from a place of state of tabula rasa for the listener before adjusting the

theory in practice in order to accommodate the culturally-informed listener.

Christopher Hasty elaborates on the notion of self-generated expectation of repetition in

Meter as Rhythm. In his “Theory of Projection,” Hasty views duration as the essential tool of

measurement for the dynamic musical process, writing, “Nothing that is actual – that is, nothing

becoming or having become – is without duration.”35 In measuring the duration of consecutive

musical events, Hasty is able to distinguish two different elements of the metrical process. First

there is the “projective,” the actual completed duration of the first event marked by the beginning

of a second event. Because the event is marked by the beginning of a second event, the projective

lies fully in the past. The completion of that event then creates an expected duration for a second

event. This is a hypothetical meaning which Hasty calls a “projective potential.” It is important to

note here that projective potential describes the expectational quality of the projective. “It is not

34 Narmour 1992, 8 35 Hasty 1997, 69

19

the potential that there will be a successor, but rather the potential of a past and completed

durational quantity being taken as especially relevant for the becoming of a present event.”36

Once a second event has been completed (or “actualized”), the conscious observer can

analyze and compare it to the projective potential created by the completion of the first event. If

they match, it means the first event was indeed relevant to the completion of the second and the

projective potential was “realized.” If they diverge, then the projective potential was “unrealized,”

meaning that the second event was, in this sense, unexpected. This analysis would be the working

out of the determinate meaning of the passage as described by Meyer. Both Narmour’s and

Hasty’s theories are hierarchical by design, so their groupings of melodic and rhythmic gestures,

respectively, can be recursively applied to generate higher levels of perception. This allows their

models to be used to construct self-generated relations between larger phenomenological

moments, in contrast to a top-down, externally imposed organizational structure.

In 1986 David Lewin, who cites Miller, Clifton, Narmour, and Hasty, offered his own general

model of musical perception that formalizes the meticulous study of multiple meanings in

different contexts while maintaining the temporal considerations necessary for deriving musical

meaning. In other words, he provides a checklist that an analyst can use to collect and interpret

all of the information necessary for working out what Meyer’s determinate meaning of a musical

passage. Lewin’s basic formula for creating this checklist is as follows:

p = (EV, CXT, P-R-List, ST-List)

Here the musical perception p is defined as a formal list containing four arguments. The argument EV specifies a sonic event or family of events being “perceived.” The argument CXT specifies a musical context in which the perception occurs. The argument P-R-List is a list of pairs (pi, ri); each pair specifies a perception pi and a

36 Hasty 1997, 85

20

relation ri which p bears to pi. The argument ST-List is a list of statements s1, … sk made in some stipulated language L.37

Mariam Moshaver has described Lewin’s model as a metaphorical representation of

mental engagement in the activity of musical perception, a procedure for recording and relating a

wide range of possible variations to one another in the perception of a given musical event.38 With

this model Lewin is able to provide a finely-detailed analysis that brings out how one can perceive

a musical event in different ways depending on the temporal context with which one observes it.

Notably, he also demonstrates how an awareness of how some expectations fail to materialize, or

are “denied,” can itself be something that is perceived in musical experience.39 This effect is

echoed in Hasty’s theory as a “projective potential” that has been “denied.”

Such memories of denied expectations and previous perceptions play a major role in

Lewin’s analysis of the first stanza of Schubert’s Morgengruß. In this analysis, which Richard Cohn

calls “the most fine-grained analysis of a single work that Lewin ever committed to paper,”40 Lewin

shows an example of a denied expectation informing the perception of mm. 12–13. He views the

A-major chord in m. 13 (in the context of mm. 9–13) to be subverting the perception of the G-

minor chord being the minor dominant of C-major (in the context of mm. 9–12). This subversion

is remembered and informs the perception of m. 14, but it is eventually cast aside as the

perception of the minor dominant is restored in m. 15. This kind of interaction with the music is

exactly what Lewin wishes to bring out in his distinctly phenomenological analysis. Moment by

37 Lewin 1986, 83 38 Moshaver 2012, 180 39 Lewin 1986, 100 40 Bard-Schwarz and Cohn 2015, 2

21

moment, the music is recontextualized by the listener while not forgetting the contexts that came

before.41

Each of these authors must and do address the issue of musical style as it relates to their

perceptual models. Fundamentally, each theory operates independently of any specific style

structure or of any learned or replicated complex of syntactic relations. Individual compositions

are unique in their relationship to a stylistic prototypical model, and an individual’s knowledge of

and exposure to style is equally unique, so no cognitive theory of perception based on stylistic

schemata or archetypical patterns could provide a universal analytical constant. However,

schemata and archetypical patterns nonetheless exist. Leading tones regularly resolve up toward

their apparent tonics, cadential motions bring sequential patterns to a close, and high-level tonal

plans influence basic formal design. Each of these types of top-down stylistic structures clearly

influence expectations of the listener, and so cognitive bottom-up models need to be able to

accommodate them. Narmour allows for top-down schemata to override his Implication-

Realization model rules when there is enough contextual information so that the musical event

can be said to implicitly mimic a recognized stylistic convention, fulfilling the psychological

requirement of “representativeness.”42 When Lewin stipulates that phenomenological

experiences are placed into a particular context (ConteXT), he argues that “tonal theory” is

understood as a component of that context, in some heuristic sense.43

41 Lewin goes even further in suggesting that perceptions can be observed as distinct mental objects that can exist independently and simultaneously in the mind, rather than a single continuously developing consciousness. While his model allows for the possibility, it is counterintuitive to believe that a person can perceive two distinctly different ways at once (like seeing both animals simultaneously in the famous rabbit/duck illusion), and I am not aware of any research in cognitive psychology that supports the claim. Lewin 1986, 115-26 42 Narmour 1992, 13 43 Lewin 1986, 95. Although this is not to say that it must be so.

22

In more recent years, Janet Schmalfeldt has achieved notoriety for how she engages

phenomenologically with the top-down archetypical patterns. In The Process of Becoming,

Schmalfeldt offers analytical examples demonstrating how retrospective reinterpretations affect

the perception of musical form in early nineteenth-century music. Although she does not engage

directly with the Husserlian case for the experience of misperception, she nonetheless applies it

as a distinct phenomenon, which she refers to as “becoming,” and notates in her examples with a

double-lined arrow (⇒). The symbol has become a more and more popular annotation in the

analysis of sonata form, in particular.44

Miller, in his examination of Husserl’s theory of perception, distinguishes between a

misperception and the experience of misperception. A misperception would be a case in which

one perceives an object to have a property which it does not, in fact, have. In contrast, the

experience of misperception is a case in which the perceiver of the object undergoes a ‘change of

mind’ about one or more of the object’s properties while recognizing that the properties

themselves remain the same. In the former, the perceiver mistakenly perceives something that

isn’t actually “there.” In the latter, what the perceiver perceives is in fact “there,” but the perceiver

recognizes that it (the something) is not what they originally thought it was.45 The latter case, the

experience of misperception, Miller illustrates through the following two formulae:

I perceivee x̅{t2}[꓿x̅{t1}[p, q, r, …], p̃, q, r, …]

or

I perceivee x̅{t2}[≠x̅{t1}[p, q, r, …], p, q, r, …]

44 Schmalfeldt 2011, 29 45 Miller 1984, 69-70

23

In the first formula, the perception of x̅ has what Miller calls “incompatible attributes” at

{t1} and {t2}, namely p and p̃. In the latter formula the perceiver must “go back” and

reconceptualize the object itself. Although it has the same attributions [p, q, r, …], the object of

the perceptual act at {t2} is found not the same object as perceived at {t1}. In this experience the

object, as Miller puts it, “has somehow been replaced by another object very similar to it.”46 The

perceptual act described in the latter formula is precisely the phenomenological experience which

Schmalfeldt refers to as “becoming.” However, she reaches this conception through a parallel

epistemological canon that she calls the “Beethoven-Hegelian tradition”.47 This tradition begins,

in Schmalfeldt’s view, with a review of Beethoven’s Fifth Symphony in 1810 by E.T.A. Hoffman in

which Carl Dahlhaus finds the proto-Hegelian concept of “pairs of antitheses.”48 The notion of

antithetical pairing was picked up in A. B. Marx’s Formenlehre, influenced by Schoenberg with his

concept of developing variation, and then later edified by Theodor W. Adorno whom explicitly

invoked the Hegelian subject-object dialectic as a part of his analysis of Beethoven’s music. As

Schmalfeldt writes, “Adorno never hesitates in referring to the composer’s original theme…as the

‘musical object’…dialectical process manifest in musical form…. Conversely, the technique of

developing variation ‘represents the process of objectivity and the process of becoming.’”49 She

later recounts how Adorno believed that music analysis neglected the “moment of becoming” and

that Beethoven’s music must “be heard multidimensionally, forward and backward through

time.”50

46 Miller 1984, 74 47 Schmalfeldt 2011, 23 48 Schmalfeldt 2011, 24 49 Schmalfeldt 2011, 29 50 Schmalfeldt 2011, 32

24

Schmalfeldt identifies Dahlhaus as the successor to Adorno in the Beethoven-Hegelian

tradition. Dahlhaus also finds Beethoven’s music to be processual in nature, and it requires an

active response on the part of the listener. The structure of musical hearing is, as Schmalfeldt

notes, the primary concern in the “Form as Transformation” section of his book Ludwig van

Beethoven published in 1977, and in this title one can see the obvious relation to Husserlian

phenomenology. In that essay, Dahlhaus produces analytical examples where the processual

nature of Beethoven’s music is revealed through what Dahlhaus calls “blending” of formal

conventions, such as the following passage discussing the opening of the Eß Piano Sonata Op. 31,

No. 3:51

Firstly, the opening of the movement starts by seeming to be an introduction, and only later reveals itself as the main theme. Secondly, the continuation (bar 18), which seems to be a transition (and indeed is such in the recapitulation), loses that role to an evolutionary section (bar 33) which must be regarded as the ‘real’ transition.52

It is from this point that Schmalfeldt picks up and elaborates on the concept of the

experience of misperception as formulated by Miller in the second formula reproduced above,

which she, following this Beethoven-Hegelian tradition, refers to as dynamic becoming. Although

the terminology and epistemological lineage differs, its application in music-theoretical discourse

remains similar. The phenomenological understanding, funnily enough, has somehow been

replaced by another object very similar to it.

One further example of phenomenological applications has been published quite recently

by John Muniz. In his article “A Tendency-Transformational Model of Enharmonic Modulation and

51 Schmalfeldt 2011, 37 52 Dahlhaus, Ludwig van Beethoven, 42, quoted in Schmalfeldt 2011, 37

25

Related Phenomena,” Muniz proposes a method of analyzing enharmonic transformations that

engages with the same reinterpretative phenomenological event which Schmalfeldt discusses.

Muniz’s model, which is built on the top-down musical convention of scale-step tendencies,

identifies the scale-degrees of a chord in the context of the chord preceding it. Then, upon the

introduction of a disrupting harmonic event, like a tonicization, those scale-step identities are

retrospectively reinterpreted in light of the context of the new harmonic object. To use his

example,

Let us assume an opening CM chord is a tonic triad composed of ^1, ^3, and ^5. Although the tonicization does not efface the key of C major, the advent of B-flat creates an applied dominant of F, such that on a “microscopic” level the CM ^1, ^3, and ^5 act retrospectively as ^5, ^7, and ^2 of F. If the motion to F major were cadentially confirmed, we would say that the ̂1, ̂3, and ̂5 in C major – the pivot chord – have been reinterpreted as ̂5, ̂7, and ̂2 in F major.53

Further, Muniz incorporates Schmalfeldt’s double-lined arrow (⇒) into his model to show

where re-interpretive events will have occurred for contextualized scale-steps. However, it should

be noted that while both Schmalfeldt’s and Muniz’s analytical styles involve the acknowledgement

of retention as part of the perceptual act, both also rely on the top-down musical conventions on

which they are based to determine succeeding temporal events. Unlike Narmour and Hasty, whose

models are bottom-up, the top-down models of Schmalfeldt and Muniz do not address the

phenomenological concept of protention as a self-generated part of the perceptual act.

The theoretical basis of this theory is founded in two key philosophical concepts. The first

is Hegel’s conception of the subject-object dialectic discussed in the Phenomenology of Spirit and

53 Muniz 2019, 3

26

Phenomenological Thinking in the 19th Century Music Theory

Science of Logic, which were published between 1807 and 1816. The second is conception of time-

consciousness posited by Edmund Husserl, whose writings were beginning to be published toward

the end of the nineteenth century. Therefore, I have chosen to limit my discussion of earlier

phenomenological applications in the field of music theory to that century.

In some ways, Gottfried Weber sets an early precedent to the phenomenological

approach. In his well-known analysis of Mozart’s K. 465 “dissonance” quartet,54 Weber provides a

narrative of the ear [das Gehör] which encounters each new note, as Jairo Moreno puts it, as “an

opportunity for dissension and an occasion for jostling expectations against disappointing

contradictions…fueled by doubt, in a manner redolent of Paul Ricoeur terms a ‘hermeneutics of

suspicion’.”55 Weber meticulously considers the ambiguities [Mehrdeutigkeiten] of each monad,

dyad, and triad for the context in which they are presented and notes at every turn where

expectations are either subverted or never allowed to materialize. The lack of ability to develop

any expectations or to have them confirmed, along with other melodic and rhetorical issues, is

why Weber believed the opening to the quartet was harsh and “disturb[ed] the ear’s

contentment.”56

The unyielding ambiguities in the opening passage of the quartet that Weber hears can

partially be attributed to the theoretical framework upon which his analysis is based. That

framework is Stufentheorie, which conceptualizes the quality and harmonic function with a key of

any and all chords in terms of the position they may hold within the fixed order given in a major

54 “‘A Particularly Remarkable Passage in a String Quartet in C by Mozart [K465 (“Dissonance”)]’ Attempt at a Systematic Theory of Musical Composition” in Bent 1994, 161-83 55 Moreno 2003, 100 56 Bent 1994, 177

27

or minor scale.57 Under this theoretical framework, there is an underlying question that is

constantly being asked by the listener and indeed by Weber in this analysis – namely, in what key

is this particular chord, or in which keys could it be? The fact that this question could always have

more than one answer (such is the nature of the concept of Mehrdeutigkeit) bias the listener to

be more suspicious of the present meaning of harmonies. Brian Hyer believes this had a paralyzing

effect, writing, “Weber insists on an impossible division between past and future in which what

appears to be an openness toward the future emergence of the music is, rather, a near permanent

indecision with regard to the musical present.”58 In other words, if one cannot determine the

meaning of the music in the present, then one cannot use that information to make observations

about the expectational states those meanings generate for the listener. This is why, as Moreno

notes, “In Weber’s analysis, causal connections hardly matter, and later events seldom illuminate

the meaning of earlier ones.”59 In short, Weber fails to articulate any sense of phenomenological

retention of past events that a listener would have and use to construct an appropriate protention

for future events.

Moritz Hauptmann is what Meyer would call an absolutist and a formalist in his approach

to musical meaning. His treatise investigates how a listener takes in the meanings, or “notions,”

that he believes to be innate to musical expressions. Hauptmann was unique in his time for his

focus on the ability of music to communicate logical expressions to the observer, and as such his

methods were uniquely phenomenological. In his writing on harmony, Hauptmann abstracts

intervallic qualities from the harmonic entity. In other words, he focuses on the structures of

57 Moreno 2003, 105 58 Hyer 1996, 94 59 Moreno 2003, 109

28

perception of intervallic qualities rather than the objective qualities of the harmonic object itself.

He lists three “directly intelligible” intervals, each of which express a particular logical notion

necessary for understanding its nature.60 These notions are imported from the Hegelian dialectical

study of being, nothing (or non-being), and becoming found in Science of Logic,61 and are related

to music (or sound generally) through intervallic ratios produced from the numbers 1, 3, and 5,

their products, powers, and reciprocal products.62 Though he found these ratios lacking in their

ability to explain the nature of harmony or the subdominant relationship to a fundamental, he

nonetheless conceded that the series “contains nothing that contradicts reality” from an

acoustical standpoint.63

Hegel writes that being, pure being, is “without further determination,” and is “equal to

itself…it has no difference within it, inwardly or outwardly.”64 It is equal only to itself, and therefore

necessarily all things apart from it are equal to it. He then goes on to say that pure being cannot

be comprehended alone. It needs context within a greater whole to be understood. It needs an

equal opposite. This opposite is “pure nothingness,” a complete absence of content or

determination. Hegel later calls this “non-being.” It is the referential relationship between being

and non-being that grants understanding of the greater whole and thus the “logic of experience.”

Hauptmann applies the same dialectical organization of thetic, antithetic, and synthetic elements

in his understanding of the elements of the triad, Octave, Fifth, and Third:

There are three intervals directly intelligible:

I. Octave

60 Hauptmann 1853, 5 61 Hegel, Science of Logic, Wallace translation, 2009 222 – 231 62 Hauptmann 1853, xxxvii 63 Hauptmann 1853, xxxvii 64 Hegel, Science of Logic, Giovanni Translation, 2010, 59

29

II. FifthIII. Third (major)

They are unchangeable.

I. The Octave: the interval in which the half of a sounding quantity makes itself heard against the whole of the Root, or fundamental note, is, in acoustic determination, the expression for the notion of identity, unity, and equality with self. The half determines an equal to itself as other half.

II. The Fifth: the interval in which a sounding quantity of two-thirds is heardagainst the Root as whole, contains acoustically the determination thatsomething is divided within itself, and thereby the notion of duality and inneropposition. As the half places outside itself an equal to itself, so the quantity oftwo third-parts, heard with the whole, determines the third third-part; aquantity to which that actually given appears a thing doubled, or in oppositionwith itself.

III. The Third: the interval in which a sounding quantity of four-fifths is heard withthe whole of the root. Here the quantity determined is the fifth fifth-part, ofwhich that given is the quadruple, that is, twice the double. In the quantitativedetermination of twice two, since the double is here taken together as unity inthe multiplicand, and at the same time held apart as duality in the multiplier, iscontained the notion of identification of opposites: of duality as unity.65

Unlike all other intervals, the Octave is a single, simple, and indivisible entity. It is created

by the sounding part of only one division of the fundamental tone (2:1), shown in Example 1.1a. It

requires no understanding of any further division from the source. Here Hauptmann follows

Hegel’s concept of “pure being.” The state of pure being is sounding body that creates the octave.

It is achieved with only one sounding musical unit contained in a greater whole. The octave is also

the only interval for which the other part of the greater whole, the unsounded part, is equal to the

sounded part. Hauptmann calls this unsounded part the determined part, but we can also

understand it as the “pure nothingness” that gives “pure being” context in the whole. This is why

Hauptmann claims that the Octave expresses unity. Its state of being is that of an indivisible unit

against another equal unit of non-being within the context of a greater whole. However, in practice

65 Hauptmann 1853, 5-6. Emphasis his.

30

and within the context of the other intervals, the Root can substitute as an “answer to the notion

of definite unity.”66

Example 1.1b shows the dialectical structure of the Fifth, and it illustrates the concept of

duality and separation in music. On the monochord, the Fifth is the interval that results from the

first unequal division of parts. It comes into being by the sounding of two third-parts against the

whole of the fundamental. Unlike the Octave, whose component parts cannot be divided, the

unequal opposition between the being and non-being parts of the Fifth reveal that the being part

can be divided against itself. The equal division of the being part is what Hauptmann observes to

be the Fifth’s dual nature. This is what Hauptmann means when he says that the two third-parts

“appears a thing doubled.”

66 Hauptmann 1853, 6

Example 1.1: Directly Intelligible Interval Dialectics

31

Hauptmann’s description of the Third is perhaps the most confusing definition of the three

intelligible intervals. In Example 1.1c we see that, as with the Fifth, the Third has an unequal,

unsounded, and therefore non-being part outside of the being part that gives the listener the

context of the fundamental. Again, this is not the feature that gives the Third its notion of

separation, but rather only the opposition necessary to understand it. Hauptmann says that both

separation and unity is perceived in the sounding body of the Third (that is, the four fifth-parts)

simultaneously. The separation is apparent in that the sounding body must necessarily be divided

into four parts. But unity is expressed insofar as that the four parts can be grouped together as

two units, and that the two units are equal to each other. Each unit of two has another unit equal

to and outside of itself, as the octave does. In short, the sounding body can be understood as both

separation and unity, and both qualities are perceivable due to the unsounded fifth fifth-part.

The logical underpinnings of the “directly intelligible” intervals serve as justification for a

fundamental premise – that a listener understands harmony as physical expression of the Hegelian

principles of Being, non-Being, and the union of Being and Non-Being, and that those principles

are evident in the absolute meanings of Root as unity, Fifth as separation, and Third as union. Each

of these meanings is unique in the quality of their being and therefore can be distinguished from

one another. These absolute meanings of intervals are abstracted from the tones that convey

them within a given harmonic context. In The Science of Logic, Hegel writes, “Content of whatever

kind it be, with which our consciousness is taken up, is what constitutes the qualitative character

of our feelings, perceptions, fancies, and ideas; of our aims and duties; and of our thoughts and

notions… [these] are the forms assumed by these contents. The contents remain one in the same…

32

the contents confront consciousness, or, are its object.”67 Hauptmann engages with this idea in

his work. Root, Third, or Fifth-meanings are not inherent in the contents of a chord. The chord

itself is a collection of acoustical frequencies, sound abstracted from meaning; it is their interaction

with our consciousness that creates Root, Third, and Fifth-meaning, and that is what makes his

theory distinctly phenomenological.

Our conscious interactions with these interval-meanings guide Hauptmann’s theory of

chordal successions. By this theory, the succession of triads is considered to be intelligible only

insofar as both can be “referred to a common element that changes meaning during the

passage.”68 In more practical terms, one could say that the logic of chordal succession is

dependent upon the treatment of common tones. On the face of it, this point of view seems fairly

unremarkable, and in practice it translates into voice-leading rules that are essentially

conventional.69 But in the context of Hauptmann’s Hegelian theoretical framework, one can see

that the agency that guides his rules of chordal succession is shifted away from the musical object

and toward the perceiving subject.

Let us consider the agency of the listening subject in the following formula:

In F-major triad, I perceivee C{t1} [=C̅{t1}[a, b, …],

In C-major triad, I perceivee C{t2} [≠C̅{t1}[a, b, …].

In this formula there are two perceptual acts. The first is the act of perceiving the tone C

within the F-major triad. The musical object C{t1} is perceived as such =C̅{t1} and as having the

qualities [a, b, …]. Those qualities would be those that distinguish the object from another, such

67 Hegel, Wallace Translation, 2009, 105 68 Hauptmann 1853, 45 69 The so called “law of the shortest way,” as described by Schoenberg, recalling Bruckner. Schoenberg 1922, 39

33

as frequency, tone color, register, etc. In the second perceptual act, the perception C̅ at {t2} is

identified as having the same qualities as the perception C̅ at {t1}, but in the second act the

perceiver reconceptualizes the object itself as something different. I recognize that the C is the

same tone, held in common between the two contexts, but I perceive the C differently in the

contexts of the separate perceptual acts. To return to Hauptmann’s terminology, I perceive the C

in the first act as Fifth-meaning, and I perceive the C in the second act as Root-meaning.

In a more conventional approach to voice-leading, the acting, “moving” parts in a chordal

succession are those tones that are not held in common. In the example above, the perspective is

that the listener perceives “motion” from the F and A of the F-major triad to the E and G of the C-

major triad, respectively. In contrast, the common tone C is “inactive” or “unmoving” in order to

preserve a desirable economy of motion. But this kind of understanding ignores the succession of

perceptual acts necessary to understand the difference between C as Fifth-meaning and C as Root-

meaning, the very processes that make the harmonic succession “intelligible.”

The notion that tones “move” is fundamentally incompatible with Hauptmann’s model of

harmonic perception. The perception of E and G does not exist at {t1}, and there is nothing inherent

within the qualities of F and A that lead into (or generate a protention of) E and G, therefore the

perception of E and G at {t2} cannot have “moved from” F and A. Instead, these tones only “move”

in the sense that they pass into and out of existence as the perceptual experience advances

forward in time. The tones F and A pass out of being and into non-being while the tones E and G

simultaneously pass out of non-being and into being. It is tone C then, binds the two chords

together as the tone undergoes the dynamic process of becoming. This conception of harmonic

34

dualism is deeply connected to Hegel’s conception of being, as I noted above, and it sets

Hauptmann apart in the theoretical canon.

As Hauptmann attempts to relate these abstract, absolute meanings to the acoustical

entities that bring their existence into being, the language he uses to describe them often becomes

muddied. But this is an easy pit into which music theorists fall. Theorists commonly refer to the

tones of a harmony as “being” a particular interval in the context of that harmony (for example,

“In this C triad, this tone C is the Root and this tone G is the Fifth.”). Of course, this is technically

inaccurate since intervals are determined by the relationship between two tones. A tone cannot

“be” an interval. It would be more accurate to say, “this G, when heard together with this C,

creates the intervallic relationship of Fifth,” but such specificity in language tends to bog down

analysis and education. So we use “G is the fifth of C” as a sort of linguistic shortcut with the

implication that we understand that when we say a tone is an interval, we mean the tone relates

to a perceived root by that interval.70 Despite his attempts to clearly delineate the concept of

interval from the tone, Hauptmann uses this shortcut when he refers to a tone having Root-, Third-

, or Fifth-meaning.

Hugo Riemann believed that determining the absolute meaning of intervallic relationships

is of little use if we cannot relate those meanings to the temporal experience of a given musical

work. In order to develop an analysis of a particular musical work, rather than speculation on the

abstract nature of music generally, one must find a way to examine how these meanings interact

70 Viktor Zuckerkandl echoes this sentiment in his work on scale-degree tendency: “though we speak of the tone c or g or b, we actually hear c=̂1 or c=̂6, g= ̂7, b=̂3, and so on…Hearing music does not mean hearing tones, but hearing…the places where they sound in the seven-tone system.” Zuckerkandl 1956, 34-35

35

with one another in succession. Riemann articulated this sentiment early in his career in “Musical

Logic: A Contribution to the Theory of Music” under the pseudonym Hugibert Ries:

What [Hauptmann’s] work contains on these subjects is unfortunately neither complete nor wholly agreeable, since Hauptmann could not decide – or it did not occur to him – to look for his notions of octave-unity, fifth-disunity, and third-unification in temporal succession, without which a piece of music is inconceivable… He has no doubt understood the unity of chords within a key, but certainly not the diverse meaning of these chords relative to each other – their logical meaning in the musical structure.71

This is not entirely accurate since Hauptmann did dedicate a chapter of this treatise to

chord succession in the harmony section, and the temporal process was essential to his conception

of meter. But it is true that Hauptmann does not offer a theory for how an actual musical

composition could exhibit his notions as a single temporal object. Again, this is because

Hauptmann’s focus is not on the musical object, but rather the understanding of those objects by

the listening subject. From this perspective, it is not the music itself but the perceptual acts of the

listener that move through time. Still, Riemann offers a solution to the problem with what he calls

the grosse Cadenz, which is essentially a I – IV – V@ —– ! – I cadence that he believes expresses

Hauptmann’s notions of unity, separation, and union through the successive changes of meaning

that the initial root undergoes. In this progression, the initial root of the tonic changes from Root

of I, to Fifth of IV, and then to Fourth against the Fifth of I@. Riemann calls this an appearance of

the root “in conflict with itself.” Finally, the root returns to Root of I, uniting the different identities.

Recalling the Hegelian dialectic, Riemann sees in the grosse Cadenz three “thetic elements”; the

tonic as thesis, the subdominant and tonic @ as antithesis or “thetic-fifth,” and the dominant with

71 Ries 2000 (1872), 100

36

final tonic as synthesis or “thetic-third.” Taken together, Riemann calls this progression the

“prototype of all musical form.”72

The grosse Cadenz is an interesting development in that it is defined by the processes that

the initially perceived root tone undergoes. It is a prototype, as Riemann says, to which we can

relate the transformations of intervallic meaning that we observe in a particular piece of music

over time. One might relate it to the Schenkerian Ursatz, or a practical application of Marx’s

pattern of “rest-motion-rest” (Ruhe-Bewegung-Ruhe), or any other juxtaposition of opposites one

could use as an abstract theoretical overlay for directed musical motion. However, one can see

that with the grosse Cadenz, Riemann models the prototype after the cognitive processes of

chordal succession that Hauptmann articulates, and tries to extend Hauptmann’s limited uses of

protensive perceptual acts to higher hierarchical levels. As such, it suggests that in a prototypical

musical work one can expect that it will begin with a thesis section, move toward an antithetical

section, and conclude with a synthetic section, thus putting those absolute meanings in time.

72 Ries 2000, 102

37

After having reviewed the ways in which phenomenology has been applied in the music-

theoretical discourse, I would like to revisit the concept of Neo-Hauptmannian theory. What is it,

exactly? Articulating a clear and satisfying answer to that question has been a challenging task.

The most basic answer would be that it is a method of analyzing harmonic progressions, but even

that statement requires some caveats that quickly obscure the definition. It is not really a method

of analyzing harmonic progressions because it is not the harmonic progressions themselves that

are being analyzed – The analysis is of the way a listener perceives those progressions. The way

that a listener perceives harmonic progressions, or indeed anything at all, is through the act of

interpreting meaning. I recall once more the summary of Mikel Dufrenne’s position in

Phenomenology of Aesthetic Experience that Clifton offers in Music as Heard. The quote refers to

melody, but it applies equally to harmony; “The unifying bond between [harmony] and me is not

a physical proximity, but a meaning which is constituted in me by the [harmony].”73 Quantifying

how that meaning it “constituted” is the study of Neo-Hauptmannian theory – It is the study of

the mental processes involved in the perception of harmonic progression.

I have chosen to call this study “Neo-Hauptmannian” because I embrace Moritz

Hauptmann’s premise that the logical succession of chords is determined by the listener’s ability

to discern a change of meaning in one or more of a chord’s constituent elements. Hauptmann

theorized that the intervals Root, Third, and Fifth, are themselves absolute meanings that are all

understood and taken in together in the conception of a triad. In hearing a triad, a listener

73 Clifton 1983, 47

38

CHAPTER II

NEO-HAUPTMANNIAN TRANSFORMATIONS

Reimagining Transformational Theory

perceives one tone to have Root-Meaning, another tone to have Third-meaning, and another tone

to Fifth-meaning. Hauptmann claimed that a chordal succession is only intelligible if the two

chords share a common element that changes its meaning through what Janet Schmalfeldt has

called the dynamic “process of becoming.”74 Here, the difficulties of discussing phenomenology

come up once again: it is important to recognize that it is not the “common element” that is taking

the action of “changing meaning.” The action is a perceptual one taken by the listener; it is the

“business of consciousness,” and not to be imposed on the musical object.75

When one attributes the action of change to the musical object, then one leaves the study

of phenomenology. For Neo-Riemannian theory, the basic definition offered above, “a method of

analyzing harmonic progressions,” often applies without caveat. The fundamental premise of Neo-

Riemannian theory is that the logical succession of chords is determined by the manner in which

the constituent elements of those chords are relatable in a geometrical abstraction we call pitch-

class space. If all chords are perceived to exist in this theoretical space, then the goal is to find the

connections – the particular pathways one or more of the constituent elements (pitches) must

travel in order to reach a different part of that space. For example, in a Neo-Riemannian Relative

(R) transformation, the fifth of a major chord “ascends” by whole-step, transforming the chord

into one whose root is a third lower (C-major to A-minor, in the key of C-major). For a minor chord,

the root “descends” by whole-step (C-minor to Eß-major). In a Leittonwechsel (L) operation, the

root of a major chord descends by half-step, transforming the chord into a minor one whose root

is a third higher (C-major to E-minor, in the key of C-major). For a minor chord, the fifth ascends

74 Schmalfeldt 2011, 29 75 Clifton 1983, 47

39

by half-step. In each of these examples, the action of change is attributed to the musical object –

it is the “moving” pitches that determine the transformational type.

However, this does not mean that the theory is inherently non-phenomenological. As

David Lewin so aptly noted, we tend to conceive of musical phenomena as existing “out there,” in

a space away from us, the observers of them.76 In contrast, what Lewin calls the “transformational

attitude” places the listener in that space.77 The listener is the one transforming, so to speak. From

that perspective, an R-transformation of a major chord, for example, would not be defined as the

fifth of a major chord ascending by whole-step, but rather, a “characteristic gesture” by which a

listener perceives a melodic ascent by the fifth of a major chord. In this way the transformational

attitude is explicitly phenomenological.78 But still, this means that the transformations Neo-

Riemannians use describe a phenomenology of melodic activity, not of harmonic activity. This is

an important difference between Neo-Riemannian and Neo-Hauptmannian theories: in Neo-

Riemannian theory, the action (or transformation) describes the perception of “moving”

element(s) between chords, the melodic elements; in Neo-Hauptmannian theory, the action (or

transformation) describes the reinterpreted meaning of the tone(s) that are held in common

between chords, which are what I would call the true harmonic elements.

In this chapter I will offer Neo-Hauptmannian transformational types that describe

perceptual actions that a listener takes when they hear certain harmonic successions. I will begin

with triads, since these deal solely with the changes of meaning in Root, Third, and Fifth –

Hauptmann’s “directly intelligible” intervals. The next section will offer a theoretical framework

76 Lewin 1987, 158-9 77 Lewin 1987, 159 78 Lewin 1987, 159

40

and historical precedent for transformations that include Seventh-meanings, what issues arise

from transforming seventh-chords, and what kinds of perceptual avenues they open. Finally, the

last section will consider the lines of communication between triads and seventh-chords, and how

they relate to current Neo-Riemannian perspectives.

Neo-Hauptmannian transformations are designed to show what happens to the meaning

of certain tones when chords change. In triads, there are three distinct tones that have unique

meanings. These meanings derive from the intervallic relationships between those tones, and they

are inherent to the conception of a triad. Those interval-meanings are Root-, Third-, and Fifth-

meanings. The act of perceiving these meanings can be illustrated in the following formula,

adapted from Izchak Miller’s formula for the structure of the act of perceiving:

In triad C, I perceivee triad C{tn} [=triad C̅{tp}[Root, Third, Fifth, …]

When I perceive triad C, I perceive the object of perception, or the “determinable-X” (triad

C̅), in the present “now” (tn); I perceive it in the context of having perceived it in the past (tp), and

I perceive it as having the discernable qualities of Root, Third and Fifth. These interval-meanings

are perceived separately, but they only come into existence in the context of the greater whole,

the triad. Moreover, these interval-meanings are independent of any particular pitch; however,

they arise only out of the relationships between particular pitches and are consciously attached

to the tones that create those meanings through those tone’s interactions with the others.

Therefore, the formula above implies each of the formulae below are also a part of the perceptual

experience:

41

Triadic Transformations

In triad C, I perceivee tone C{tn} [= tone C̅{tp}[Root, 261.63hz, 65dB, …],

In triad C, I perceivee tone E{tn} [= tone E̅ {tp}[Third, Major, 329.63hz, 65dB, …],

In triad C, I perceivee tone G{tn} [= tone G̅ {tp}[Fifth, Perfect, 392hz, 65dB, …]

The interval-meaning is one of the tone’s distinguishable phenomenological qualities,

along with hertz, decibels, tone color, and any other quality one can perceive from that

phenomenon. In separating out these phenomenological qualities, I must also note that interval-

meaning is a phenomenological quality that can be conceptualized separately from interval-

qualities, such as major or minor. Interval-meaning is a “unity at a higher level,” to invoke the semi-

Hegelian dialectic from which Hauptmann works. The tone E in the formula above is has the

qualities of “Third” and of “Major.” If the tone were an Eß the interval-quality of it in relation to

the triad C is “Minor.” But in relation to the triad C, they are both still perceived as “Third.” 79 The

same is true of Fifth-meaning. A Fifth can be perceived as such in perfect, diminished, or

augmented interval-qualities. Therefore, interval-quality exists as a lower-level notion of the

higher-level “unity” of the interval-meaning. Both will come into consideration in the

dissemination of the Neo-Hauptmannian transformations which are to follow. I will return to this

subject later in the discussion of Quality-transformations.

The most fundamental Neo-Hauptmannian transformations illustrate the perception of

passage from one interval-meaning to another within a common tone. When chords advance from

one to another, if they share a common tone, that common tone loses the phenomenological

79 David Lewin pondered the application of this Hegelian dialectic in general mathematics in the context of a discussion of Hauptmann’s treatise. In some unpublished lecture notes, he writes, “The parts here are “nothing” and “one thing.” The relation between thesis and antithesis gives rise to the idea of 3 higher-level things, namely: “nothing,” “one thing” and “two things.” We can conceive that synthesis as a new unity on a higher level, calling the new idea “3.” And so on indefinitely, generating all the numbers. This Hegelian analysis of our concepts of numbers is very close to the formal development of the subject in present-day mathematical logic. Transcript of a lecture by David Lewin, in the David Lewin Papers, Box 20 Folder 4, Library of Congress, Washington DC.

42

quality of one interval-meaning and gains another. The dialectical opposition between interval-

meanings is what guides this method of harmonic analysis. Understanding this “becoming” of one

interval-meaning to another is a perceptual action taken by the perceiver, and it is a goal of Neo-

Hauptmannian theory to define and categorize these actions. Consider for example, the same F-

major to C-major triadic succession I discussed in the previous chapter regarding Hauptmann’s

harmonic theory:

In F-major triad, I perceivee tone C{tf} [=C̅{tf}[Fifth, 261.63hz, 65dB, …],

In C-major triad, I perceivee tone C{tc} [≠C̅{tf}[Root, 261.63hz, 65dB, …].

Through the act of perceiving, the tone C at {tf} ceased to exist and became tone C at {tc}.

Since the phenomenological quality that changed was the interval-meaning of the Fifth, I refer to

this type of perceptual act as a Fifth-meaning transformation, or an F-transformation. In similar

fashion, I call perceptual acts in which the interval-meaning of a Root is changed a Root-

transformation, or an R-transformation, and those perceptual acts in which the interval-meaning

of a Third is changed are called Third-transformations, or T-transformations.

In triadic harmony, there can also be chordal successions in which more than one tone can

be held in common, of course. In the chordal succession of C-major to A-minor, there are two

common tones, C and E. The structure for the act of perceiving the changing interval-meanings for

this would be:

In C-major triad, I perceivee tone C{tc} [=C̅{tc}[Root, …], tone E{tc} [=E̅{tc}[Third, …],

In A-minor triad, I perceivee tone C{ta} [≠C̅{tc}[Third, …], tone E{ta} [≠E̅{tc} [Fifth, …],

43

In this kind of chordal succession, there are two perceptual acts that occur simultaneously;

the perceiver interprets the change of interval-meaning for the Root and the interval-meaning of

the Third at the same moment in time (ta). I call this type of perceptual act a RT-transformation.

Interestingly, the necessity to multi-task, so to speak, for the RT-transformation, does not mean

that the mental act is more complex or harder to “do.” In fact, it is generally claimed to be the

case that perceiving that kind of transformation is easier. Hauptmann certainly made this claim –

that kind of transformation would be considered more “intelligible,” because they share an

additional common element. In Neo-Riemannian theory, that type of transformation is one of the

three basic types – it is called a Relative (R) transformation, because the operation results in the

motion from one chord to its relative major or minor. From a phenomenological perspective, I

take the position that every chord transformation requires a complex mental act. Deciding which

transformations are “harder,” is entirely dependent upon what aspects of the act the analyst

wishes to focus. I would reframe the issue as such: These perceptual acts exist on a spectrum, as

shown below in Example 2.1. On one side there are harmonic motions, and on the other, melodic

motions. Changing two interval-meanings rather than one does not make the perceptual activity

more complicated; it just makes it more harmonic.

Example 2.1: Spectrum of Musical Perception

44

As one familiar with Neo-Riemannian theory may suspect, there is another type of Neo-

Hauptmannian transformation that requires two perceptual acts that occur simultaneously. That

is the TF-transformation, which occurs when the perceiver interprets the change of interval-

meaning for the Third and the interval-meaning of the Fifth at the same moment in time. In triadic

harmony, this transformation is analogous to the Neo-Riemannian L-transformation. From a C-

major chord, for example, the Third tone of the chord, E, and the Fifth, G, would be held in

common. Perceptually, those interval-meanings at the time of the C-major chord (tc) are

reinterpreted as Root and Fifth, respectively, at the time of the following E-minor chord (te) . This

is illustrated in the following formula:

In C-major triad, I perceivee tone E{tc} [=E̅{tc}[Third, …], tone G{tc} [=G̅{tc}[Fifth, …],

In E-minor triad, I perceivee tone E{te} [≠C̅{tc}[Root, …], tone G{ta} [≠G̅{tc} [Third, …]

The next type of Neo-Hauptmannian transformation in triadic harmony is what I call a

Quality-transformation, or a Q-transformation. A Q-transformation is the perceptual act of

interpreting only a change of quality (major/minor) in a chordal succession. In triadic harmony,

this would be analogous to the Neo-Riemannian Parallel-transformation (P). Unlike the other Neo-

Hauptmannian transformations, the Q-transformation does not involve an exchange of interval-

meaning among one or more common tones. Instead, the triad as a whole is perceived to shift to

an alternate harmonic system while the interval-meanings of the common tones remain constant.

The alternate system for a major chord is, in this case, the minor harmonic scale. The structure for

that perceptual act would be the following:

In triad C-minor, I perceivee tone C{tn} [=tone C̅{tp}[Root, …], tone G{tn} [=tone G̅{tp}[Fifth, …],

triad C{tn} [=triad C̅{tp}[Root, Third, Fifth, Major].

In triad C-minor, I perceivee tone C{tf} [=tone C̅{tn}[Root, …], tone G{tf} [=tone G̅{tn}[Fifth, …],

triad C{tf} [≠triad C̅{tn}[Root, Third, Fifth, Minor].

45

The harmonic quality of a chord is also one of its phenomenological qualities, along with

the interval-meanings of Root, Third, and Fifth. In Hauptmann’s dualist approach to harmonic

theory, the difference between a major triad and a minor triad is what he calls their state of

“unity.” In a major triad, the Root of the triad is the “determining” interval, because the Fifth and

the (major) Third are only understood in relation to it. In this sense, Hauptmann writes, the Root

“has” a Fifth and a Third. For him, “having is an active state,” and this active state of the Root

interval invokes a sense of “positive” unity. In contrast, it is the tone that has Fifth-meaning that

is “determining” the Root and the (major) Third intervallic relationships for the minor triad.

Because the Fifth is the determining tone, it has the assertive, active role in the minor triad, forcing

the Root into a “passive” state of “being had” by the Fifth. Hauptmann claims this state of a Root

“being had” by a “determining” Fifth invokes a sense of “negative” unity.80 Later, Hauptmann

argues that these two states of unity are intimately related, writing:

To every key-system, the opposite system with like name will always stand in near relationship… For here the transformation acts upon the tonic interval of Fifth, which passes from positive to negative or from negative to positive meaning, but in both determinations always contains at once the positive of the one and of the other.81

I – II II – I

Hauptmann uses the Roman numeral I to represent the part of the triad that has Root-

meaning, and II to represent the part that has Fifth-meaning.82 What he is illustrating above

suggests that the Root and the Fifth exchange interval-meanings with each other when a chord

passes from major into minor, or the reverse, so that the Root becomes the Fifth as the Fifth

80 Hauptmann 1853, 14 81 Hauptmann 1853, 165 82 Although it is not directly addressed in this section, the Roman numeral III represents the part of the triad that has Third-Meaning.

46

becomes the Root. The formula for that perceptual act is provided below. In the major triad at

time-point {tn}, the tone C has the phenomenological quality of Root-meaning, and the tone G has

the quality of Fifth-meaning. In the minor triad at time-point {tf}, the quality of tone C has become

Fifth-meaning, and the quality of tone G has become Root-Meaning. This is, essentially the

Riemannian dualistic conception placed into the temporal experience.83

In triad C-major, I perceivee tone C{tn} [=tone C̅{tp}[Root, …], tone G {tn} [=tone G̅{tp}[Fifth, …],

In triad C-minor, I perceivee tone C{tf} [≠tone C̅{tn}[Fifth, …], tone G {tf} [≠tone G̅{tn}[Root, …].

However, judging from the text of the quotation, and from Hauptmann’s earlier claims on

an interval’s “state of unity,” the idea that the interval-meanings become the other does not seem

accurate. When Hauptmann claims that the “transformation acts upon the tonic interval of Fifth”

during a passage from major into minor or minor into major, I believe he is saying that one still

perceives the Root and the Fifth as such – it is another kind of phenomenological quality that is

added or subtracted from the tone of the Fifth: the quality of “determining.” In the shift from

major to minor, the Fifth, which itself is determined by the Root, gains the phenomenological

quality of “determining,” the major Third and Fifth below it. In the shift from minor into major,

that determining quality is shed, leaving the Fifth only the quality of being determined.84 This is

what Hauptmann means when he says that the Fifth “in both determinations always contains at

once the positive of the one and of the other.” The corrected formula would then be the following:

83 The notion of the Fifth of the chord “determining” the structure of the minor triad is echoed in Riemann’s introduction of Harmony Simplified, where he suggests that the Fifth of a minor triad is the “prime” tone of the chord, from which the “under-third” and “under-fifth” are derived for the construction of the minor triad, which he calls an “underclang.” Riemann 1900, 1-9 84 This conception may contribute to the common poetic interpretation of a minor triad “having a downward drawing weight” as Hauptmann put it. In a manner of speaking, Hauptmann is claiming that the Fifth of a minor triad is literally heavier with the additional phenomenological quality. Hauptmann 1853, 17

47

In C-major triad, I perceivee tone G {tn} [=tone G̅{tp}[Fifth, Determined, …

In C-minor triad, I perceivee tone G {tf} [≠tone G̅{tn}[Fifth, Determined, Determining…].

In this respect, one could claim that a Q-transformation is actually a species of F-

transformation, since it is only the Fifth that undergoes a change of meaning. But I hold this

transformation as a separate type because unlike an F-transformation, a Q-transformation does

not interpret a change of interval-meaning in the Fifth. The perceiver does not perceive the Fifth

having become a Root or a Third; the Fifth remains as such. Or alternatively, it could be called a

RF-transformation, since both the Root and the Fifth are held in common during the change. But

again, it is not the existence of common tones that define R, F, T, RT, or TF-transformations. What

defines them is the phenomenological act of perceiving those common tones as having their

interval-meanings change from one kind to another. In the Q-transformation, the interval-

meanings of the common tones do not change. It is the perception of quality for the triad as a

whole that changes, not any Root, Third, or Fifth-meanings.

Example 2.2: Basic Neo-Hauptmannian Triadic Transformations Transformation Annotation Major Example Minor Example

1 Root & Third ⇒ Third & Fifth RT CM → Am Cm → AßM

2 Third & Fifth ⇒ Root & Third TF CM → Em Cm → EßM

3 Root ⇒ Third R3 CM → AßM Cm → Am

4 Root ⇒ Fifth R5 CM → FM/m Cm → FM/m

5 Fifth ⇒ Root FR CM → GM/m Cm → GM/m

6 Fifth ⇒ Third F3 CM → EßM Cm → Em

7 Third ⇒ Root TR CM → EM Cm → Eßm

8 Third ⇒ Fifth T5 CM → AM Cm → Aßm

9 Chord-Quality Q CM → Cm Cm → CM

48

Let us now review the types of triadic Neo-Hauptmannian transformations I have

introduced thus far using Example 2.2. For now, I will restrict the discussion to chordal successions

between major and minor triads. In effect, there are three different types of transformations that

can be applied to those triads: There are transformations where two common tones are shared

between chords, such as RT and TF (Rows 1-2), transformations where one common tone is

shared, such as R, F, and T (Rows 3-8), and the transformation whereby only the quality of the

chord changes, the Q-transformation (Row 9). These transformations identify phenomenological

actions taken by the perceiver, at two different points in time, as a means to interpret a connection

between the two chords. In the first two types, the perceiver perceives the interval-meaning of

the common tones named in the transformation (R, F, T, or a combination) in the first chord at

one moment in time, and then perceives those tones has having a different interval-meaning at

the next moment in time. In the case of the Q-transformation, the perceiver perceives one chord

quality at first, and then another chord quality later.

An RT-transformation can only point to one musical outcome in triadic harmony,

depending on the quality of the original chord. As shown in the examples in Row 1, if the first

chord is major, then the second chord will be minor and its root will be a minor-third lower; If the

first chord is minor, then the second chord will be major and its root will be a major-third lower.

In similar fashion, a TF-transformation also can only point to one musical outcome, as shown in

the examples in Row 2. If the first chord is major, the second chord will be minor and its root will

be a major-third higher; If the first chord is minor, then the second one will be major and its root

will be a minor-third higher. This is because of the limited number of interval-meanings in the

triadic framework; An interval can only be a Root, Third, or Fifth – so if there are two common

49

tones, as with an RT, one of those tones must gain the interval-meaning that is not R or T, namely

the Fifth, and the other common tone must take the interval-meaning of the one that became the

Fifth. This is admittedly some confusing verbiage, so it may be easier to think of the interval-

meanings as “shifting” up or down. As shown in Example 2.3, an RT-transformation “shifts” the

interval-meanings of the common tones up, so that the Root of the first chord becomes the Third

of the second, and the Third of the first chord becomes the Fifth of the second. Likewise, a TF-

transformation shifts the common tones down, meaning the Third of the first chord becomes the

Root of the second, and the Fifth of the first chord becomes the Third of the second. With this in

mind, it may be helpful to add subscripts to the RT and TF-transformations so that they denotate

the interval-meanings which those intervals “become,” so that they read R3T5 and TRF3

respectively. However, in the context of triadic harmony the additional clarification is technically

redundant.

Example 2.3: Shifting RT, TF Interval-Meanings

50

R, F, and T-transformations, which are defined by their single common tones, have two

options in regard to what other interval-meaning they can become in triadic harmony (the other

two). Therefore, we can make subcategories for each of these transformational types using

subscripts to clarify what those interval-meanings become. These subscripts allow an analyst to

show more precisely to which chords these transformations would take the music. As we see in

Row 3 of the table, for example, a R3-transformation from a major chord leads to a major chord

whose root is a major-third lower, and from a minor chord it leads to a minor chord whose root is

a minor-third lower. It will not be necessary to go through each row of the table in this manner,

but it is worth pointing out that for the R5 and the FR, shown in Rows 4 and 5, neither the original

interval-meaning nor the one which that tone becomes are the quality-defining Third. Therefore,

the subcategory does not clarify whether or not the resulting chord will be major or minor. An R5

from a C-major chord may lead to an F-major chord, or it may lead to an F-minor chord; Either

option would satisfy the notion that the common tone that meant Root has become the Fifth of

the succeeding chord.

Neo-Hauptmannian theory, like the theories of Christopher Hasty and Eugene Narmour, is

a bottom-up theory of musical perception by design, meaning that it functions independently of

any specific stylistic structures or cultural archetypical patterns. The analytical constant in this

system is the perception of interval-meaning, which exists regardless of any top-down stylistic

framework or convention. So far, I have restricted the applications to major and minor triads,

independent of any consideration of musical key. However, one of the advantages of using these

Neo-Hauptmannian transformations is that they can accommodate stylistic frameworks, such as

diatonicism, should the analysis require it.

51

Take the TF-transformation in Example 2.4 as a case in point. The TF, as I noted above,

would take a major chord to a minor chord whose root is a major-third above it (C-major → E-

minor). This would be the case if the analyst were operating within a framework that deals solely

with major and minor triads, such as a Riemannian Tonnetz. However, if an analyst wishes to

operate within a particular tonal framework, say F-major, a TF-transformation from a C-major

chord would lead to an E° chord. The requirement that the perception of the Third and Fifth

shifting down to become Root and Third is met in both cases. This demonstrates a flexibility in the

Neo-Hauptmannian system that allows it to be applicable in tonal and non-tonal contexts.

As we broaden the application of these transformations outside of the major/minor

system, we can consider other applications for the Q-transformation. Recall that a Q-

transformation, unlike the other types of Neo-Hauptmannian transformations, does not identify

an exchange of interval-meaning for a common tone from one to another. Instead, a Q-

transformation recognizes that the interval-meanings remained the same, but there was a change

in quality for the triad as a whole. Consider Example 2.5 below. At first, I only demonstrated how

a Q-transformation would lead from a major chord to a minor chord, and vice versa. However, a

Q-transformation could also lead to diminished or augmented chords with the same root, or a

Example 2.4: No-Key vs Key Contexts

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major chord with a flattened fifth, for that matter. The Root-meaning of the common tone remains

constant, so the phenomenological change in the perception of the chord quality occurs in the

same way, i.e., the following formula:

In triad C-major, I perceivee tone C{tn} [=tone C̅{tp}[Root, …],triad C{tn} [=triad C̅{tp}[Root, Third, Fifth, Major],

In triad C°, I perceivee tone C{tf} [=tone C̅{tn}[Root, …], triad C{tf} [≠triad C̅{tn}[Root, Third, Fifth, Diminished].

Example 2.5: Quality and Interval-Quality Transformations Transformation Annotation Major Example Minor Example

1 Chord-Quality Q CM → Cm/+/°/ß5 Cm → CM/+/°/ ß5

2 Third-Quality TQ CM → Dßm Cm → BM

3 Fifth-Quality FQ CM → B+ Cm → Cƒ°

4 Third & Fifth-Quality TFQ CM → Cƒ° Cm → B+

There is one final type of triadic transformation, which I call Interval-Quality

transformation. An interval-quality transformation is similar to a Q-transformation in that it does

not recognize a change of interval-meaning for a common tone. But unlike a Q-transformation,

which identifies a change of quality for the triad as a whole, an Interval-Quality transformation

identifies a change of quality for a specified interval. For example, the TQ-transformation, as shown

in Row 2 of the table, identifies a change in quality for the common tone Third of an initial chord,

from major to minor or vice versa.85 The TQ is one of only two involutional operations in Neo-

Hauptmannian triadic transformations, meaning that the operation, if applied twice, will result in

a return to the original chord.86 If the first chord is major, then the second chord will be minor and

85 In practice, the TQ is analogous to David Lewin’s SLIDE transformation, which exchanges two triads that share a third. 86 The other is a particular subtype of Ascent/Descent-transformation which transposes a chord by an interval of a tritone, which I will discuss in the next section.

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its root will be a semitone higher. If the first chord is minor, then the second chord will be major

and its root will be a semitone lower.

The FQ-transformation identifies a change in quality of the common tone Fifth of the initial

chord. The Fifth, of course, has three possible interval-qualities in triadic harmony; perfect,

diminished, or augmented. The FQ affects each of them differently. If the Fifth is the only common

tone in an FQ-transformation, and that tone’s perception as Fifth-meaning is to be maintained,

then the results for triadic transformations are as follows: For a major chord, an FQ leads to an

augmented triad whose root is a semitone lower. For a minor chord, an FQ leads to a diminished

chord whose root is a semitone higher. For a diminished chord, an FQ leads to a minor chord whose

root is a semitone lower. And finally for an augmented chord, an FQ leads to either a major chord

whose root is a semitone higher, or a diminished chord whose root is a whole-tone higher.

Lastly, the TFQ-transformation perceives a change in quality for two common tones, the

Fifth and the Third. This transformation functions in as the inverse of an FQ; when applied to a

major chord, the result is a diminished chord whose perceived root is a semitone higher, and when

applied to a minor chord, the result is an augmented chord whose perceived root is a semitone

lower. A TFQ from an augmented chord leads to a major a semitone higher, and from a diminished

chord, a minor chord a semitone lower or augmented chord a whole-tone lower would follow.87

87 I recognize that by introducing the idea of interval-specific quality transformations, I open a theoretical can of worms. If the common tone can be perceived to change not only its interval-meaning, but also its quality, then the door opens for R, F, and T-transformations to lead to diminished and augmented triads in a variety of new ways. While I find that there is nothing logically inconsistent with this this avenue of harmonic possibilities, it leads to a subcategory of transformations will have limited practical use. Therefore, I have decided that such a discussion will lie outside of the scope of this project.

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There are, of course, chord successions wherein there are no common tones. At first

thought, one might be inclined to consider these types of transformations, to use Hauptmann’s

term, “unintelligible.” There is no common element which changes meaning during the passage,

and so either the chords are not relatable or they must be related through an implied “mediating”

chord.88 But to think of it in this way would deny that there is any mediating perceptual activity,

and that is not the case. There is a mediating perceptual activity, but since there are no common

tones, the mediating process is not at all harmonic but fully melodic.

In melodies, the activity that mediates the relationship between one note and the next is

either “ascent” or “descent.” In Example 2.6, there is a dialectical relationship set up between two

tones, C4 and D4. To advance from the former to the latter, the listener must perceive the activity

which we call ascent. At one moment, the listener perceives one tone filling a particular pitch

space in a particular pitch-class space, and then at the next moment they perceive another tone

in a different pitch space within a different pitch-class space. Similarly, to advance from C4 to B4,

the listener must perceive the activity we call descent. This is, essentially, the process of melodic

88 Hauptmann 1853, 48

Example 2.6: Melodic Dialectic

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"Harmonic" Successions Where there are No Common Tones

succession. 89 Chord successions that have no common tones follow the same melodic dialectic. It

may be helpful to think of chord successions where there are no common tones not as chord

successions at all, but rather as three melodic successions happening simultaneously.

As a matter of process, the latter chord occurs entirely as a result of melodic activity, not

of harmonic activity. These melodic activities may occur within the context of a key derived from

the former chord, i.e., C-major to D-minor or C-major to B°, or they may occur independently from

key, i.e., C-major to D-major or C-major to B-minor. In either case the mediating activity that

connect them remains either ascent or descent. Although these musical events are not technically

(by my definition) harmonic transformations, but simultaneous melodic transformations governed

by a different mediating process, they nonetheless cannot be omitted from this Neo-

Hauptmannian language. As such I call these “harmonic” perceptual acts in which there are

entirely melodic ascents Ascent-transformations (A-transformations), and perceptual acts where

there are entirely melodic descents Descent-transformations (D-transformations).

89 Technically, pitch-class space is agnostic to the notions of “ascent” or “descent,” as it does not distinguish between pitches that are octave-related. When one thinks about a musical tone ascending or descending, they are considering pitch space. C4 can ascend to B5 or descend to B4, for example. Whether one thinks of Ascent-transformations and Descent-transformation in terms of up or down or to the left or right along a chromatic circle is ultimately of little consequence. The relevant detail is that each tone of the chord is moving in the same direction in pitch-class space.

Example 2.7: Alternative A and D Transformations

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Ascent and Descent-transformations are defined by the perception of melodic ascent or

descent by each individual tone of a chord. But this does not mean that the tones to which they

move necessarily have the same interval-meaning as the tones from which they came. Such is the

case with the examples listed above – From the C-major chord, the tone C has Root-meaning and

moves melodically up to the tone D, which in its own context also has Root-meaning. The tone E

has Third-meaning in the former chord, then moves up to F (or Fƒ), which in its own context also

has Third-meaning. And so on. But consider Example 2.7a. In this example, all three tones descend

melodically: The tone C moves down to Bß, the tone E moves down to Eß, and the tone G moves

down to Gß. Yet, in the context of the latter chord it is in fact the Eß and not the Bß that has Root-

meaning. As one can see, the Descent-transformation as a category of “harmonic” activity includes

any chord progression in which each tone is perceived to move melodically down by step. It does

not discriminate by whether or not those steps are half-steps or whole-steps – so long as they are

moving in parallel motion. Example 2.7b shows a similar case, this time for the Ascent-

transformation. From the C-major chord, the tone C moves up to Cƒ, the tone E moves up to Fƒ,

and the tone G moves up to A. But in the context of the latter chord, Fƒ is the tone that has Root-

meaning.

Example 2.8: Ascent or Descent?

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The case for determining what kind of process is used for moving from C-major to Gß/Fƒ

major is somewhat trickier, as shown in Example 2.8. On one hand, one could say that it is another

kind of Descent-transformation. From the C-major chord to a Gß-major chord, the tone C moves

down to Bß, the tone E moves down to Dß, and the tone G moves down to Gß. On the other hand,

one could say that it is a kind of Ascent-transformation. From the C-major chord to an Fƒ-major

chord, the tone C moves up to Cƒ, the tone E moves up to Fƒ, and the tone G moves up to Aƒ. In

either case, the tones that are being perceived are the same. In a true rabbit/duck scenario, the

difference is in where the listener assigns the augmented-second melodic motion. Does the tone

G move up to Aƒ, or does the tone E move down to Dß? This is a question of melodic process, not

of harmonic process, and so it may not be possible to come up with a definitive answer while the

context is limited to two harmonic entities. Chord position and surrounding melodic context will

need to be investigated. If one is to maintain a narrow focus on harmonic study as we have been,

one can only conclude that it could be either one, and that in any case, this particular subtype of

“harmonic” transformation is involutional.

Example 2.9: The Uncanny Transformation

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This brings us to one final type of no-common-tone transformation, and to echo Richard

Cohn, there is something wrong with Example 2.9.90 Unlike the Ascent and Descent-

transformations, this particular transformation does not have a uniformity of direction for the

simultaneous melodic motions; in this chord progression, two of the tones, C and E, move down

by a semitone while the other tone, G, moves up by a semitone. The contrary melodic motion

produces a unique musical effect which many theorists, from Hugo Riemann to Susan Youens,

have associated with the bizarre, the strange, or the magical.91 In his 2004 article, Cohn settled on

the word “uncanny” (or in German, “unheimlich”) to describe the harmonic relationship, and so

following him, I will call this kind of transformation an Uncanny-transformation (U-

transformation). Within the context of a major/minor triadic framework, the U-transformation

takes a triad to what Cohn has called it’s “hexatonic pole,” which for a major triad is the minor

triad whose root lies a major-third below it, or for a minor chord, a major chord whose root lies a

major-third above it.

The duality of Being and non-Being as part of a transcendental whole is very much at the

core of Hauptmann’s intelligible intervals. It is the unification of the three elements as triad that

gives him a framework to develop his key system, tuning preference, and suspension theory.

Hauptmann believed that Root, Third, and Fifth-meanings were discernable qualities of the triad,

which can then be perceived as part of a single, complex perceptual act. To recall the perceptual

model offered by Miller, the triad would be recognized as the Husserlian “determinable-X,” and

90 Cohn 2004, 285 91 Cohn 2004, 285

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The Indirectly Intelligible Intervals

the interval-meanings would be the specific qualities of that phenomenological object. This could

be formulated as:

I perceivee Triad{t1} [R{t1} [=R̅{t1}[a, b, …], T{t1} [=T̅{t1}[a, b, …], F{t1} [=F{̅t1}[a, b, …]]

Or if one were to omit the perceptual qualities of each tone from the formula to more

effectively convey a sense of “next level” perception:

I percievee Triad{n(t1)}[Root, Third, Fifth]

However, there does not appear to be, or at least Hauptmann does not offer, a

philosophically grounded objection to extending the argument for intelligibility to other intervals.

He argues that there is a qualitative distinction between the intelligible intervals and dissonant

tones; but ultimately, he fails to present any evidence of that claim beyond his insistence of a “felt

understanding” innate to the nature of “humanly reasonable existence.”92 Similarly to the building

of previous theoretical systems upon the first few overtones of the overtone series, such a

limitation seems to be practical rather than logical and imposed to satisfy the perceived

naturalness of the major triad and by extension the diatonic system. Therefore, it is subject to the

same criticism that Schoenberg laid in his book, Harmonielehre, against theories that use the

overtone series, i.e. that the difference between a so-called directly intelligible interval and a less

intelligible one “is a matter of degree, not of kind.”93 Speaking directly to the supposed necessity

of intelligibility, Schoenberg later writes,

The sense of form of the present does not demand this exaggerated intelligibility produced by working out the tonality. A piece can also be intelligible to us when the relationship to the fundamental is not treated as basic; it can be intelligible even when the tonality is kept, so to speak, flexible, fluctuating. Many examples

92 Hauptmann 1853, xl 93 Schoenberg 1922, 21

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give evidence that nothing is lost from the impression of completeness if the tonality is merely hinted at, yes, even if it is erased.94

In short, there is no reason why the perception of a harmony could not be modeled as:

I perceivee Tetrachord{n(tj)}[Root, Third, Fifth, Seventh]

or

I perceivee Pentachord{n(tj)}[Root, Third, Fifth, Seventh, Ninth]

Such perceptions can be supported using the same logical steps that Hauptmann takes for

the intelligible intervals. Consider Example 2.10a. The major Second, which has a 9:8 interval ratio,

is dialectically similar to the major Third in the following ways: The Second has an unequal,

unsounding part that gives the listener the context necessary to understand the whole (a ninth

94 Schoenberg 1922, 128

Example 2.10: Dialectics of the Indirectly Intelligible Intervals

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ninth-part). It also has a sounding part (the eight ninth-parts) that can be divided against itself into

eight equal parts (the major Third has four equal parts). These eight parts can be grouped into

pairs of parts that are equal to each other, and each pair can be grouped with another pair to

create a larger unit that also has an equal outside of itself. This gives the Second a similar quality

to Third in that it expresses both unity and duality as union. The difference between Second and

Third is that in the Second, the expression of both duality and union is compounded. Thus the

absolute meaning of Second, or more commonly in harmonic practice, minor Seventh, is that of a

compounded union.

Concerning the Fifth, Hauptmann writes that it contains acoustically “the determination

that something is divided within itself,” and that this is the quality that gives it the notion “duality”

and “inner opposition.”95 As I noted earlier, the two-part division of the sounded part gives the

Fifth its sense of duality. Inner opposition, however, can also be found in the acoustical

determination of the Fourth (4:3), as shown in Example 2.10b. The sounding body of this intervallic

relationship is also “divided against itself,” only its division is into three equal parts. Those parts,

when taken with the whole, determine the fourth fourth-part, and gives the appearance of a thing

tripled. Therefore both the Fifth and the Fourth contain within themselves the notion of inner

opposition, but they are distinct from each other in that where the Fifth, with its equal division of

the sounding body, also expresses the notion of duality, the Fourth, with its tripartite division of

the sounding body, expresses the notion of triality.

When I speculate about the notions of the minor third (6:5) in Example 2.10c, I find that

the notion of separation is found in two places. In one place, separation is found in the division of

95 He also uses the term “separation” as an alternative descriptor for the Fifth. Hauptmann 1853, 6

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the sounding body, as is the case with every interval presented thus far with the exception of the

octave; In another, separation is found in the unequal division of the sounding body. By grouping

the first two sixth-parts and the 3rd – 5th sixth-parts (or the other way around), it creates the notion

union of duality and triality. Duality in the first and second sixth-parts, and triality in the 3rd – 5th

sixth-parts. Finally, Example 2.10d shows that in the interval of the minor second (16:15) we find

that the sounding body is divided into 15 equal parts, determining an unsounded sixteenth part.

These sounded parts can be grouped together into three equal groups of five, expressing the

notion of triality also found in the Fourth. Those 5-part groups consist of a group of two and a

group of three, expressing the notions of union of duality and triality also found in the minor Third.

These two distinct levels of separation are taken in together to give the highest order of musical

understanding: chromaticism.96

In working out the intelligibility of these other intervals, I am simply extending the same

Idealist dialectic for working out absolute meaning that Hauptmann employs. Such an extension is

not unprecedented. The work of philosopher Karl Christian Friedrich Krause (1781 – 1832) is one

such precedent. Krause was a contemporary of Hauptmann’s, and reportedly an underappreciated

writer of his time, despite having studied under both Fichte and Hegel. He also had background in

music and published a piano tutor in 1808. As Jennifer Hughes notes, his contribution to idealist

philosophical speculation on music theory was unique in that he was well-experienced in both

areas.97 According to Hughes, Krause suggests that the universe undergoes a constant process of

96 This kind of speculation is similar to Plato’s idea of the composition of the soul, found in Timaeus 34b-37c. 97 Hughes, 1996. Krause has two published works on music theory, Darstellungen aus der Geschichte der Musik nebst vorbereitenden Lehren aus der Theorie der Musik (Gottingen 1827), and Anfangsgründe der allgemeinen Theorie der Musik (Gottingen 1938).

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development, “which involves the formation of ever-ascending layers of higher unities, whose

ultimate stage is the identification of the world with God.”98 This understanding of “world as

process” comes through in his music-theory speculation. Unlike Hauptmann, Krause describes

seventh and ninth harmonies as dissonant extensions of the triadic intervals. They are not

antithetical to the concordant intervals of Root, Third, and Fifth, but rather they are the “coming-

to-be” of higher levels of musical unity. The increased number of possible resolutions for seventh

and ninth chords allow music to transition seamlessly from one key to another, expanding

harmonic possibilities and acting as a bridge between distinct levels of musical unity. From this

perspective, there is an Idealist goal of allowing for the connection of one chord to any other. This

would establish an understanding in which the entire system of harmonic thought can be unified.

If we accept the premise that one can perceive an interval as having Seventh-meaning,

then we can begin to explore the possibilities of the Seventh-transformation, or S-transformation.

An S-transformation is a perceptual act whereby the perceiver interprets the change of interval-

meaning for the tone of the Seventh. Like R, T, and F-transformations, the S-transformation has

only one common tone that is shared between the first chord and the second, the tone which in

the first chord had Seventh-meaning. The addition of transformations whereby a Seventh-

meaning interval becomes a Root, Third, or Fifth, or vice versa, opens up a new axis of perception.

This axis tilts both ways, of course, meaning that the triadic transformations I have already covered

have a new “place to go,” or to be more precise, they now have an additional interval-meaning

which they can become. One can perceive a Root becoming a Seventh, for example, in the same

98 Hughes 1996, 5

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S-Transformations

fashion that one can perceive a Seventh becoming a Root. This additional axis of perceiving

harmonic motion creates logical, phenomenological connections between harmonies that tonal

and Neo-Riemannian theories would consider harmonically distant, requiring multiple operations

to reach.

As I noted earlier in the section on triads, Neo-Hauptmannian transformations operate

around the perception of interval-meanings, and that perception occurs separately from the

perception of interval-quality. The same principle applies to seventh-chords. So long as the

interval-meaning of “Seventh” can be perceived, a transformation can occur around the tone that

expresses it, regardless of interval-quality. Just as a Third is a Third whether it is major or minor, a

Seventh is a Seventh whether it is major, minor, half-diminished, or fully-diminished. This allows

S-transformations to be applied within a diatonic context or a non-diatonic context, depending on

the needs of the analyst. That makes seventh-chord single-common-tone transformations highly

flexible. From a G7 for example, the Seventh (F) can become Root of any quality F seventh-chord,

the Third of a Dm/Ø/° or Dß7/maj7 seventh-chords, or the Fifth of a Bß dominant, minor-minor, or

major-major tetrachord. One could also perceive a Quality-transformation to a G minor, half-

diminished or fully-diminished chord, or an interval-quality transformation of the seventh, which

would lead to a Gß seventh-chord – and all of this does not include any consideration of

chromatically altered dominant seventh-chords.

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Consider Example 2.11. Originally, I had considered offering a list of subcategories for

seventh-chord transformations denotated with subscripts, as I have provided for triadic

transformations. A transformation where a Seventh becomes a Root, for example, could take a G7

chord to an F7 or a Fm7 chord and can be called an SR. An S5, alternatively, could take a G7 chord

to a Bßm7 chord. However, an exhaustive list of examples for this new axis of perception, including

the ways in which it can be combined with other common tones and the manner in which they

can be applied to Mm7, mm7, MM7, half-diminished, fully-diminished, and other chromatically

altered seventh-chords, has proven to be excessively burdensome. Further, some subcategories

rarely occur in practice. To offer examples for each of these transformations would quickly lead

into esoteric irrelevance, for the number of possibilities that are effectively never explored in

western musical canon far outnumber the possibilities that are. To echo Dmitri Tymoczko’s

sentiment regarding musical objects, to treat each subcategory of transformation as a unique

phenomenological object would be of limited analytical usefulness, and so particular as to be

uninteresting.99 Therefore, I will instead review these broader categories of S, FS, TS, RF, and TFS-

99 Tymoczko 2011, 75

Example 2.11: Tetrachordal Transformations

Transformation Major-Minor Example

Minor-Minor Example

Half-Diminished Example

Major-Major Example

1 S G7 → F7 Em7 → Dm7 BØ7 → Am7 CMAJ7 → G7

2 FS G7 → Dm7 Em7 → BØ7 BØ7 → F7 CMaj7 → EßØ7

3 TS G7 → Cƒ7 Em7 → Gm7 BØ7 → D7 CMaj7 → E7

4 RF G7 → EØ7 Em7 → Cƒm7 BØ7 → G7 CMaj7 → Aßmaj7

5 TFS G7 → BØ7 Em7 → G7 BØ7 → Dm7 CMaj7 → Em7

6 RTF G7 → Em7 Em7 → CMaj7 BØ7 → G7 CMaj7 → Am7

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transformations and provide a few examples for each, with the disclosure that this is not an

exhaustive accounting.

It may be beneficial to begin with the ways in which S-transformations can be used that

have already been considered by Hauptmann himself in his treatise. Concerning the succession of

seventh-chords, Hauptmann writes that there are six “series of joined Seventh-harmonies” that

he deems “intelligible,” three “progressing toward the subdominant side” and three “progressing

toward the dominant side.”100 On the subdominant side, the first series contains three common

tones – Root, Third, and Fifth. Those tones are held in common while the remaining tone descends,

creating a chord progression that is related by third, i.e., G7 to Em7. Since the Root, Third, and Fifth

are the common tones for this type of chordal succession, I call this an RTF-transformation. The

first series on the dominant side works in similar fashion. The three common tones in a succession

toward the dominant side are the Third, Fifth, and Seventh, and this also creates a chord

progression that is related by third, this time ascending rather than descending, i.e., Em7 to G7. I

call this type of succession a TFS-transformation. For the TFS and RTF-transformations, it is helpful

to return to the idea of “shifting” interval-meanings up or down. In the case of the RTF, the

interval-meanings shift upward, meaning that those common tones become the Third, Fifth, and

Seventh of the latter chord. In the example above, an RTF on a G7 chord would shift the interval-

meanings up, leading to an Em7 chord. The Root tone (G) would become the Third, the Third (G)

would become the Fifth, and the Fifth (D) would become Seventh. In contrast, the TFS

100 Hauptmann 1853, 81-88

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transformation would shift the interval meanings down, so that in the case of Em7, the resulting

chord would be rooted on G.101

The second of Hauptmann’s series on the subdominant side contains two common tones

– the Root and the Third. The RT-transformation is one that I have already discussed. In the context

of triads, the common tones in an RT could only become the Third and the Fifth of the following

chord. Those interval-meanings could only “shift up” once. But now that we have opened this new

axis of perception on the Seventh, we can consider chord successions in which we perceive those

common tones to shift their interval-meanings up twice, to Fifth and Seventh. Such a

phenomenological act is what is occurs here, as shown in Example 2.12. This “double-shifting”

creates seventh-chord progressions that are related by descending fifth, i.e., G7 to Cmaj7. The

second series on the dominant side has the Fifth and the Seventh as common tones from one

chord to the next. These progressions I call FS-transformations, and they create chord

progressions that are related by ascending fifth, i.e., Cmaj7 to G7. As in the previous example where

101 If one is thinking in terms of scale-step theory, I might point out that interval-meanings shifting up or down has the effect of shifting the root of the latter chord in the opposite direction. So if the interval-meanings of a C7 chord are shifted up, then the root of the chord is shifted down a minor third to A7. Likewise, if the interval-meanings are shifted down, the result would be a chord whose root is shifted up a major third, to E7 in this case. The interval-meaning shifts and scale-step shifts are inversely correlated.

Example 2.12: RT and FS Double-Shifting

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the common tones’ interval-meanings can be said to double-shift upward, an FS-transformation

has its common tones double-shift their interval-meanings downward to Root and Third.

The third series on the subdominant side has one common tone from one chord to the

next, and in the first chord that common tone has Root-meaning. In this series, the Root becomes

the Seventh of the following chord (R7), i.e., D7 to Em7. This is, again, a new perceptual axis for the

R-transformation, which allows for a chord progression that is related by ascending second. And

finally, there is the third series on the dominant side, where the common tone between chords is

the one that has Seventh-meaning, i.e. G7 to Fmaj7. In this diatonic series, the S-transformation

creates chord progressions that are related by descending seconds.

In the series of chord progressions that Hauptmann considers, he confines himself to

diatonic applications. In a diatonic context, it may be best to think of S-transformations simply as

extensions to the rules of triadic progressions, as Hauptmann does. However, there are a

multitude of non-diatonic applications that fall into the same phenomenological families. As is the

case with the other Neo-Hauptmannian transformations, the actual harmonic outcome for

Seventh-chord transformations can vary even when the defining common tones are retained. The

TFS transformation is a fine example. In the diatonic context presented above, a G7 chord leads to

a BØ7. In this case, the G7 chord could just as easily lead to a B°7; here, the way the perceiver

interprets the chord changes is still a TFS-transformation.

Once one exits the confines of diatonicism, the question of where two-common-tone

transformations lead becomes a matter of which kind of dyad the tones are preserving. The TS-

transformation preserves the interval relationship between the Third and the Seventh of the first

chord while the other tones change. If the first chord is a Mm7, then the dyad that is preserved is

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a tritone. To preserve that tritone while the other tones change, there are two paths the harmony

could take. The Third and Fifth could shift up to Fifth and Root of a half-diminished chord whose

root lies a whole-tone below the former chord, i.e., G7 to FØ7. Or, the interval-meanings of the

Third and Seventh could exchange with each other, so that the Third becomes the Seventh and

the Seventh becomes the Third. This phenomenological link connects a Mm7 chord to another

Mm7 chord that is related by tritone, i.e., G7 to Cƒ7. For minor-minor, half-diminished, and major-

major seventh-chords, on the other hand, the dyad being preserved is a perfect fifth. In those

cases the common tones shift down to Root and Fifth and the resulting chord would be one whose

root is a major third higher, i.e., Em7 to Gm7. RF-transformations work in similar fashion. The RF-

transformation preserves the interval relationship between the Root and the Fifth of the first

chord while the other tones change. In triads, an RF-transformation could not take place, because

the perfect-fifth dyad could not be reinterpreted as anything else in the context of any other triad.

In terms of shifting interval-meanings, there was simply no room to move in either direction. But

in the context of seventh-chords, the Root and Fifth interval-meanings can shift, up, to Third and

Seventh.

The FS-transformation is more flexible than the TS and RF-transformations because the FS,

along with the RT and TF, preserves major or minor-third dyads, which occur in more positions

within a tetrachord. In the case of Mm7, mm7, and fully-diminished seventh-chords, the FS

preserves the minor-third dyad in the upper part of the tetrachord – that dyad can be

reinterpreted as the other minor third dyad in several ways. From a G7 chord, for example, an FS-

transformation could theoretically lead to its fully-diminished or half-diminished mediant (B°7 or

BØ7), its major-minor chromatic mediant (Bß7), or to its minor-minor dominant (Dm7). In each case,

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the D-F dyad is held in common and those tones take on other interval-meanings. In the case of

the half-diminished seventh-chord, the FS preserves a major third. So from a GØ7 chord, this would

lead either to a Bßm7 or to the even further removed harmony of Dß7.102

The same principle applies to seventh-chord RT and TF-transformations. RT-

transformations, as I have already discussed, can double-shift the meanings of those tones up to

Fifth and Seventh. From a MM7 or Mm7, this kind of RT would preserve a major-third dyad, which

would lead to a MM7, as in C7 to Fmaj7. From a minor-minor, half-diminished, or fully-diminished

seventh, the RT would preserve a minor third dyad, which would lead to a non-MM7 chord, as in

Cm7 to F7. In the context of seventh-chords, the TF-transformation now has the option to shift

once in either direction, to become the Root and Third or the Fifth and Seventh of the following

chord. This allows for a progression of chords related by minor-third or major-third, i.e., the

progression C7 – A7 – Fƒm7 – Dmaj7.

When one adds Seventh-meaning to this Neo-Hauptmannian conception of common-tone

transformations, the library of possible harmonic relationships the listener could perceive is

exponentially increased. This is especially true considering the fact that I have made no attempt

to control for the quality of chord to which these transformations can be applied, or for the quality

of chord to which such a transformation would lead. If I were to, for example, construct a subset

of two-common-tone transformations (RT, TF, TS, FS, and certain Q-transformations) which, when

applied to a dominant or half-diminished seventh-chord, could only lead to either another

102 An FS applied to a fully-diminished seventh-chord could theoretically lead to a dominant-seventh with a

flattened fifth that is rooted a semitone lower (from G°7, GßY7%), but I would be hard-pressed to find an example ofsuch a progression.

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Lines of Communication

dominant-seventh or half-diminished seventh-chord, the list of possibilities would be much more

manageable. From that list, one could even construct geometric networks of those harmonic

relationships that demonstrate maximally parsimonious voice-leading among those chords. This

was the aim of several Neo-Riemannian theorists twenty years ago. In his 1998 article, “Moving

Beyond Neo-Riemannian Triads: Exploring a Transformational Model for Seventh Chords,” Adrian

Childs devised a set of transformations using the parameters I have just described, which he called

S and C-transforms, shown in Example 2.13. “S” refers to transformations where the non-fixed

tones move by semitone in similar motion, and “C” refers to those where the non-fixed tones

move by semitone in contrasting motion. Childs then used this set to construct a cubic network of

harmonic relations, reprinted in Example 2.14, which contains eight members of set class 4-27

which are subsets of the same octatonic collection.103

103 Childs 1998, 187-8

Example 2.13: Adrian Child’s S and C Transforms

+ and – refer to dominant and half-diminished seventh-chords, respectively

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In the same 1998 Journal of Music Theory Fall publication, Edward Gollin also created a

geometric network of connections between dominant and half-diminished seventh-chords. In his

article, "Some Aspects of Three-Dimensional Tonnetze,” Gollin created his own subset of common-

tone transformations and used them to construct his own systems of harmonic relations.104 In

104 Gollin 1998, 199-201. Unfortunately, Gollin beat me to the term “Neo-Hauptmannian,” which he uses to identify his dualistic labeling of chord tones for set class [0258]. However, beyond the use of Roman numerals, the connection to Hauptmann’s theory is largely superficial, writing that he does not necessarily embrace Hauptmann’s “dialectical connotations,” and that his use of the word “Einheit” was completely “arbitrary.”

Example 2.14. Adrian Child’s Cubic Network of Seventh-Chords Within One Octatonic Collection

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“Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited

Transposition,” Jack Douthett and Peter Steinbach used a collection of three-common-tone

transformations, which they called “P1,0-relations,” to build their own networks of dominant,

minor-minor, and half-diminished seventh-chords within an octatonic collection called

“Octatowers.”105 The drawback to constructing these types of geometric networks using smaller

collections of transformations is that they are limited in their capacity to explain harmonic motions

that take the music outside of themselves. They are closed, independent systems, and they require

a transitionary chord to serve as a bridge between networks. This is true for triadic and

tetrachordal geometric networks. Douthett and Steinbach, for example, require a P1,0-related

augmented triad to pass from one set of major and minor chords related by major third, (Richard

Cohn’s “hexatonic cycle”) to another set that is transposed one semitone away from the former

set (to another “hexatonic system”). This creates a system of networks in harmonic relation, which

Douthett and Steinbach call a “Cube Dance.”106 The augmented chords are the only way to

traverse between hexatonic poles when the method of travel, i.e., the transformations, are

confined to P1,0-relations, as is the case in the Cube Dance. Among Octatowers, the bridging chord

is the fully-diminished seventh, and the network of networks is called “Power Towers.”

105 Douthett and Steinbach 1998, 245. “P” refers to “parsimonious,” The first subscript number represents a non-fixed tone that moves by half-step. The second number is a non-fixed tone that moves by a whole-tone. So seventh-chords are P1,0-related if three tones are held in common, and the one non-fixed tone moves by a semitone. 106 Douthett and Steinbach 1998, 254. The major and minor chords, when combined with augmented triads that are P1,0-related, fill in the eight vertices necessary to create a cube, hence the name “Cube Dance.” Richard Cohn also embraces the role of the augmented triad and fully-diminished seventh-chords as connecting bridges, illustrating them as “water bugs” and “Boretz Spiders” in Audacious Euphony, Cohn 2012, 33.

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In other words, the bridges are narrow when you only use one kind of material to build

them. The bridges get even more narrow when one is trying to travel between triads and seventh-

chords, because the two musical objects inhabit different kinds of conceptual space. Richard Bass

called this problem an “absence of lines-of-communication.”107 Since Bass’s claim, Julian Hook has

proposed some new “lines” in the form of what he calls “cross-type transformations,” which,

under certain conditions, can connect triads to tetrachords.108 A cross-type transformation is an

operation whereby a chord object is transformed from one type into another type.

In his 2009 article, “Cross-Type Transformations and the Path Consistency Condition,”

Hook applies cross-type relations not just to triads and seventh-chords, but also to related

intervallic organizations, melodic lines, and even thematic structures. However, the primary focus

is on the connection of triads and seventh-chords, for which Hook demonstrates two types. Hook’s

sample progression is reprinted here as Example 2.15. The first is the “inclusion transformation,”

which maps a triad onto a dominant or half-diminished seventh-chord that contains it (i.e., C-major

107 Bass 2001, 41 108 Hook 2007, 4

Example 2.15: Jay Hook’s Omnibus Progression

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to Am7). The other is called an “Lˈ” transformation. The Lˈ, named for its similarity to a

Leittonwechsel transformation, takes the fifth of a minor triad and splits it chromatically while

holding the other tones constant in order to create a dominant seventh-chord related by its

submediant (i.e., A-minor to F7). In effect, Hook systematizes Clifton Callender’s “split” and “fuse”

techniques as such: for any major or minor triad X, Lˈ (X) is the unique dominant or half-diminished

seventh-chord that contains all the notes of L(X) in it.109 Still, Hook’s cross-type transformations

can only be applied in the limited scope for which he offers them.

These Neo-Riemannian approaches treat triads and seventh-chords as each existing in

their own conceptual spaces, and that perceiving their differences is a matter of imagining moving

between those spaces (and networks of spaces) by recognizing a specified maneuvering of non-

fixed tones. That is what a Neo-Riemannian transformation is – a specified maneuvering of non-

fixed tones. In contrast, the Neo-Hauptmannian approach is not defined by the manner in which

a chord moves through an abstract space, but by how a listener interprets the meanings of tones

and how those meanings change across a span of time. While the addition or subtraction of tones

may change the interval-meanings of common tones, the mental process by which the listener

comes to understand those meanings is unchanged. In regard to the transitions between triads

and seventh-chords, the conceptual space of time, so to speak, remains the same. Time remains

unidirectional; there are no new dimensions added to the listener’s perception of it.

There does not need to be a Seventh-meaning tone in a former chord in order to interpret

a change of meaning into one in a latter chord. There is no Seventh-meaning in a C-major triad,

but when it passes to an A-minor seventh-chord, the tone G loses Fifth-meaning and gains

109 Callender 1998

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Seventh-meaning. Likewise, a chord succession does not need to preserve a Seventh-meaning

from one chord to the next. When an A-minor seventh-chord passes to an F-major triad, the

Seventh-meaning that was found in the tone G ceases to exist. Yet in both of these examples, a

logical connection can be found in the common tones. In the former, there is an RTF

transformation as the interval-meanings shift up. In the latter, there is an RT-transformation as

those interval-meanings shift up. Within the framework of common-tone transformations,

Seventh-meaning comes into and out of the listener’s perception as needed for the interpretation

of chord progressions.

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By this point, I hope that I have made clear that Neo-Hauptmannian transformations define

interpretive actions that are taken by the perceiver over a given period of time, rather than

operations that are applied to chords within an area of conceptualized harmonic space. The

interpretive action is the reinterpretation of interval-meanings for common tones and the period

of time is measured from the beginning of one harmonic entity (chord) to the beginning of

another. Neo-Hauptmannian transformations deal with the time of harmonic progression, not the

space of it. Let’s review this briefly with the following formula the describes the perceptual action

of an RT-transformation:

In C-major triad, I perceivee tone C{tc} [=C̅{tc}[Root, …], tone E{tc} [=E̅{tc}[Third, …],

In A-minor triad, I perceivee tone C{ta} [≠C̅{tc}[Third, …], tone E{ta} [≠E̅{tc} [Fifth, …].

At the time of the C-major triad {tc}, the tone C has Root-meaning and the tone E has Third-

meaning. At the time of the A-minor triad {ta}, {tc} has become past, including the perceptions of

tones C and E as having the phenomenological qualities of Root and Third. In the now-point of

time {ta}, the tones C and E exist as different phenomenological objects, different perceptions.

Though they are the same acoustical objects, the tones C and E at {ta} are different mental objects

from tones C and E at {tc} in that they have the phenomenological qualities of Third and Fifth-

meaning instead of Root and Third-meaning. An RT-transformation is the action of perceiving that

difference from {tc} to {ta}. That action is possible because the interval-meanings at {tc} are retained

in the memory of the perceiver and the perceiver relates them to what they are listening to in the

present {ta}.

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CHAPTER III

THE PROCESS OF HARMONIC SUCCESSION

Objects of Perceptions

As I noted in Chapter One, David Lewin explored this method of relating different

perceptions of the same musical objects in his 1986 article, “Music Theory, Phenomenology, and

Modes of Perception.” Using his perception model (p = (EV, CXT, P-R-List, ST-List), Lewin examines

the same few chords (mm. 9 – 15 of Schubert’s “Morgengruß”) in multiple contexts as distinct

phenomenological objects that relate to each other in ways that affect the interpretation of the

music as it advances through time. At different moments (p1, p2, p3, etc.) the music is being

recontextualized and informed by the perceptions of the past. The primary difference between

his phenomenological analysis and my own is the perceptual level to which the model is applied.

Where Lewin uses it to explain perceptual relationships between chords within the context of

tonality, I am using it to explain perceptual relationships between common tones within the

context of chords.

By comparing perceptions as distinct phenomenological events, Lewin is able to identify

how the objects of those perceptions, i.e., the chords, interact with the events of the past as

continuations, reinforcements, realizations, denials, etc. He can also identify ways in which those

chords imply future events. Just as the present harmony is informed by the one of the past, so too

does the present harmony generate an expectation for another one in the future. I argue that this

is true not only within the tonal framework in which Lewin operates, but also at the level of

common-tone transformations operating independently from tonal function. One of the primary

goals of this project is to explore how the process of harmonic succession can itself generate

expectations for future harmonies from the bottom-up.

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There are two bottom-up models of phenomenological analysis that serve as a foundation

for studying the process of harmonic transformation, which I reviewed in Chapter One. The first is

Eugene Narmour’s Implication-Realization model, shown in Example 3.1. The “basic theoretical

constants” for this model are, essentially, that A+A implies A, meaning that “sameness or similarity

causes the subconscious expectation of more sameness or similarity,” and that A+B implies C,

meanings that “differentiation causes the expectation of further differentiation.”110 Narmour uses

this model to evaluate melodic motions. For example, two stepwise ascending motions implies

another stepwise ascending motion because there is a sameness that can be found between the

two melodic elements (ascension). Likewise, if there is an ascending motion followed by a

descending motion, it implies a future ascending motion because there is a difference causing an

expectation of further difference.

The second model is Christopher Hasty’s Projection Theory, which constructs a Hegelian

dialectic between two successive rhythmic events, shown in Example 3.2. When Hasty compares

two purely rhythmic successive events, what separates them is the perception of beginning for

the latter event. That perception of a second beginning (Rhythm B) creates a measurable duration

– the period from the beginning of the first event to the beginning of the second (lower-case a).

110 Narmour 1992, 1

Example 3.1: Narmour Implication-Realization Model

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That duration in turn generates the expectation of a second event of equal duration that lies

outside of it. The expectation of a second event of equal value is the “projective potential,”

indicated by the dotted line. As is the case in Narmour’s theory, it is the existence of the second

event, its perceived opposition to the first event, and the perception of a synthesizing action that

generates the expectation for a potential realization of a third.111 In Narmour’s melodic theory,

the synthesizing action is the perception of melodic motion ascending or descending. In Hasty’s

rhythmic theory, it is the perception of duration enduring.

When one is comparing two purely melodic or rhythmic successive events, what separates

them is the perception of beginning for the latter event. There is the beginning of note A and the

beginning of note B, or the beginning of the first beat to the beginning of the second beat. But in

conventional harmonic analysis, common-tones are not necessarily recognized as having a second

beginning from one chord to the next. In analysis, the language of harmonic motion generally

directs our attention to the melodic event by which one or more acoustical objects (tones) replace

others. “The fifth of this C-major chord, G, moves up to sixth of the C-major scale, A, to create an

A-minor chord.” Such is the basis for typical transformational and functional models. The activity

111 Hasty 1997, 85

Example 3.2: Hasty’s Metrical Dialectic

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is found in the melodic motion of G to A. But when we focus our attention on the replacing (or

“movement”) of one acoustical object to another, we deemphasize the mental process involved

in reevaluating the meaning of the tones held in common that the movement triggers. There is

not a recognition of the fact that the common tones exist as separate phenomenological objects

from one chord to the next. The common tones are viewed as static, rather than

phenomenologically dynamic.

In the passing of a G-major triad to an E-minor triad, one of the parts move melodically

while the other two remain, changing the interval-meanings of their tones. The mental process for

this interval-meaning transformation, the RT-transformation, might be articulated as follows; I

understand this simultaneity of tones, G, B, and D, to, in the context of each other, signify Root,

Third, and Fifth, respectively. These meanings allow me to understand a context of a G-major triad

in the greater context of a G-major key. Now this tone D has ceased to be and is replaced by that

tone E. What results from this action is thus; The tone G, which had previously signified to me the

meaning Root in the context of a G-major triad, following the movement of this tone D to that

tone E, has ceased to signify Root and now signifies Third. Likewise, the tone B has ceased to signify

Third and now signifies Fifth. The new tone, E, signifies Root meaning. This new triad, E-minor, fits

into the greater context of the G-major key as being a sixth way from tonic. This kind of

articulation, while admittedly verbose, more accurately and completely describes the complex

mental processes and perceptual structures that are involved in relating the two harmonic objects.

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When one recognizes the common tones between two chords as distinct

phenomenological objects, they can examine them dialectically in the same way that Hasty does

for rhythmic objects. Consider Example 3.3. When the second beginning occurs (the E-minor

chord), it creates a measurable unit in which a phenomenological activity connects the latter E-

minor chord to the former G-major chord. The activity is that of the interval-meanings “becoming”

via RT-transformation. Like a unit of duration does in Hasty’s projection theory, the intervals

becoming create the expectation of a third event generated from the same kind of activity

(another RT-transformation) that lies outside of it. In the same way that two rhythmic beginnings

generate the expectation of a third of equal measure, two harmonic beginnings generate the

expectation of a third that it is achieved through the same means. To use Hasty’s terminology,

there is a “projective potential” that is generated by the motion from the G-major chord to E-

minor chord for a future C-major chord.

This kind of repetition also conforms to the Gestalt “Law of Good Continuation,” which

states that a shape or pattern will, all things being equal, tend to be continued in its initial mode

Example 3.3: Neo-Hauptmannian Harmonic Dialectic

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of operation.112 In a diatonic framework, the activity yields the same effect as a descending-third

harmonic sequence in a given key. But the notion of key is overlaid on top of pre-existing, self-

generated harmonic expectations created through the interval-meaning dialectic between the

first two chords. “Key” is a higher-level perception that is dialectically derived from the first chord

and the chords built on its upper and lower fifths.113 Within the context of a key, RT-

transformations can continue and appear significant and meaningful in the sense that they can be

understood as motion toward a goal – the goal being a return to tonic which, barring any

disturbances, would be reached after seven iterations. But at the chord-to-chord level of

perception, the self-generated expectations of continuing the pattern will go on until interrupted

by some change in harmonic process.

In the previous example, I established that the dialectic of two chords, mediated through

the common-tone transformational process (the process of becoming new interval-meanings)

generates the expectation of a second transformational process of the same type. The

phenomenon is repeated in Example 3.4a. From a C-major chord, an A-minor chord “actualizes”

an RT-transformation, meaning that the RT process has been completed and exists in fully the

past, phenomenologically speaking. The actualization of the RT-transformation in turn generates

a projective potential for another RT, which is then “realized” or “confirmed” if/when the F-major

chord sounds. When the F-major chord does sound, it creates another phenomenologically

distinct object from which a new dialectic can be made. From the A-minor chord to the F-major

112 Meyer 1956, 92 113 Hauptmann 1853, 8

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Perceptual Hierarchies

chord, the transformational process generates an expectation for the following D-minor chord in

the same way that the C-major and A-minor chords generate the expectation for the F-major. But

one can also examine the dialectical relationship between the first and third chords. One finds that

the F-major chord actualizes an R5-transformation that occurs at this separate level of perception.

At this new level of perception, the R5 projects a repetition of its own transformational type across

two harmonic events, which would be realized in the event of a B° chord.

Example 3.4a: Hierarchies of Expectations

Example 3.4b: Perception List p Event Context Perception-Relation List Statement List p1 C C-triad - Ex. 3.5a p2 Am C – Am, p1, RT-transformation, p3 expectation Ex. 3.5b p3a F Am – F p2 realization, RT-transformation, p4a

expectation Ex. 3.5c

p3b F C – F p1, R5-transformation, p5b expectation Ex. 3.5d p4a Dm F – Dm p3a realization, RT-transformation, p5a

expectation Ex. 3.5e

p4b Dm C – Dm p1, A-transformation, Em expectation Ex. 3.5f p4c Dm Am – Dm Am, R5-transformation, Gm expectation Ex. 3.5g p5a B° Dm – B° p4a realization, G expectation Ex. 3.5h p5b B° F – B° p3b realization, R5-transformation, Em

expectation Ex. 3.5i

p5c B° Am – B° Am, A-transformation, C expectation Ex. 3.5j p5d B° C – B° p1, D-transformation, Am expectation Ex. 3.5k

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With each new harmony, there is another distinct phenomenological object from which an

analyst can draw additional interpretive material. In other words, there is a new time-context in

which one could study the implications of a particular musical perception. This is, of course, exactly

what David Lewin does in his Morgengruß analysis. In Example 3.4b, I show a list of distinct

Example 3.5: Perception Statement List

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phenomenological objects, using Lewin’s perception model, to study how the harmonic processes

generate expectations across multiple levels of perception, independent of any metrical or

functional considerations. Selected statements are supported by the illustrations provided in

Example 3.5.

The first perception, p1, is of the first harmonic event, the C-major chord, in its own context

(ex. 3.5a). The cell in the Perception-Relation List column for this row does not indicate a

perception of any transformational type, because at this point in the perceptual experience there

is no other event to which the C-major chord is relating. As Lewin states, “this inferentially asserts

that it is not crucial to hear p1 in relation to other perceptions hereabouts, in order to perceive

‘what we are hearing when we hear measure 12 in its own context.’”114 We need not hear another

chord to perceive the C-major chord as such. At p2, one hears the A-minor event in the context of

the C-major triad (p1). In this context, one perceives that the A-minor triad appears after the C-

major triad through the process of an RT-transformation (Ex. 3.5b). As I noted above, this

generates an expectation for another RT-transformation to F-major. On the arrival of that third

event, F-major, two perceptual levels are observable. I have already discussed these two levels,

represented here as p3a and p3b. p3a is the original chord-to-chord level (Ex. 3.5c), which realizes

the first RT projection and itself projects an expectation for another RT to D-minor. p3b is the next-

level perception (Ex. 3.5d) that realizes an R5-transformation and itself projects another R5 further

into the future, beyond the most immediately anticipated chord to a B° triad.

Unlike the chord that preceded it, the F-major chord actualizes two harmonic processes

simultaneously, the RT at p3a and the R5 at p3b. This dual role gives the F-major chord additional

114 Lewin 1986, 96

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phenomenological weight relative to the A-minor chord. Essentially, it feels more meaningful

because it actualizes more phenomenological processes. The additional phenomenological weight

strengthens the projective capability of the chord, meaning that the perceiver is not as willing to

conclude that the projection is denied if the resolution isn’t immediately heard. So long as the

other level of expectation is not denied, there is at least one greater degree of what Heinrich

Schenker called “long-distance hearing” (Fernhören), the ability to hear musical connections

beyond the most immediate chord-to-chord or note-to-note level. The added phenomenological

weight and strengthened projective capability introduces a greater than/less than relationship

between the perceivable harmonic events. At p3, the A-minor triad actualizes fewer harmonic

processes than the F-major triad, and is therefore less meaningful in retrospect,

phenomenologically speaking. Therefore, its role in the context of the F-major chord is a passing

one, bridging the gap between the chords of the greater dialectic between C-major and F-major.

With the fourth harmonic event, the D-minor chord, three different levels of perception

can occur. At the most surface level, p4a realizes the expectation of an RT-transformation the was

projected by the F-major chord that preceded it (Ex. 3.5e). As with the other perceptions at this

level, the completed RT-transformation projects another one toward the future. p4b puts the D-

minor chord in the context of the C-major chord that began the passage (Ex. 3.5f). In this context,

there are no common tones, so the process by which the former chord becomes the latter is

through three melodic ascents, what I have called an A-transformation. In this example, the D-

minor chord plays actualizes transformations at three different phenomenological levels, granting

it greater perceptual weight than the A-minor and F-major chords. This allows for an even greater

degree of long-distance hearing (an even further extended projective capability), and it relegates

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the previous chords once again to a passing function relative to it. And finally, at p4c the D-minor

chord actualizes an R5-transformation from the A-minor triad (Ex. 3.5g). In this perception, the A-

minor triad is taken to be the “true” starting chord of the sequence and the C-major chord

preceding it to be a lower-level perception, like a pick-up chord. However, in the context of this

progression such as perception would most likely be understood in retrospect, after some event

that would lead the listener to reevaluate the A-minor triad as the “true” beginning, such as a

cadence in A-minor. I will discuss this phenomenon in greater detail in the next section.

At p5 the context of a B° triad creates yet another level of perception. It is a realization of

the RT-transformation from p4a at the lowest level (Ex. 3.5h), the realization of the R5 from p3b (Ex.

3.5i), an A-transformation from the A-minor triad (Ex. 3.5j), and a D-transformation from the

original perception, p1 (Ex. 3.5k). Each level of perception reinforces the levels above it, granting

the most recent chord the greatest phenomenological weight. Further, by actualizing the R5

expectation that was generated at p3b, the B° triad also has the effect of phenomenologically

elevating the F-major chord that projected it above the A-minor and D-minor triads. Here the F-

major chord is confirmed at two levels of perception simultaneously, at the RT lower level and the

R5 mid-level. While still a passing-chord in the context of the transformation from the C-major

chord to the B° chord, this double confirmation gives the F-major chord a greater

phenomenological weight relative to the other passing chords.

As we can see, the longer a chain of transformations continues, the further into the future

one could expect a particular outcome. However, if there is a change in harmonic process, then

the entire expectational structure crumbles as the listener’s attention is immediately drawn to

what is new and different. In the next section, I will detail exactly what a change of harmonic

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process is in Neo-Hauptmannian theory, how musical expectations are affected by it, and how

changes in process interact with the perceptual hierarchies discussed above to create what one

would call a harmonic phrase.

Continuing a sequential process to its logical conclusion can create a satisfying musical

event. One notable example would be the descending-fifth sequence in mm. 18-21 in Mozart’s K.

545, shown in Example 3.6. The sequence repeats an R5-transformation of the chords until they

return to the original harmony, G-major, which has the perceptual effect of linking them all in the

greater context of a G-major key area. But the return to G-major does not in itself disrupt the

series of R5 transformations. Like the clicking of a metronome, the pulse does not stop, nor is it

expected to, simply because we can conceptually link the first and eighth pulses together in the

mind. The cycle is perceived to be complete only when the listener detects a change in harmonic

process, a place where the R5-transformations cease, as is the case when the A-minor chord arrives

in Measure 22. This would be the metaphorical disruption of the clicking hand on the metronome.

If one were expecting further repetition, as the Law of Good Continuation would suggest, then the

next chord would start the cycle over again by going to C-major. But instead, the G-major chord in

Measure 21 “resolves deceptively,” one would say, to A-minor. In other words, there is an A-

transformation rather than the expected R5. It is this denial of expectation that groups together

the series of R5 transformations as its own higher-level phenomenological object, that of a

complete descending-fifth cycle. This distinguishes mm. 18-21 from the musical phrases that

surround it.

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Changes in Harmonic Process and Subverting Expectations

Process continuation is the norm of musical progression, but of course, it is the deviation

and disturbances of those processes that make musical works unique and meaningful. Consider

the earlier sequence in K. 545 from mm. 5-8 shown in Example 3.7. Mozart begins, through

repetition, a descending-second harmonic sequence. Following Narmour’s Realization-Implication

model (A+A=A), one could imagine a scenario where Mozart continues this descending-second

motion for three more measures in order to return to the harmonic position in which is began,

perhaps with a major third this time to signify the modulation to G-major. This would confirm the

expectations created from the previous chords through to its logical conclusion in the same way

the latter sequence does. However, in this case the alternate scenario would disrupt the four-bar

metrical phrasing that was established in the first four bars of the music, and it may put the

additional flurry of sixteenth notes in danger of sounding monotonous. So instead, Mozart breaks

the descending-second sequence early by moving from A-minor to D-minor in m. 9.

Example 3.6: Mozart K. 545, mm. 18 – 21

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By jumping from A-minor to D-minor in mm. 8-9, Mozart changes the process by which

one harmony moves to the next, from descending-second motion to a descending-fifth motion.

This denies the harmonic expectation of a G-major chord that the pattern had established,

privileging a realization of the metrical expectation of a four-bar phrase instead. The disruption

reinitializes the pattern-making process of the harmonies at the most surface level. At mm. 8-9,

the new dialectic is between A-minor and D-minor, which is mediated through the R5-

Example 3.7a: Mozart K. 545, mm. 5 – 12 (original)

Example 3.7b: Mozart K. 545, hypothetical extension of mm. 5 – 12

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transformation. The R5 generates a new expectation, projecting forward another R5 to G-major,

which is confirmed at m. 11.

In Example 3.7 I focus on expectations that are generated through the harmonic process

and how it was specifically that process continuation that was disrupted. Leonard Meyer describes

two ways in which process continuation may be disrupted – temporal breaks where a process is

halted and then restarted, and changes in process where one manner of progression takes the

place of another, or a “process reversal.”115 The first of these is more relevant in rhythmic and

melodic considerations. This would be akin to a physical disruption of the clicking hand on a

metronome. But the second is directly related to the meaning-transformations I have discussed.

Meyer views process reversal from a melodic perspective, considering the breakaway from a

sequence to be a “major change in process,” like the m. 11 arrival of the G-major chord in the

Mozart example.116 However, he also considers changes in types of sequences to be “slight”

reversals, each having their own “point of tension.” 117 What Meyer calls changes in types of

sequence, I call changes in the harmonic process, and their effects can be more than slight. In the

case of the Mozart example, it solidifies the four-bar phrase and generates the expectation for the

dominant G-major chord.

As I describe in the previous section, Neo-Hauptmannian theory establishes a dialectic

between two harmonies, which is then mediated through the phenomenological activity of

interval-meaning transformations. The time of that activity, once it is completed and existing fully

in the past, then generates an expectation, or “projects,” a repetition of it for a future event.

115 Meyer 1956, 93 116 Meyer 1956, 93 117 Meyer 1956, 93

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Harmonic process in this way then follows the Law of Good Continuation, as one transformational

type begets another, and then another, continuing until there is a change of process. In this sense,

a change in process is analogous to what Hasty calls a “denial of projective potential.” In the same

way that a rhythmic event that comes too early or too late denies the projective potential of the

rhythmic event that came before it, a harmonic event that comes about through a

transformational process that was not the one that was projected from the previous harmonic

event is a denial of what was expected.

Example 3.8a illustrates a denial of a harmonic expectation. The passage begins with an

RT-transformation from C-major to A-minor. When the second chord begins, the first RT-

transformation is actualized, meaning the Root and Third have completed their transformations

and have fully become Third and Fifth. The actualization of a completed transformational event is

indicated by an arrow pointing to the succeeding chord. The actualized RT generates a projective

potential for another transformation of the same type. The expectation is for another RT-

transformation, which would be actualized in the sounding of an F-major triad. That projective

potential is indicated by the dotted line. But when the third chord begins, the listener finds that

the expected RT-transformation did not come to fruition. The red (RT) and (F) in the example

Example 3.8a: Denial of Harmonic Expectation

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indicate that the projective potential of the actualized RT was denied. Instead, the D-minor chord

actualized an R5-transformation in its place. The difference in harmonic process draws attention

to this point in the music, “marking” it in our perception, in Robert Hatten’s sense of the word.118

In this example, the D-minor chord is marked in other ways as well: as the beginning of a second

pair of chords of equal duration, the D-minor chord is marked metrically, and apart from the

dialectic relationships between the harmonic events, function theory would deem the D-minor

triad marked as a predominant-functioning chord. But what Example 3.8a shows is that a form of

markedness can be determined independently of these, through the harmonic process alone.

When the D-minor chord begins and the R5-transformation is actualized, it creates a new dialectic

between the A-minor chord and the D-minor one. This new dialectic, mediated by the R5,

generates a new projective potential – the potential for another R5. This time, the expectation for

a continuation of the harmonic process is confirmed at the beginning of the fourth chord, the G-

major. The expectation is confirmed because the projective potential of the R5 is realized, unlike

the projective potential of the previous RT, which was not realized.

The analysis of this perceptual level shows how the D-minor triad in Example 3.8a becomes

a marked moment in the harmonic progression through the observation of a change in harmonic

process. But it also suggests that the G-major and C-major chords that follow are relatively less

marked, since they realize the expectations that the R5 process generates. Such a suggestion would

not be accurate. To explain this, we must reconsider the idea of perceptual hierarchies, which we

can do using the table provided in Example 3.8b and the graphics supporting the Statement List in

Example 3.9.

118 Hatten 1997

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Example 3.8b: Perception List

p Event Context Perception-Relation List Statement List p1 C C - Ex. 3.9a p2 Am C – Am, p1 RT-transformation, expectation of F Ex. 3.9b p3a Dm Am – Dm p2 denial, R5-transformation, expectation of p4 Ex. 3.9c

p3b Dm C – Dm p1, A-transformation, expectation of Em Ex. 3.9d p4a G Dm – G p3a confirmation, expectation of p5 Ex. 3.9e p4b G Am – G p2, D-transformation, expectation of F Ex. 3.9f

p4c G C – G p1, FR-transformation, expectation of Dm Ex. 3.9g p5a C G – C p4a confirmation, expectation of F Ex. 3.9h p5b C Dm – C p3 D-transformation, expectation of B° Ex. 3.9i p5c C Am – C p2 TF-transformation, expectation of Em Ex. 3.9j

p5d C C – C p1 confirmation of C-major Key, p3b denial Ex. 3.9k

As is the case with any established “beginning” of a harmonic progression, the initial chord

is the first perception, p1, and it exists only in the context of itself, as shown in Ex. 3.9a. At p2, the

listener hears the completion of an RT-transformation, which projects forward another RT that

would be realized in the event of an F-major chord. This is illustrated in Ex. 3.9b. At p3a, the arrival

on a D-minor chord denies the expectation projected by p2, and instead realizes an R5-

transformation. Once more, the denied projection is indicated with a red dotted-line in Ex. 3.9c.

This denied expectation marks the D-minor chord as the first moment of a change in harmonic

process, and a moment where a new kind of process can be expected at this chord-to-chord level

of perception. Ex. 3.9d shows perception p3b, which places the D-minor chord into a dialectic with

the first chord, C-major. This perceptual level realizes an A-transformation, which in turn projects

another A-transformation that would be realized in the event of an E-minor chord.

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Example 3.9: Perception Statement List

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Before continuing, it is worth noting here that in perceiving this A-transformation between

the C-major starting chord and the D-minor chord (Ex. 3.9d), one relegates the A-minor in between

them to a passing function, much as we observed in the previous section on perceptual hierarchies

(refer to Examples 3.4 and 3.5). But unlike in those examples, the A-minor chord in Example 3.8 is

heard as a passing chord despite the fact that the projection it makes at the chord-to-chord level,

namely an RT-transformation to F-major, is never realized (Ex. 3.9c). This shows that it is not

necessary to hear a confirmation of one process at a lower level in order to hear the completion

of another process at a higher level. If anything, the change of harmonic process that one

understands upon the arrival of the D-minor chord emphasizes the transitory nature of the lower-

level A-minor chord. In short, the middle chord simply becomes part of the process of getting to

the latter chord. This allows the listener to build the lower-level harmonic transformation into

their projection for the higher-level transformation. In this case, that would mean expecting to

hear a passing B° chord along the way to an expected E-minor chord. Even though a B° chord

would technically be another change in harmonic process, it wouldn’t disrupt the higher-level A-

transformation projection because that higher-level projection accounts for that particular passing

chord as part of its own process.

At this point in the musical experience of Example 3.8a (which as a reminder is only three

chords into it) there has only been one opportunity to confirm a harmonic expectation. That

opportunity was denied when the D-minor chord was heard instead the F-major chord projected

by p2. It was not until the G-major chord arrives that an expectation was finally confirmed. That

expectation is at the level of p4a, where the R5-transformation projected by p3a was realized. Where

the D-minor chord is marked for not satisfying a projected expectation (F-major, via p2), the G-

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major chord is marked because it does satisfy that expectation. In short, this G-major chord is the

first time in the musical experience where the harmony is what it is supposed to be, and as such it

is marked in the listener’s perception.

The G-major also can be placed into the contexts of A-minor at p4b and C-major at p4c. From

the A-minor chord, a D-transformation was realized and projects the potential for an F-major

chord. From the C-major chord, an FR-transformation was realized and projects the potential for a

D-minor chord. As a matter of process, both of these potential outcomes are reasonable to expect.

However, neither are realized due to the fact that the progression concludes before they have

time to be realized. These denials of projective potentials do not come about as a result of a

change in harmonic process, but because of the other way that Meyer notes that a process can be

disrupted – through a temporal break where process is halted altogether. When nothing follows

the final C-major chord, there is a temporal break where the harmonic process is halted. This gives

a unique phenomenological quality to the final C-major that no other chord in the process has.

Namely, the quality of being the end – and being the end of a passage creates its own perceptual

markedness.

Being the final chord of the passage is not the only way in which the last C-major chord is

marked. In fact, the idea that the final C-major chord is only marked because there does not appear

to be something else that follows it does not adequately align with the experience of it. That idea

seems to lag behind the more immediately felt understanding that the final C-major chord is

significant at the time in which we experience it. There must be something else in hearing that

final chord that gives it such a unique sense of meaning. At the chord-to-chord level, p5a, we find

that the C-major chord confirms the expectation of another R5-transformation that was projected

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from p4a. The completion of that transformational process in turn generates another R5 at that

level but, as will be the case with p5b and p5c, those expectations will be denied due to the

aforementioned temporal break (the end of the passage), rather than a change in harmonic

process.

At p5d one can make two important observations. The first is that the C-major chord denies

the expectation of an E-minor chord that was projected by p3b. Interestingly, this is the first point

in the musical experience where there is a confirmation of a projected expectation at one level,

p4a, and simultaneously a denial of an expectation at another, p3b. This by itself gives this C-major

chord a unique perceptual marker, relative to the other chords. But perhaps more importantly,

there is the dialectic between the final C-major chord and the original one. This perceptual object

does not complete a harmonic transformation, obviously, but instead it both realizes and confirms

the higher-level conception of a C-major key area.119 The dialectic between the two C-major

chords in this example completes the duration of the entire musical experience, creating a fully-

realized phenomenological object; a complete experience. Through their dialectic, the final C-

major chord is understood to be “end” relative to the original C-major chord “beginning.” This

shows that the final C-major chord is not perceived to be the end of the passage merely because

the listener eventually realizes that the harmonic expectations that were created in the middle

never ended up happening, like a joke that trails off before getting to the punchline. It is through

the perceptual act of placing the final chord into the context of the beginning chord that a listener

can understand that the final C-major chord is the punchline, the end of the thought.

119 One might even go so far to say that it is a temporal realization of the “octave unity” that founds Hauptmann’s entire proto-Hegelian conception of the nature of harmony in a manner somewhat similar to Riemann’s Grosse Cadenz.

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Let us consider one more example of how the phenomenology of harmonic expectations

can determine the structure of a musical phrase independently from any melodic, rhythmic, or

stylistic information. See Example 3.10 above, which depicts another common iteration of the

basic harmonic phrase model: Tonic-Prolongation – Predominant – Dominant – Tonic. The first

chord, G-major, progresses to the second chord, D7, through an FR-transformation. At the chord-

to-chord level, that transformation projects forward another F5-transformation to A-minor.

However, when one hears that the third chord is in fact G-major, they can say that the expectation

for another F5-transformation was denied, and an R5-transformation was realized in its place. As

was the case in the previous example, placing the latter G-major chord in the context of the former

confirms the higher-level conception of a G-major key area. By completing the duration of that

segment of the musical experience, it creates a fully-realized phenomenological object which I

have labeled a G-major harmonic “object.”

Example 3.10: Completing Harmonic Units

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Returning to the chord-to-chord level, one finds that in realizing the R5-transformation, the

G-major chord projects forward yet another R5. Upon the arrival of the fourth chord, C-major, one

finds that this time their expectation was confirmed by another R5. The C-major chord marks

another unique moment in the experience of the progression, for that chord marks the first time

so far where one can observe that there was an expectation for a particular kind of transformation

and that expectation was confirmed. The C-chord chord marks the first harmonic realization that

is what is was supposed to be. A third iteration of the R5-transformation would produce an Fƒ°

chord, but this time the harmonic expectation is denied once more. The fifth chord, D7, realizes an

R7-transformation instead.

If one places the fifth chord, D7 into the context of the third chord, G-major, one finds that

it realizes an FR-transformation. At this point in the musical experience, the listener realizes

something, consciously or otherwise – they have heard this particular transformation between

these particular chords before. This is the same harmonic process that occurred between the first

and the second chords. This realization allows the listener to think back and recall what happened

the first time they heard that particular harmonic process between these particular chords. With

the visual aid of this example, we see that the chord-to-chord projection of another F5 was denied,

and instead an R5 took its place. With this knowledge, the listener can adjust their expectations

moving forward. Essentially, this is a sort of “fool me once, shame on you, fool me twice, shame

on me” type of scenario. Without the memory of the harmonic process that came before, a

listener must rely on the chord-to-chord level transformation to generate an expectation of the

next harmony. In this case it would be a replication of the R7-transformation which would lead to

Em7. But with the memory of what happened before, particularly in an example like this when the

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occurrence is so recent, the listener can avoid this erroneous expectational state and expect an

R5-transformation instead. When the sixth chord, G-major, confirms that correctly adjusted

expectation, the listener can delight in the fact that their musical memory has served them well.

The final chord also completes another G-major harmonic object between it and the middle G-

major as its own distinct phenomenological object, and by putting in the context of the original

chord, it completes the total musical experience of a G-major phrase.

With these examples, I have shown how an analyst can use Neo-Hauptmannian

transformations to study the phenomenology of harmonic progression. Through these

transformations, an analyst can consider a dialectical relationship between any two chords,

determine the process through which one becomes the other, and study how that process

completes a distinct phenomenological object that generates expectations for future chords. This

gives the analyst the tools to explain how musical expectations are created, confirmed, or

subverted though purely harmonic means. They can then use this phenomenological evidence to

complement and strengthen their analytical interpretations. In the final chapter, I will

demonstrate this by providing analyses of three musical selections, using Neo-Hauptmannian

theory to support my conclusions.

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Example 4.1: “Thus Saith The Lord”, mm. 1 – 14

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CHAPTER IV

ANALYTICAL APPLICATIONS

G.F. Handel, "Thus Saith The Lord" from Messiah

Example 4.2: “Thus Saith the Lord,” mm. 1 – 14, Statement List

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Through the precise analysis of the phenomenology behind the harmonic progression that

Neo-Hauptmannian theory offers, an analyst is able to isolate important perceptual distinctions

between what might otherwise be dismissed as a relatively unremarkable series of chords. The

opening measures of Handel’s “Thus Saith the Lord” from Messiah, for example, demonstrate how

a seemingly straightforward harmonic progression can create a sense of surprise and change as

the listener moves through the musical experience. The score, annotated with marked perceptual

moments, is provided in Example 4.1 and further analysis is supplemented with the graphs

provided in Example 4.2.

The piece begins with a strong assertion of D-minor in the first measure by the orchestra,

followed by an arpeggiation of the D-minor triad in the opening statement by the baritone, “Thus

saith the Lord,” in the following measure. This single triad in its own context establishes a context

of tonality and a D-minor key within that context, as shown in Example 4.2a. It is the first

perceptual object of the work, p1. The next perceivable harmonic moment, p2, occurs on the

downbeat of m. 5, aligning with the conclusion of the second statement, “Yet once a little while.”

Here, the harmony shifts from D-minor to C-major through the process of a Decent-transformation

(D). Through this initial dialectic, the music offers enough perceptual data points to generate an

expectational state for the listener. If the proper context for this piece is in fact a D-minor key

within a framework of tonality, and the harmonic process is repeated via another D-

transformation, then the chord at p3 will be a Bß-major chord. This is shown in Example 4.2b. If one

were to assign a functional analysis to the progression, it would be i – VII – (VI).

However, at p3 the listener’s expectation is “shaken” out when the music settles on F-

major, rather than the expected Bß-major. In Example 4.2c, one can see that the F-major chord

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denies the expected Bß-major that was generated by p2, and, when put into a dialectic with the C-

major chord, reveals that an R5-transformation has occurred instead. This is the first instance in

the music where the harmonic progression creates a small musical surprise through a change in

process. With this third perceptual moment, the listener can now make new observations at

different hierarchical levels. At the most surface level, they can expect a repetition of the R5-

transformation as the process by which they come to the next perceptual moment, p4. This would

result in a Bß-major chord, as shown in Example 4.2d. Alternatively, they could reflect on the

dialectic between the F-major chord and the beginning D-minor chord, and they may come to the

conclusion that the TF-transformation between them should be the privileged perception, with

the C-major chord being a relative passing chord. A repetition of that larger phenomenological

object would result in a progression to an E° followed by A-major. Already, at only three chords

into the piece, the listener is presented with their first interpretive crossroad – Do they focus on

the initial chord-to-chord R5 transformational process as a tool for generating further

expectations, or do they privilege the longer-range TF process has having greater

phenomenological weight, and therefore as being a more accurate tool? In other words, should

they expect a i – VII – III – (VI) progression, or a i – VII – III – (ii°) – (V) progression? Both are

plausible, given the phenomenological evidence at this point in the piece.

The next phenomenological moment, p4, happens when the music arrives on the Bß-major

chord in m. 8, on the word “earth.” Of the two possible expectational states that were suggested

by the previous chord, it was the more surface-level expectation of another R5-transformation,

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the latter former option in Example 4.2d, that ended up being correct.120 To reinforce success and

to follow the Gestalt Law of Good Continuation, one could expect a third R5-transformation to

follow, which would take the music to an E° chord, perhaps with a greater degree of confidence

than the music had allowed previously. Additionally, the Bß-chord effects a delayed realization of

the original D-transformation that was projected by the first two chords. In that context, one can

conclude that the previous F-major chord was, in retrospect, a hierarchically lower-level dominant

inserted in between the higher-level voice-leading from D-minor, to C-major, to Bß-major (i – VII –

VI). If this is the case, then the listener could expect another D-transformation, passing through

the E° chord that is already expected at the chord-to-chord level transformational process, that

would lead to a dominant A-major chord. Both of these expectations are represented in Example

4.2e.

But alas, the listener’s expectations are thwarted once more, this time on both fronts. At

p5, the actual event is a G-major chord. There is another change in process at the surface level;

this time the harmony progressed via a T5 transformational process instead of the expected R5.

This creates the next significant moment of surprise in the music. It also introduces a chord that is

foreign to the D-minor context that was established at the beginning of the piece. This begets a

crucial question about the musical experience thus far: Is this piece, in fact, in D-minor? It was

assumed to be so, since it was the beginning chord, and up until this point there was no conflicting

harmonic evidence to suggest otherwise. One could argue that the piece appears to be modulating

or tonicizing another key, but upon further reflection, there was never any harmonic confirmation

120 I find it poetically interesting to note that the confirmation of what I would call the more “surface-level” expectations coincides with the word “earth,” which is of course a more “surface-level” concept than the word it is juxtaposed with, “Heavens.” But I will try not to read too much into that for now.

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of the D-minor chord before this foreign chord was introduced. There was never any cadential

moment in D-minor that would create a complete D-minor phenomenological object. Therefore,

I would not call this harmonic progression an example of a modulating phrase, but rather as an

example of an auxiliary cadence. Though the music began on a D-minor chord, there is now

enough phenomenological evidence to suggest that it was not the true tonic of the piece. Or at

least, that appears to be the case at this point in the musical experience.

With a narrow focus on the harmonic process, one could observe an expectational state

that is generated for the next harmony based on the dialectic between the G-major and any of the

previous chords in the piece, as I have shown here and in the previous chapter. At the chord-to-

chord level, the Bß – G transformation (T5) could generate an expectation of an E-major or minor

chord. From the F-major chord, an A-transformation to an A-minor chord, and so forth. But here,

the stylistic convention of the time and context of the work needs to be considered. Just as Eugene

Narmour allows for top-down schemata to override his Implication-Realization melodic theory

when there is enough contextual information to support it, so too should we accommodate

stylistic conventions. When the tone Bß moves chromatically up to B∂, the established melodic

conventions dictate that the note be treated as a leading-tone, which should resolve up to the

apparent tonic, which is C-major in this case.121 Therefore, the stylistically adjusted expectation

for the next harmonic process should be an R5 to C-major, and shown in Example 4.2f.

At the C-major event of p6, the listener gets confirmation that the stylistically adjusted

expectation was indeed warranted. This is also the first moment in the musical experience so far

where there is a return to a previously-sounded harmony. One can phenomenologically link the

121 One could also view this as a fulfillment of Narmour’s bottom-up rule of melodic progression, A+A=A.

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two C-major chords and consider them a completed C-major harmonic object. This could be the

true tonic of the music, since there is a return to that C-major chord, and it is conventionally

supported by an authentic cadence. However, after reflecting upon the functional implications of

that conclusion, one finds that it may not be very likely. If C-major is the tonic, then that means

that the harmonic progression is ii – I6 – IV – ßVII – V – I, which would be rather unusual for music

of this time, even for an auxiliary cadence. Given the stylistic context of the piece, I find the

dialectic between the latter C-major chord and the initial moment of surprise, the F-major chord

at p3, to be a more convincing reading. Consider Example 4.2g. If F-major is the relative “beginning”

chord, then the functional chord progression would be a much more stylistically appropriate vi –

V6 – I – IV – V/V – V. Additionally, if true it would coincide with the expectation of another R5 that

is already phenomenologically generated by the chord-to-chord level transformational process (G

– C – F). So, with the knowledge of the stylistic conventions, the listener can determine which

transformational process has the greatest chance for an accurate state of expectation among the

perceptual possibilities. The R5-transformation is the best option in this case – there is both a

conventional top-down argument for it and a bottom-up phenomenological argument for it.

Finally, the next harmonic moment p7 comes at m. 10, where the stylistically and

phenomenologically expected F-major chord arrives. It is at this moment where the listener finally

hears what a Schenkerian would call a “structural” tonic.

As I noted at the start of this chapter, with this type of precise analysis of the

phenomenology behind the harmonic progression the analyst is able to isolate important

perceptual distinctions between what might otherwise be dismissed as a relatively unremarkable

series of chords. One particularly important distinction would be the one between the first F-major

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chord at m. 7 and the latter one at m. 10. At m. 7, the F-major chord is comfortably couched within

the context of the apparent tonic at the time, D-minor. Although the chord was not expected, in

that it denied the projection of a Bß-major chord that the D-transformation generated from the

first two chords, there was still no harmonic evidence at that point to suggest that D-minor was

not actually the true tonic of the piece.

There is also phenomenological evidence to suggest that the F-major chord was actually a

lower-level dominant between a higher-level descending-second progression, as I noted earlier. It

was not until two chords later that there was even a hint that D-minor was not the real tonic. In

contrast, the F-major chord at m. 10 has both stylistic and phenomenological evidence to support

the idea that it can be and should be perceived as tonic. A “more final” reading of the passage,

one where the analyst constructs an interpretation equipped with the knowledge of how it ends,

might apply the label of “structural tonic” to the F-major at m. 7. It is, after all, implied by the half-

cadence on C-major in m. 9. But hearing the F-major at m. 7 as a structural tonic is something that

could only be done retrospectively, as indicated by the arrow in 4.2g pointing backward. To label

that first F-major chord as though it was heard as tonic would ignore much of the perceptual

complexities that occur during the experience of the music. It would therefore be a much stronger

and complete reading to deem the F-major at m. 10, the one for which there is conventional and

phenomenological evidence to expect and to hear as tonic before it even arrives, to be the actual

structural tonic.

The structural tonic in this example works like a reset button for the listener’s tonal

orientation. The piece begins in a way that makes the listener think the piece is going to be in D-

minor, but by the time they get to m. 10, there is stronger evidence to suggest that the piece is

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actually in F-major. However, that evidence is circumstantial. There has still not yet been a

complete experience of a decidedly F-major passage of music – there has only been the implication

of it in the form of a half-cadence. In other words, there has not yet been a complete F-major

phenomenological object that in fact begins as such. For the reasons I have discussed above, the

F-major chord in m. 7 is only understood to function as a tonic retrospectively. But the F-major at

m. 10 functions as tonic as soon as it comes into being. In my opinion, this is part of what makes

it sound structural. This aspect of structural identity is usually granted by default to the opening

harmony of a musical work, but as we see here, that does not always end up being accurate.

A structural tonic must be heard as the true “beginning” of a musical work to be deemed

structural, but it still needs to be phenomenologically confirmed as such. Otherwise it could lose

that status and be supplanted by another, as D-minor was replaced by F-major by the end of the

first phrase of this piece. But following the F-major at m. 10, the listener can use the

retrospectively understood F-major harmonic object to infer a longer-range expectation – that of

another F-major harmonic object which would confirm the F-major key. In the following measures,

as shown in Example 4.2h, that expectation comes to fruition. The music advances from F-major

through Bß, G, and then C chords on the word “shake” (the same word where F-major was originally

introduced) before cadencing on F-major at m. 14. The chord progression is exactly the same as

the progression that was just heard in mm. 3-6, with the small exception that the G-major chord

is adjusted to minor in order to fit into the context of an F-major key.122 The authentic cadence on

m. 14 (p8) completes the F-major phenomenological object that the structural F-major chord in m.

122 I would argue that the adjustment is conventionally appropriate and not different enough to disrupt the longer-term harmonic projection.

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10 began. Upon hearing that cadence, the listener has clear phenomenological confirmation that

the music is decidedly in the key of F-major.

In the previous section I laid out two criteria for what constitute a structural tonic. First,

the structural tonic needs to be heard as tonic at the time in which it is sounded. This criterium is

usually granted to the beginning harmony of a work, since classical convention demonstrates that

a piece generally begins with the tonic chord. But as I showed in “Thus Saith the Lord,” this does

not always end up being the case. That is why there is a need for the second criterium; a structural

tonic must be phenomenologically confirmed by a return to that chord. This creates a completes

a distinct phenomenological object that reinforces that assumed structure.

Peter Smith observes similar phenomena in this 1995 article, “Structural Tonic or Apparent

Tonic? Parametric Conflict, Temporal Perspective, and a Continuum of Articulative Possibilities.”

Smith pays special attention to the “temporal perspective from which analytical statements are

rendered,” employing David Lewin’s perception model to guide his analysis.123 With it, Smith is

able to demonstrate how the status of a tonic chord as “structural” can shift, depending on the

temporal context in which it is heard. In his first analytical example, the Minuet from Bach’s E-

Major French Suite, BWV 817, Smith argues that the perception of tonic that is given by the

unharmonized melody in the first measure (his p1) is reinforced by the harmonized tonic chord

that immediately follows it (his p2) , which grants the unharmonized material from the first

measure a “structural” status. But when that same material returns in m. 17 and is subsequently

not “confirmed” by a root-position tonic chord in m. 18, the structural status is retrospectively

123 Peter Smith, 1995, 251

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J.S. Bach, E-Major French Suite, BWV 817, Minuet

shifted from m. 1 to m. 2. The full score of the minuet with my own annotations marking harmonic

perceptions is provided in Example 4.3.

Smith criticizes a Schenkerian graph of this piece offered by Larry Laskowski, as well as

Schenkerian analysis generally, for frequently illustrating “more final” readings, which would

depict a retrospectively applied interpretation of the music, while omitting discussion of the “less

final” original perceptions. He writes, “For our purposes, what Laskowski’s graph offers is not the

ultimate ‘truth’ about the thematic return, but the disconfirmation of p1 that occurs at p2… My

point therefore is not to say that Laskowski’s graph is incorrect; the central issue is that p1 is an

important aspect of our listening experience, and should not be cast aside because it conflicts with

Example 4.3: Bach, Minuet, Full Score

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more final perceptions.”124 This is a criticism with which I largely agree, and it is these kind of

perceptual distinctions that my methodology hopes to capture and carefully detail. However, my

reading on the phenomenology of this piece is quite different than Smith’s.

Smith marks the unharmonized tonic material in m. 1 and the harmonized I – viiØ7 – I

material in m. 2 to be separate phenomenological moments, with the latter reinforcing the sense

of “structural” tonic in the former. I find this to be generally correct, but lacking in detail. I agree

with the conclusion that the unharmonized material in the first measure creates a sense of tonic,

although I will note that Smith relies entirely on a recognition of established common practice to

come to this conclusion rather than a phenomenological investigation of the melody itself, with

statements like “Tonal music, as we all know, usually begins with a statement of the tonic,” and

“Because of the overwhelming consistency of this practice, we tend to infer…”125 One could make

the phenomenological argument that the melodic material begins to suggest tonic-implying

harmonic information once the Gƒ – E dyad is established in the listener’s musical memory, citing

Edmund Husserl’s concept of a temporal “running-off,” but such a discussion is involved and I will

not take the time to explore it here.126 It will suffice here to say that the tonic harmony is heard

within the first measure.

124 Smith 1995, 253 125 Smith 1995, 249 126 Husserl’s “Running off” concept is the notion that each temporal moment, or “now-phase,” can be related in a succession of “now-phases” within an ever-expanding conscious whole, or “time-object.” Husserl 1966, 125. We have already explored this theory in the previous chapter in our efforts to place each succeeding harmony in a progression into a dialectic with each of the others that came before. Husserl applies this concept to melody in his writings, and it was recently explored in that context by Jessica Wiskus at the 2018 Society for Music Theory Convention in San Antonio.

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Example 4.4: Bach, Minuet, mm. 1 – 8, Perception List

p Event Context Perception-Relation List Statement List p1 E E, m. 1 – – p2 DƒØ7 E – DƒØ7, m. 2, b. 2 D-trans., expecting D/SR- trans. to Cƒ Ex. 4.5a

p3 E E – E, m.2, b.3 A-trans., p2 denial, complete E-object Ex. 4.5b p4 Dƒ° E – Dƒ°, m. 3 D-trans., expecting A-trans. to E –

p5 E E – E, m. 4, b. 1 A-trans., confirms p4, complete E-object – p6 Fƒ7 E – Fƒ7, m. 6, b. 1 R7, expecting R7 to Gƒ7 Ex. 4.5c

p7 B Fƒ7 – B, m. 7, b. 1 R5, p6 denial, expecting R5 to E Ex. 4.5d

p8a E B – E, m. 1 (repeat) R5, confirms p7, expecting D-trans. to dƒØ7 –

p8b E E – E, m. 1 (repeat) Completes E-object tonal object Ex. 4.5e

Example 4.5: Bach, Minuet, mm. 1 – 8, Statement List

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However, it is my view that the tonic harmonic moment (p1) extends until the second beat

of the second measure (p2), where the viiØ7 chord is introduced, as shown in the perception list

provided in Example 4.4. Harmonically speaking, there is no difference between m. 1 and the

downbeat of m. 2, and so it is not until the second beat of m. 2 that there is a harmonic “other”

with which one could enter into a dialectic. This is shown in Example 4.5a.The passage of E-major

chord into a Dį7 chord (with an omitted third) at p2 is the result of a Descent-transformation, and

so if one were to expect a repetition of that transformation, or rather, it’s seventh-chord

equivalent (SR), then the next chord would be a Cƒ-minor triad or seventh-chord. However, at p3

that expectation is denied as another E-major chord is heard. Instead, an Ascent-transformation

took its place, bringing the listener back to where they began. It is at this third beat of measure

two that a complete E-major harmonic object is created, as shown in Example 4.5b.

The melodic material in the third measure returns the listener to a Dį7 harmonic

perception for p4, in the same fashion that the first measure gives an E-major harmonic

perception. Here, the listener finds that the music progressed to the E-major chord to the Dį7

chord using the same process as before, a Descent-transformation. Now familiar with the context

of the first two measures, the listener can adjust their expectations and allow for the possibility of

an Ascent-transformation to follow, once again returning them to the E-major chord. At p5, that

expectation from p4 is confirmed, and there is a repetition of the E-major harmonic object. This

repetition reinforces the E-major tonic impression. Although a conventional authentic cadence

has yet to sound, the persistent return to E-major certainly privileges it as an accented harmony,

independent of any functional context. And within a functional context, there is no

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phenomenological evidence to suggest that E-major is not the tonic from the first moment one

hears it harmony in m. 1.

At p6 a new harmony is introduced with the Fƒ7 chord. From the E-major chord, the

transformation that brings it to Fƒ7 is an R7. Once more, one could expect a repetition of the same

transformational process, which would make the next chord a Gƒ7, as Example 4.5c illustrates. But

as Example 4.5d shows, one finds the expectation from p6 to be incorrect when the actual

transformation was an R5 to a B-major chord at p7. This R5-transformation in turn suggests another

R5 to E-major for the next harmonic moment, which is confirmed upon reaching p8a, the repeat of

m.1. The confirmation of that R5 expectation from p8 has the added perceptual effect of

completing yet another E-major harmonic object, this time at the eight-measure phrase level, p8b.

Each of the E-major harmonic objects at the two-measure, four-measure, and eight-measure

levels are illustrated in Example 4.5e. If there was ever any doubt that m. 1 was the definitive

structural beginning of the passage (and there was no phenomenological evidence to suggest that

there should be, harmonically speaking), it is clear at this point in the experience that it was the

true, structural beginning of the piece. Moreover, the manner in which the E-major harmony

returns, i.e., the same unharmonized material, allows the listener to recall the results of what

happened in the music they just heard and infer new expectations accordingly; They can expect a

Descent-transformation to Dį7, and then once that is confirmed, they can expect that the music

will return back to E-major via an Ascent-transformation, as so on. This is essentially what a musical

repeat is – an opportunity for the listener to experience a phenomenological confirmation for each

one of a series of expectational states. This can be a very intellectually satisfying experience. After

all, who doesn’t like being proven right over and over again?

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Example 4.6: Bach, Minuet, mm. 9 – 24, Perception List p Event Context Perception-Relation List St. List p9 AƒØ7 B – AƒØ7, m. 10, b. 2 D-trans., expecting A-trans to B Ex. 4.7a p10 B AƒØ7 – B, m. 10, b. 3 A-trans., confirms p10 (neighbor-chord) – p11 Cƒ B – Cƒ, m. 12 A-trans., expecting A-trans. to Dƒ or R5 to Fƒ Ex. 4.7b p12 B7 Cƒ – B7, m. 14 D-trans., p12 denial, expects R5 to E Ex. 4.7c p13 E B7 – E, m. 15 R-trans., confirms p13 – p14 B E – B, m. 16 FR, completes 8-bar B-object, expecting R5 to E Ex. 4.8a p15 E B – E, m. 17 R5, p15 confirmation, expects 8-bar object – p16 B E – B, m. 19 FR, expecting R5 to E – p17 E B7 – E, m. 21 R5, confirms p17, completes 4-bar E-object Ex. 4.8b p18 E E – E, m. 24 Confirms p16, completes 8 & 32-bar E-objects –

Example 4.7: Bach, Minuet, mm. 9 – 16, Statement List

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The perception list for the next set of harmonic perceptions is provided in Example 4.6,

and the selected statements are supported with the illustrations in Example 4.7. After the

conclusion of the repetition, the listener has phenomenological evidence to believe that an E-

major chord should come next in order to complete the musical thought. However, the harmonic

rhythm is disrupted at m. 9 as the B-major harmony persists longer than expected. It is not until

the second beat of m. 11 (p9) where there is finally a change in harmony, but the new harmony is

an Aį7 chord, not the E-major chord the listener could have expected a measure before. There

was an A-transformation instead of the expected R5, as shown in Example 4.7a. This Aį7 chord

moves quickly back to a B-major chord in the next beat (p10), completing a B-major harmonic

object through the same series of transformations that have been used since the beginning of the

piece to complete these two-measure objects, Descent → Ascent. Or to use more conventional

music theory terms, the AƒØ7 is a neighbor-chord. At p11, a new Cƒ-minor chord is introduced in m.

12. At this point, it is clear that the return to E-major, the expected R5-transformation from m. 8,

was a deception. The expectation was delayed and then denied as an A-transformation to Cƒ-minor

was realized instead, as indicated by the red dotted line shown in Example 4.7b. That Cƒ-minor was

then promptly confirmed with the completion of its own two-measure object via the neighbor-

chord.

From looking purely at the harmonic relationship between the B-major two-measure

object and the Cƒ-minor two-measure object from mm. 9 – 13, one finds that a larger A-

transformation has occurred. With this information, one could expect another A-transformation

to continue the rising second progression to Dƒ. Alternatively, one could recall that the last time in

this piece where there was an A-transformation that wasn’t part of the neighbor-chord figure, the

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following transformation was an R5 leading to the dominant, B-major. So if that pattern were to

repeat, then the next chord would be the local dominant of B, Fƒ. These options are shown in

Example 4.7b. Both seem plausible enough, perhaps with a preference to the latter option given

the tonal context. But either way, both expectations are denied when there is a return to B-major,

this time with an added chordal seventh, at m. 14 (p12). This return to a B chord provides two

particularly interesting pieces of new information beyond the most immediate level of denied

expectations, shown in Example 4.7c. First, it suggests a complete larger B-major object. But while

completing a B-object, the added chordal seventh creates a sense of instability within the tonal

context of the piece, giving it a “lesser than” status relative to the larger harmonic object of the E-

major triad. Second, this return to a B chord completes a larger-scale reversal of the neighbor

chord figure that has been present through the work. Where at the most surface level there has

been a repeating lower-neighbor chord figure (Descent → Ascent), here at this two-measure level

there is an upper neighbor chord figure (Ascent → Descent). This motivic reversal is illustrated in

Example 4.7d.

Since the entirely of the music from mm. 9 – 14 has revealed itself to be a large B-object,

one could think back to what happened earlier in the music where a B chord was heard when they

consider what to expect next; in every case, E-major chords have followed B-major chords via R5-

transformations. If this recalled knowledge of the recurring harmonic pattern were not enough,

there is ample conventional knowledge to push the listener to that expectation as well, such as

the concept that chordal-sevenths resolve downward, and when a dominant seventh-chord is in

third inversion, the following chord is typically a tonic chord in first-inversion. In this case both

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conventional and phenomenological evidence cause the listener to expect an R5-transformation

to E-major, and in m.15 (p13), that expectation is confirmed.

At m. 16 (p14) B-major returns, this time without the added chordal seventh, in an upbeat

hypermetrical position and in a more stable melodic position (root-position) than the one in m.

14. This B chord, rather than the one at m. 14, is a much stronger ending to the B-major harmonic

object that was begun in m. 9. It also points very strongly toward E-major for the next chord for

the same melodic and metrical reasons and for the same phenomenological reasons that the B

chord from m. 14 did – Every time there is a B chord (excluding the neighbor-chord figures), an E-

major chord follows. Doing so would conclude an eight-measure B-major harmonic object and

begin a new E-major object, as depicted in Example 4.8a At m. 17 (p15) , the listener gets that

confirmation.

Example 4.8: Bach, Minuet, Phrase-Level Harmonic Objects

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It is at this point in the analysis where I have the most significant disagreement with Smith.

Smith argues that while the E-major unharmonized material in m. 17 reinforces the perception of

the first measure as structural, it requires a “confirmation” of its harmony with a full, root-position

E-major chord in m. 18 in order for the listener to continue hearing the first measure as

structural.127 When the expected root-position E-major does not arrive in m. 18, Smith argues, it

denies the perception of the first measure as structural, retrospectively diminishing it to a lesser

“apparent tonic” role relative to the true structural tonic of m. 2. As I noted above, Smith criticizes

Laskowski’s Schenkerian graph for only showing the “apparent tonic” role of m. 17 and ignoring

all the time of the experience where it is perceived as structural. Smith’s point is that it is not

accurate to say that m. 1 never really was structural; it is better to recognize that at first it was

structural, but then after m. 18, it wasn’t.

My interpretation of the phenomenology for this piece is that m. 1 was perceived as

structural, and when m. 18 comes around, it is still perceived that way. In my view, the time of the

B-major harmony in m. 16 is strongly perceived to be completing a B-major harmonic object that

spans from mm. 8 – 16. When that object is complete, there is significant phenomenological

evidence to suggest that the next chord will be an E-major chord and it will begin a new E-major

object. At m. 17 that is exactly what happens. Essentially, I believe that the E-major at m. 17 is

confirming, rather than seeking confirmation. It marks the end of an eight-measure B-major object

as well as a larger sixteen-measure E-major object, what we can call at this point a tonic-object.

While it is true that the harmonized E-major in m. 18 in a weaker position relative to the one in m.

2 (second-inversion rather than root-position), it does not take away from hearing the harmony

127 Smith 1995, 249

123

as tonic, nor does it take away from the perception that, following another neighbor-chord figure,

it begins its own two-measure E-major harmonic object.128 In short, I draw a phenomenological

distinction between a I@ and a cadential V@, and this E-major in m. 18 is a I@; specifically, it is a I@

that continues an E-major harmonic perception that began in m. 17 and was likely perceived as I!.

It is not until m. 19 (p16) that the harmony moves back toward B-major, returning once

again with an added seventh. Upon hearing the B-major chord, the listener is again prompted to

expect a return to E-major, not only because of the conventional resolution of dominant seventh-

chords but also because they can recognize the well-established phenomenological pattern that

when a B-major or B7 chord is heard, an E-major chord should follow. This is once again confirmed

at m. 21 (p17) , creating a four-measure E-major harmonic object, just as in the beginning. Finally,

that FR → R5 pattern is repeated twice more, giving the listener another opportunity for a series of

satisfyingly confirmed expectations while completing another eight-measure E-major harmonic

object (p18).

The essential difference between my reading and Smith’s is that Smith stresses a

contrapuntal connection between the bass tone G in m. 16 and the bass tone G in m. 18, whereas

I stress the confirmation of the harmonic process that was expected in m. 16 and realized in m. 17

(R5). I also use the concept of distinct harmonic objects to highlight the boundaries between

harmonic phrases in the music. By observing how these harmonic objects are constructed, one

can see that the E-major at m. 17 is structural in that it begins a new phrase, just as the first

measure does. This is illustrated in Example 4.8b. The fact that the perception of E-major in m. 18

128 Technically, there are only G-major-third and A-minor-third dyads in m. 18. But for the same reasons that the unharmonized content conveys a perception of E-major, I believe that the perception of the tone E persists into m. 18, especially given its temporal context. Likewise, I think the Dį7 chord is implied for the neighbor-chord figure.

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is in a relatively weaker chord position than the E-major at m. 2 does not take away from the sense

of beginning that the perception of E-major in m. 17 had. I also do not believe that it diminishes

the sense of beginning that m. 1 had, a sense that has been so consistently supported by the

harmonic process.

One might argue that my reading puts the harmonic and contrapuntal evidence of the

music into irreconcilable conflict. A Schenkerian in particular might scoff at the idea of my

discounting the weak chord position of the tonic in m. 17. However, I believe the second repeat

significantly affects the experience of the music in a way that addresses this concern. When the

repeat returns the listener to m. 9, the B-major harmony is put into the context of the E-major

chord from the last measure, rather than the one from the first measure. That means when the

music ends, it completes another 16-measure E-major object. At first thought, that might seem

relatively inconsequential, but it actually rounds out the form of the piece very nicely. Without the

repeat, there are three complete harmonic objects for the tonic – an eight measure one, then a

sixteen-measure one, and then another eight-measure one. But with the repeat, the listener

experiences a more balanced 8 – 16 – 8 – 16 formal pattern. This is shown in Example 4.8c.

Notably, this recasts m. 17, the most contested measure between my reading and Smith’s,

as a midpoint of the repeat rather than the beginning of the closing eight measures. In this “more

final” reading, m. 17 is in fact not as much of a “beginning” as it was in every other context up to

this point. But this is not because the I@ in m. 18 “creates a retrospective connection” to the tone

B in the bass from m. 16, as Smith argues;129 it is because at this final time, there is a built-in

expectation of eight more measures of music to come. This might be the reason that Bach

129 Smith 1995, 252

125

introduces the apparent conflict between the contrapuntal elements of the music (“the absence

of an explicit bass” in m. 18)130 and the harmonic and metrical elements. While not effective

enough to disrupt the sense of beginning in m. 17 the first time around, it aids the perception of

a longer 16-measure formal section the second time around.

I will end this chapter with an analysis of “Erwartung,” Op. 2, No. 1, one of Schoenberg’s

earliest art songs, which was composed in 1899. It may seem like quite a leap to go from an excerpt

from an oratorio by Handel and a minuet by Bach to a Lied by Schoenberg. However, the latter

piece deals with many of the same perceptual concepts we have been exploring in the former two

– Where is the true “beginning” of the music, and what assumptions do we grant to the first chord?

Is the music modulating, or did the music begin with an auxiliary cadence, and what are the

phenomenological differences between the two? How are the listener’s harmonic expectations

confirmed or denied as the music progresses through time? Each of these questions come into

play in the analysis and interpretation of “Erwartung,” which appropriately enough, translates to

“Expectation.” Additionally, at this point in Schoenberg’s compositional career he is still very much

writing his music within the context of tonality, so there is still a common context (in the Lewinian

sense) among the pieces to which we can refer in order to frame the discussion. The full score

with annotations for the referenced harmonic perceptions is provided below in Example 4.9, a

translation is available in Example 4.10, and the perception list for the first phrase (mm. 1 – 5) is

provided in Example 4.11.

130 Smith 1995, 253

126

Arnold Schoenberg, "Erwartung" Op. 2 No. 1

Example 4.9: “Erwartung,” Op. 2, No. 1, Annotated Full Score

127

Example 4.9 (Continued): “Erwartung,” Op. 2, No. 1, Annotated Full Score

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Example 4.11: “Erwartung,” Op. 2, No. 1, mm. 1 – 5, Perception List

p Event Context Perception-Relation List St. List

p1 Eß Eß, pick up to m. 1 – Ex. 4.12

p2 Cß9 Eß – Cß9 m. 1, b. 1 R3, expecting R3 to Aßm or G –

p3 Eß Eß – Eß, m.1, b.3 TR, p2 denial, complete Eß-object –

p4 Cß9 Eß – Cß9 m. 2, b. 1 R3, expecting A-trans. to Eß (confirmed) Ex. 4.13

p5a Aß7 Cß9 – Aß7, m. 3, b. 3 T5F7, expecting T5F7 to F7 Ex. 4.14

p5b Aß7 Eß – Aß7, m. 3, b. 3 R5, expecting R5 to d° _

p6 Cm Aß7 – Cm, m. 4, b. 1 TRF3, p5 denial, expecting TRF3 to Eß (?) _

p7 Fm9 Cm – Fm9, m. 4, b. 2 R5, p6 denial, expecting R5 to Bß Ex. 4.15

p8 G9 F9 – G9, m. 4, b. 3 A-trans., p7 denial, expecting cadence in C Ex. 4.16

p9 C Eß – C, pickup to m. 6 Incomplete C-object, implies C tonic Ex. 4.17

Example 4.10: “Erwartung,” Op. 2, No. 1, Translation

Aus dem meergrünnen Teiche From the sea-green pond neben der roten Villa near the red villa unter der toten Eiche beneath the dead oak scheint der Mond. the moon is shining.

Wo ihr dunkles Abbild Where her dark image durch das Wasser greift, gleams through the water steht ein Mann a man stands und strieft einen Ring von seiner Hand and removes a ring from his hand.

Drei Opale blinken Three opals glimmer durch die bleichen Steine among the pale stones schwimmen rot und grüne Funken red and green sparks swim und versinken and sink away.

Unt er küßt sie, And he kisses her und seine Augen leuchten and his eyes gleam wie der meergrüne Grund: like the sea-green depths: ein Fenster tut sich auf A window opens.

Aus der roten Villa From the red villa neben der toten Eiche near the dead oak winkt ihm eine bleiche Frauen Hand… a woman’s pale hand waves to him…

129

The piece begins in a somewhat similar fashion as the Bach minuet. The initial harmonic

perception, p1, is that of an Eß-major triad. Immediately following that is a chord which I hear as a

Cß9 chord, with the A∂ being perceived as a Bßß and holding the Eß tone in common (p2). This R3-

transformation, in its own context, generates an expectation for repetition in the form of another

R3, perhaps to an Aß-minor chord if the piece is using modal mixture during a descending-third

progression, or perhaps to a G-major chord if this if the goal is to preserve the major-third

descending interval. It could also be that the Cß9 chord is to be heard at a lower hierarchical level,

mediating the transformation of a higher-level ascending third progression. Both of these

possibilities are illustrated in Example 4.12.

But of course, there is simply not enough information to make a defensible argument

about hierarchies at this point, as there are only two chords. All one can say for now is that one

harmonic transformation begets another, and in keeping with the Law of Good Continuation, one

can expect the same kind of transformation assuming all things being equal. However, p3 denies

both of these possible expectations when the listener hears another Eß-major chord instead. The

realized TR-transformation’s result is a complete Eß-major harmonic object spanning one measure

Example 4.12: Statements for p1 – p3

130

plus the pick-up. The complete harmonic object allows the listener to perceive that the Cß9 chord,

in retrospect, was a pedal-tone passing chord; a chromatic alteration of the common I – IV@ – I

harmonic progression.

When the Cß9 chord returns on the downbeat of the next measure (p4), the listener is

equipped with the experience of the previous one and can now expect a repetition of the entire

Eß-major harmonic object via the same TR-transformation as before, as shown in Example 4.13.

This time, the listener’s expectation is confirmed as the music does indeed return once more to

the Eß-major chord on the third beat of the third measure. The third time the Cß9 chord returns on

the downbeat of m. 4, it would be expected to follow the pattern. But at p5, the pattern is disrupted

with an Aß7 chord. At this moment, the listener finds that a T5F7-transformation has occurred,

rather than the expected TR. This causes a degree of surprise.

Example 4.13: Statements for p4

131

With this denial of expectations, new ones can be posited. Two in particular come to mind,

as shown in Example 4.14. First, one could (as always) project a repetition of the chord-to-chord

level transformation, the T5F7, which could lead to an F7 chord. Alternatively, one could maintain

the premise that the Cß9 chord is still a pedal-tone passing harmony, and so the Aß7 chord is better

placed in the context of the Eß-major chord. In that case, the harmonic transformation was an R5,

and a repetition of that would lead to a D° chord, assuming Schoenberg is staying within a tonal

context.

However, once more these attempts to find a pattern fails as p6 reveals a C-minor chord,

realizing a TRF3-transformation.131 Back to the drawing board yet again, one’s pattern-seeking

mind might say. The harmonic form of this piece is proving to be not so easily perceived. Although,

as the data accumulate and the more harmonies are heard, the more accurately a listener could

infer expectations for the future. So what are the possibilities now? In Example 4.15, I show how

another TRF3-transformation would lead to an Eß-major chord at the chord-to-chord level of

131 Interestingly, this pair of little surprises coincides with the words “dead tree” (toten Eiche), which may seem slightly out of character for the pastoral setting of the poem thus far (Green ponds, red villa).

Example 4.14: Statements for p5 – p6

132

perception, which would have the added effect of completing a larger Eß-major harmonic object,

reinforcing the structural perception of that harmony. One could also place the C-minor chord in

the context of the opening harmony, Eß-major, preferencing the perception of an RT-

transformation from the former to the latter. A repetition of that transformation would lead to an

Aß-major chord. The counterpoint for the music better supports this reading, as it is a common

form of tonic-prolongation often referred to as a “5 – 6 exchange.”

A potential third harmonic perception is also possible, where the C-minor chord is placed

in the context of the Cß9 chord. For this relationship, the listener would be preferencing the hearing

of a Third-Quality-transformation (TQ). This perception also gives greater analytical weight to

downbeat harmonies, which is often preferable. However, the drawback for this reading is that it

Example 4.15: Statements for p7

133

essentially dismisses the idea of a tonal framework for the music, which I do not believe is

appropriate for Schoenberg’s literature at this point in his compositional career. For that reason,

and as the phenomenology of the rest of the piece will evidence, I consider this reading to be less

convincing.

Just before the third beat of m. 4, the Fm9 chord at p7 denies these expectations as well.

With low confidence, one continues to try to make logical connections between these harmonies

which are persistently thwarting their attempts to do so. Example 4.16 shows the next set of

expectational possibilities. In the context of the C-minor chord, the Fm9 chord realizes an R5T7, or

in conventional terms, a falling-fifth motion. A repetition of this transformation would bring the

music to a Bß7 chord. Tonally and metrically, this progression would make a good deal of sense, as

it would bring the music to the dominant harmony of the original Eß-major chord and set up an

authentic cadence on a hypermetrically strong downbeat. Alternatively, one could argue for a

perceptual connection between the Fm9 chord and the original Eß-major, hearing an Ascent-

Example 4.16: Statements for p7

134

transformation between the two.132 A repetition of that transformation would lead to a harmony

rooted on G. But such a reading would essentially ignore the metrical aspects of the work

altogether. Additionally, the Fm9 is in a weak melodic position, with the ninth is in the bass. These

things make the notion that such a perceptual connection can or should be made difficult to justify.

And yet, the latter option is in fact what happens. On the third beat of m. 4 (p8), there is

an apparent confirmation of an A-transformation with the sounding of a G9 chord.

Phenomenologically, one might take this confirmation as evidence for an expectation of another

A-transformation to an Aß-major chord in the future. However, a recognition of tonal conventions

suggests a stronger “more final” reading of this phrase. The tone E at this moment appears to be

a passing tone moving down toward D in the left hand of the piano and up toward F in the right

hand and in the voice part. This, along with its metrical position, indicates that this chord should

be heard as a cadential @ to an implied C-major tonic harmony. As such, a listener can adjust their

expectations to match the implied resolution of this cadence; they can expect an R5 to a C-major

chord. That R5 expectation is then confirmed by the C-major harmony on the pickup to m. 6, which

begins the second phrase (p9).

The G9 chord, with its cadential positioning, severely disrupts the impression of an Eß-major

key for this song. In retrospect, the first phrase appears to have been an auxiliary cadence to the

“real” tonic of the music, C-major, or at least C generally, given the generous amount of modal

mixture. Poetically, this harmonic surprise aligns with a revelation in the text. At the beginning of

the phrase, the poem describes a pastoral scenery with green ponds (meergrünnen Teiche) and a

132 If we wanted to dive into the realm of ninth-chord transformations, this is technically a “Third becomes Ninth” transformation, or a T9.

135

red villa (roten Villa). Normally in musical representations, a pastoral setting conjures imagery of

a sunny day. But right when the G9 harmony surprises the listener, the text reveals that the moon

is shining (scheint der Mond), and that this is actually a night setting. Upon hearing this new piece

of information about the poetic setting, the listener must recontextualize the entire phrase.

Similarly, the listener must do the same with their harmonic impressions. This retrospective

analysis of the phrase is depicted in the graph provided in Example 4.17.

Some might argue that this is a direct modulation – that the music was in Eß-major and

then moved to C-major. But that kind of description does not truly capture the phenomenology of

the harmonic process. As was the case in “Thus Saith the Lord,” the initial Eß-major was never

confirmed with any kind of cadential motion; there was no larger Eß harmonic object. In other

words, the music never really was in Eß-major, it merely gave that impression until its true nature

Example 4.17: p8, mm. 1 – 5 Analysis In Retrospect

136

was revealed later on in the musical experience. Elsewhere I have made the argument that this is

analogous to a plot twist in a movie, where a supposed friend ultimately reveals themselves to be

a villain.133 There is a significant phenomenological difference between a scenario where a

character, through unfortunate experience, becomes villainous (the new Joker (2019) movie

directed by Todd Phillips comes to mind), and a scenario where a villainous character feigns

friendship until it no longer suits their needs. The former scenario one can see coming, or rather,

there was a prolonged expectation that is ultimately confirmed, whereas the latter is not seen

coming and the movie goer has to recontextualize their entire experience of that character

retrospectively. Similarly, the text of “Erwartung” requires the listener to recontextualize the

setting of the poem when they eventually learn that the scene takes place at night, and the

harmonic process requires them to recontextualize the setting of the musical key.

The analysis continues with the next Perception List in Example 4.18, which covers the

analysis through m. 15. From this point, the selected perceptions on the Perception Lists will not

include a detailed accounting of every harmonic transformation, and every possible perceptual

avenue they might suggest. The reason for this is to avoid the pitfall of being “so particular as to

be uninteresting,” as Tymoczko put it. Instead, I will limit the analysis to the possibilities I find to

be most likely and reflective of my interpretation of the poem.

133 I presented a version of this analysis at the 2019 Society for Music Analysis Conference (SOTONMAC 2019).

137

The second phrase begins in the same manner which the first phrase began, by moving

immediately from the apparent tonic C-major to an Aß9 chord, using the tone C as a pedal point

(p10). This is shown in Example 4.19. Having heard the first phrase of the song for context, the

listener can expect a reverse of this R3-transformation to follow, creating a complete C-major

object. That expectation is confirmed when the C-major chord on the third beat of m. 6 is heard.

This transposition of the opening pattern allows the listener to make a longer-term expectation

for the remainder of the phrase, based on the experience of the first phrase.

Example 4.18: “Erwartung,” Op. 2, No. 1, mm. 6 – 15, Perception List

p Event Context Perception-Relation List St. List

p10 Aß9 C – Aß9, m. 6, b. 1 R3, expecting TR to C (confirmed) Ex. 4.19

p11 Eß F7 – Eß m. 9, b. 1 SR, denial of expected Aß Ex. 4.21

p12 Fƒ°7 Eß – Fƒ°7, m.9, b.3 R7, expecting A-trans. to G –

p13 Fm7 Eß – Fm7 m. 10, b. 1 R7, expecting R7 to G –

p14 G9 C – G9, m. 10, b. 3 R7, confirms p13, expecting R5 to C Ex. 4.22

p15 D9 G9 – D9, m. 12, b. 3 FRS3, denial of p14 Ex. 4.23

p16 G9 G9 – G9, m. 13, b. 1 R5, completes G9-object _

p17 A9 G9 – A9, m. 14, b. 1 A-trans., expecting A-trans to B9 _

p18 B9 A9 – B9, m. 15, b. 1 A-trans., confirms p17, expecting A-trans. to B9 _

Example 4.19: Statements for p10

138

I find two likely options based on the current musical context, which are represented in

Example 4.20: Option One – the implication of a tonic C-major that we were given by the first

phrase is the true key of the music, so this consequent phrase will confirm that key this time with

a cadence on C-major, thereby completing a C-major tonic object. Option Two – “Fool me once,

shame on you fool me twice, shame on me.” This transposition could be exactly that, so one could

anticipate a harmonic process that is the same or similar to the one before, which diverted at the

last second to a half-cadence on the key area a minor third lower. If this interpretation is accurate,

it would lead to an E9 chord that implies a half-cadence of an apparent A-major tonic.

Example 4.20: Possible Expectations for mm. 6 – 10 Option 1

Option 2

139

Both possibilities prove to be accurate until the downbeat of m. 9 (p11), where an Eß-major

chord is heard. That Eß-major chord denies the expectation of an Aß-major chord, which should

have followed if the music was repeating the phrase model of mm. 1 – 5. As one can see in Example

4.21, the Eß-major chord is the first moment of surprise in this phrase. The Eß-major chord then

descends through a chromatic Fƒ°7 chord (p12) to an Fm7 chord on the downbeat of the next

measure (p13). At this moment, the listener can place the Fm7 chord in the context of the Eß-major

chord from the previous measure, recognize the R7 harmonic process, and expect another R7

toward a future G9 chord. The metrical position and contrapuntal similarity to the first phrase

might also have the listener recall what happened the last time they heard an Fm7 harmony (m.

4), which was that it led to a G9 chord. For those reasons, as well as the phenomenological

Example 4.21: Statements for p11 – p13

140

connection between the Fm7 chord and the Eß-major chord of the previous measure, the arrival of

the G9 chord on the third beat of m. 10 (p14) is not nearly so surprising as the first.

A retrospective analysis of the second phrase in provided in Example 4.22. While the

phrase does not exactly confirm the phrase-level expectations that were generated at the

beginning, the G9 chord does confirm more surface-level expectations, and recalls elements from

the harmonic process of the first phrase. It also reinforces, while not confirming, the apparent C-

major tonic with a repetition of the half-cadence. At the moment of the Eß-major chord, which

again, is the first moment of surprise in the second phrase, the poem begins to describe a man by

the pond removing his ring. Why he does this is unclear right now; it is a plot point to be resolved

later. But I believe it is significant that this action occurs as the first unexpected harmony happens

in this phrase.

Example 4.22: p14, mm. 5 – 10, Analysis in Retrospect

141

Graphics supporting the analysis of mm. 11 – 16 are provided in Example 4.23. This

third phrase of the song continues to withhold any strong confirmation of the apparent C-major

tonic. The unresolved cadential figure that the listener hears with the G9 chord is repeated three

times before it is transposed via FR to a D9 chord on the third beat of m. 12 (p15). That D9 turns out

to be a local dominant to the G9 chord, as the transformation is then reversed via R5 to return the

listener back to a G9 chord on the downbeat of the next measure (p16). That reversal then

completes a G9 harmonic object. That G9 object begins to repeat as the music progresses to D9

once more, but on the downbeat of m. 14 there is an A9 chord rather than the expected G9 (p17).

Over the next two measures, the listener finds that they are an exact transposition of the previous

two, suggesting an ascending stepwise pattern. That pattern is continued as a B9 chord is heard

on the downbeat of m. 16 (p18). Once the B9 chord is heard in m. 16, another potential expectation

is generated. If the listener is to maintain the perception of an apparent C-major tonic, they might

conclude that ascending pattern is reaching toward the C-major that it had descend from in the

previous phrase, and expect a C-major tonic chord to arrive following m. 16. However, that

Example 4.23: Statements for p15 – p18, mm. 11 – 16

142

possibility dissipates as the pattern stalls once it reaches that B9 harmony, “sinking” away, as the

text suggests.

A list of the remaining harmonic perceptions in this piece that are relevant to this analysis

is provided in Example 4.24. As the music continues, we find that the lingering B9 chord turns out

to be an inflection moment in the counterpoint. From the downbeat of m. 18 (p19), the piano sinks

downward from an Eß-major chord in second-inversion through a series of chromatic harmonies,

obscuring the sense of a C-major tonality the listener might have retained up to this point. But

then on the downbeat of m. 21 (p20), there is another Eß-major chord in second-inversion and a

slowing of the harmonic rhythm, which allows the listener a moment to reorient themselves. From

this point, another retrospective analysis is provided in Example 4.25.

Example 4.24: “Erwartung,” Op. 2, No. 1, mm. 18 – 32, Perception List

p Event Context Perception-Relation List St. List

p19 Eß B9 – Eß, m. 18, b. 1 A-trans., denial of expected C Ex. 4.25

p20 Eß Eß – Eß m. 21 Completes Eß-object, expecting R5 to Bß –

p21 Cß9 Eß – Cß9, m. 23 R3, denial of p20 –

p22 Eß Cß9 – Eß m. 25 TR, expecting R3 to Cß9 (confirmed) Ex. 4.26

p23 Bß7 Eß – Bß7, m. 30 FR, expecting R5 to Eß _

p24 Eß Bß7– Eß, m. 32 R5, confirms p23, completes Eß-major song-object _

143

There are a number of conventional and phenomenological reasons for why this Eß-major

chord is a particularly marked point of perception. First, it is the same chord that began the phrase

on the downbeat of m. 18, and so it completes an Eß-major harmonic object. The Eß-major chord’s

contrapuntal and metrical positions also suggest that it is a cadential @. This cadential positioning

has the phenomenological effect of recontextualizing the B7 chord on the pickup to m. 18 at a

German augmented-sixth. And finally, it sets up an expectation of a motion to Bß-major, followed

by an authentic cadence on Eß-major, which would be another significant plot twist to the story of

the piece since so much of it thus far as implied that C-major was the real key of the song. However,

the return of the Cß9 chord in m. 23 (p21) denies the listener that Dominant-Tonic resolution in as

deceptive a cadence as one can find. It is as if the expectations that the Eß-major chord creates go

right out the window that opens at that moment in the poem (ein Fenster tut sich auf). The Cß9

chord is also particularly striking insofar as it recalls the context in which it was initially heard at

the beginning of the song. Although completely unexpected, the Cß9 chord, together with its

subsequent return to the Eß-major chord in the next measure, unifies the music up to that point in

Example 4.25: Statements for p19 – p21

144

a way that the individual phrases could only imply – It completes a large-scale Eß-major harmonic

object.

Example 4.26: Possible Expectations for mm. 25 – 30 Option 1

Option 2

Option 3

145

The Eß-major chord on the pickup to m. 26 (p22) brings the music back to where it began,

and this return is perceivable right away. But now, given the context of the rest of the song, I find

that the listener has three reasonable options if they were to try to infer how the phrase should

unfold. These possible expectational states are illustrated in Example 4.26. For the first option,

one could note that the first phrase ended with an incomplete harmonic object. This phrase could

proceed in the same way by diverting at the last moment to a half-cadence on a G9 chord. Then

the following phrase would conclude the music, probably on an Eß-major chord, although possibly

on a C-major chord. This ending would offer a satisfyingly symmetrical conclusion to the song form,

as it would balance the apparently antecedent first phrase with a consequent second phrase. For

the second option, one could remember that the first phrase acted as an auxiliary cadence to what

was perceived as the structural beginning, the second phrase. If the second phrase was more

structural, perhaps this phrase will proceed in a similarly structural way. It could accomplish this

by having the left hand of the piano move chromatically down, but this time finally resolving to

the anticipated Eß-major chord. And for the third option, a listener could take the position that the

musical and poetic complications of the song have been resolved, and now the root progression

that was originally produced will at last conclude with a perfect authentic cadence.

As the phrase progresses, one finds that the first and third options appear to be accurate

through m. 29, but then at m. 30, the Bß7 chord (p23) solidifies the third option as the most accurate.

Although, Schoenberg does obscure things with accented dissonances of Cƒ, G, Cß, and E∂ before

they ultimately resolve to the Bß7chord. He also ends the vocal phrase a measure before the piano

cadences, further complicating the perception. But eventually, the expectation of an authentic

cadence on Eß-major is unambiguously confirmed on the downbeat of m. 32 (p24). That

146

confirmation is then reinforced by a repetition of the cadence and three full measures of Eß-major

to conclude the piece.

As we can see, the song’s tonic was in fact Eß-major after all! So then, what does all of the

perceptual ambiguity, all of the misleading expectations, mean for the work? I believe that it is

poetically connected to the man who removed his ring earlier in the song, and this woman that

beckons him into her villa in the middle of the night (winkt ihm eine bleiche Frauen Hand…). That

image alone suggests to me that the man might be about to commit an act of adultery, and he is

outside trying to decide whether or not he wants to go through with it. The Cß9 chord on m. 23,

where the window opens, is a critical decision point for the man. Will he ignore (or spite) the

shadowy image of his wife in the water to go meet this other woman, or will he chasten himself

and protect his honor? This is the question that the final phrase answers.

I think that if the song had ultimately moved back away from Eß-major for the last phrase,

either to cadence in C-major, or not cadence at all and linger on the Cß9 chord, it would support

the interpretation of a less-than-moral man who ultimately decides to commit adultery. But the

resolution in Eß-major suggests to me a more optimistic interpretation. In that light, I see a man

whose wife had passed away, and now he is trying to move on. He thinks of her fondly as he stares

into the pond outside the villa, takes off his ring, and with tears in his eyes, casts it into the pond

and watches as it sinks away, as if to kiss her goodbye. After this emotional event, he then goes to

meet this new woman, perhaps uncertain of the future, but finally willing to take the chance.

147

I have provided a “final” reading of “Erwartung” in Example 4.27 to illustrate how a

Schenkerian might look at the structure of the song in its entirety. One may be inclined to simply

label the Eß-major chords at the beginning and ending of the piece as tonic and move on, as I have

done here, and look for poetic qualities elsewhere in the music (the enharmonic respelling of the

tone Cß into B∂ and back again is an interesting point of discussion, for example). But as far as the

overall “final” harmonic structure is concerned, so what if it starts and ends on the tonic? Nearly

every composition does that. But if one carefully considers the time-experience of this particular

song, one can find a great detail of poetic insight in what otherwise might seem a rather mundane

aspect of the work. Although an Eß-major key was suggested at the opening of the first phrase, it

was not at all clear that it was in fact the key for most of the song. On the contrary, the half-

cadences implying C-major that conclude the first and second phrases, along with the failed

attempt to reach a C-major harmony in the third phrase, all suggested that Eß-major was an

auxiliary key area. The musical experience lasted twenty-one measures before it even looked like

it might cadence in Eß-major, and that cadence was evaded. It was not until the final phrase that

Example 4.27: “Final” Reading of “Erwartung,” Op. 2, No. 1

148

the possibility that the song will cadence in Eß-major returns, and like a good movie, if and how

that would happen was only revealed at the very last possible moment.

149

As I consider the time-experience of this dissertation, I must return to the stated goals of

the introduction and evaluate whether the body of this work has confirmed the expectations that

I laid out there. Of course, this is the standard and proper action any writer must take if they wish

for their work to be perceived as complete. But as I do so, I also reflect on the process itself. Such

has been the primary subject of this project, at least as it relates to harmonic progressions. How

does the content of the work generate expectational states in the listener’s (or reader’s)

consciousness? Were those expectations met, and if so, how? If not, what was different about the

realized process in comparison to what was expected?

Hugo Riemann stated in Harmony Simplified that the theory of harmony “is that of the

logically rational and technically correct connection of chords.” Many recent forms of Neo-

Riemannian transformational theory tend to approach the logical connection of chords as though

harmonies exist and are perceived in the context of an abstract pitch-class space. In this abstract

pitch-class space, one can construct networks of chords that are connected by one or more

vertices (i.e. the Tonnetz). Within those networks, the technically correct connection of chords

becomes a matter of rotating a starting chord around those vertices, along one axis or another,

until the chord arrives at the desired harmonic space. With this methodology, the underlying

premise is that chords are perceived as discrete, individual objects that move through a

metaphorical space.

My theory of the phenomenology of the harmonic process seeks the same result, the

logically rational and technically correct connection of chords, but I approach the issue from a

different perspective. I do not view a chord as a discrete object in a particular place in space, but

150

SUMMARY AND CONCLUSIONS

rather as a marked moment in time, where the sounding pitches have specific, perceivable,

interrelated meanings – Root, Third, Fifth, or Seventh. Those interval-meanings come into being

when the pitches to which they are attached are heard within the context of each other in that

moment, that chord. They then pass out of being as soon as that moment, that chord, becomes

past. A chord becomes past only when it is replaced by another chord, or rather, when a new,

marked moment in time is perceived. When that happens, common tones will have lost their

original interval-meanings and gained new ones, because the introduction of one or more non-

common tones will have changed the intervallic context of the common tones.

The loss of one interval-meaning and gain of another is achieved through an experiential

process – an act of perceiving over a set duration. As Christopher Hasty stated about the

perception of things, “Nothing is actual – that is, nothing becoming or having become – is without

duration.” In harmonic progressions, that duration is set by the progression of chords, from the

beginning of the perception of one chord to the beginning of the perception of the next. The Neo-

Hauptmannian transformations that I have developed here describe what kind of perceptual

action is taken by the listener in order to rationalize and logically connect those chord

progressions; they are designed to articulate how the interval-meanings of sounding pitches

change over a durational period. Each transformational type is defined by what pitches are being

retained, which interval-meanings those pitches had in the context of the former chord, and what

interval-meanings they have in the context of latter chord. With the information provided by these

transformations, an analyst can observe the expectational states that are generated in the

listener’s consciousness as a result of those perceptual actions.

151

The detail that can be uncovered through a Neo-Hauptmannian transformational analysis

can be quite extensive, especially if the musical work being analyzed regularly subverts listener

expectations, as was the case with Schoenberg’s Op. 2, No. 1, “Erwartung.” Therefore, it may be

most effective when applied toward individual sections or phrases of a larger work, or smaller

works such as art songs or small-scale piano pieces. Also, in this project I have limited the

discussion to triadic and tetrachordal harmonies, chords for which there are clearly discernable

Root, Third, Fifth, and Seventh interval-meanings. While there is theoretically no reason not to

expand the scope of transformational types to include extended tertian harmonies (Ninths,

Elevenths, and Thirteenths) and chromatically altered tetrachords (such as Fr6 chords or

tetrachords with augmented fifths) an analyst may find diminishing returns on the application of

the methodology.

Finally, I wish to stress my belief that this Neo-Hauptmannian analytical methodology has

the capacity to offer insight into musical phenomena that might initially seem mundane or routine.

In the case of Bach’s E-Major French Suite, BWV 817, Minuet, the repeated sections in the work

played a vital role in the experience of the work as a whole, clarifying an apparent contradiction

between the contrapuntal, harmonic, and formal elements. Likewise, in the Schoenberg piece the

phenomenological analysis highlighted a uniquely powerful poetic effect that came from the

ultimate confirmation of an Eß-major tonic that a “more final” reading might easily overlook. Music

is a temporal art, and its changing form is understood through the listener’s act of perceiving

through time. With this methodology, it is my hope that we as analysts can better understand

those perceptual acts, and through them, the phenomenology of harmonic progression.

152

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