THE COGNITIVE PEDAGOGY OF AURAL TRAINING

Orlando Musumeci - Conservatorio Alberto Ginastera - Buenos Aires

“. . . to look at rather than through the lens that is shaping the materials . . . “

Jeanne Bamberger: The Mind behind the Musical Ear

INTRODUCTION

Music psychology and aural training

This paper is concerned with the ways in which research in cognition in general and in

music psychology in particular can inform the pedagogy of aural training/music theory in

conservatories and music schools. A review of the scarce literature on the topic shows no

more than just polite complaints and good wishes, both from researchers and educators, that

the psychology of music should inspire aural training, but almost nothing that might be

considered as a direct undertaking of that task. An increasing number of people within the

conservatories and schools of music is slowly becoming aware of the tremendous importance

that psychological and cognitive findings may have for music teaching (cf. Butler 1997,

Cook 1994, Covington and Lord 1994, Musumeci 1998a-b). Common sense and musical

experience strongly suggest that plenty of links should exist between both domains. Almost

everybody agree in that “taking into account some basic properties of human brain and

senses would be of much help in taking decisions concerning music pedagogy” (Rakowski

1999: 33); aural training has been equated with “brain training” (Henson 1987: 73) and both

psychologists and pedagogues readily acknowledge that “what is aural training, after all, if it

is not the acquisition of cognitive skills in music?” (Butler 1997: 47). But all the thrust

provided by this opinions vanishes when it comes to make such links explicit, and as a

consequence such endeavours, the development of a “cognitive pedagogy of music”, are late

to arrive. Psychologists are strongly reluctant, short of interest, or unable, to speak of the

didactic implications of their findings, and the literature shows scarce efforts to relate both

disciplines in an explicit manner.

The teaching of aural training in conservatories and music schools - strongly linked to the

teaching of notation - is consistently regarded by teachers and students as a challenging task.

There are lots of obscure points in the pedagogic theory that are left to be explained by

imprecise concepts like musical gifts, or the mysterious possession or absence of a “musical

ear”. Aural training courses, like the whole milieu of the music schools, are still explicitly or

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implicitly very reliant on the myth of giftedness, and the inefficacy of the pedagogical

procedures is masked by the belief that “talent” will fill in the didactic gaps. Even at the

most elementary level nobody can be sure that he/she will pass an aural education course. It

is not like other subjects like history, language, or even mathematics: in ear training

education, no matter the effort invested, the learner is always in danger of bumping into an

insurmountable obstacle: to run short of “ear”.

In this paper I will try to put together existing findings in the psychological literature and

anecdotal evidence gathered in the conservatory classroom. Drawing on some ideas from the

research literature I will attempt to find a cognitive explanation - though perhaps somewhat

preliminary and broad - for didactic processes which I believe are effective for teaching

aural training. Many times it can be found that psychological findings indeed confirm what

particularly insightful ear training teachers noticed. We have indeed some excellent books

and pedagogic treatises (i.e. Aguilar 1978), mainly based upon musical intuitions, that many

times coincide with some principles corroborated by psychological research. In that cases the

educational implications are not foreseen but confirmed by later psychological findings. The

further gathering of empirical psychological data should be guided by a framework that

should include theoretical and practical issues pertaining to music pedagogy. Only after this

preliminary work has been performed is that further suggestions could be made about the

areas where music education can profit from past and present findings in music perception

research. I will try to show how the intuitions of the accomplished music teacher can be

explained by some extant findings in music psychology, since I am strongly convinced that

there is already large enough empirical data on music perception to allow the outline of a

broad theoretical perspective taking into account elements from both fields.

Aural training and Standard Musical Notation

The term aural training has been applied in relation to many different skills from singing

solfeo lessons, tapping rhythms, singing scales, writing down dictations, to discriminating

musical textures, forms and timbres (Henson 1987). In fact aural awareness can be seen as

an ability concomitant with any musical activity, but in this work I am concerned with the

concept of aural training focused in the teaching of Standard Musical Notation (henceforth

SMN).

The use of notation is a constitutive feature of Western music. In its origin notation was

simply a tool for remembering the tunes, a mnemonic devise that really did work: all music

prior to this century has reached us by notational means; and it is precisely that usage what

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still mainly justifies its teaching in the conservatories: to have access to the vast “written”

repertory accumulated from the Renaissance to our days. Important as it goal may be, its

status has been erroneously exaggerated in conservatories’ academic circles to the point of

being considered the main goal of music theory courses1.

Western-tonal music grew increasingly dependent on symbols, both for compositive and

performance terms, not only for needs of recording and transmission but to achieve high

levels of complexity. If in its origin notation was only a kind of by-product of music, along

the centuries notational symbols in turn also shaped the way of thinking about music (cf.

López Puccio 1978). If we consider notation as the final output of the cognition of music, as

the formalization of abstract relations among sounds, it is made evident the usefulness of any

notation for music teaching and learning. When we put musical ideas on paper, they “hold

still” and “talk back” (Bamberger 1991: 118), and this two-way confrontation is central for

the development of musical understanding, as it was during the history of Western music.

The above arguments justify my view that music literacy - by means of any notational

system - is paramount for the study of music, and not just an accessory skill: it is essentially

“an act of reflection . . . of which features are most salient and in need of recording”. . . [a]

“post hoc consideration of a piece of music” (Serafine 1988: 37). Accordingly, we can

assume that any attempt to teach notation should start by re-constructing this sequence in the

novice music learner, guiding the reflection over the features that are prominent in his/her

representation of the music. To assess that we must consider first how the illiterate listener

listens to music.

FIGURAL AND FORMAL KNOWLEDGE

How people listen to music

Musical listening is a multidimensional experience. The physical stimulus offers us many

interacting dimensions - rhythm, melody, harmony, timbre, text - integrated in a perceptual

continuum. To this wholeness our cognition adds even more layers of “meaning”, ranging

from low level grouping strategies involving a few events to abstract relations at higher

structural levels, and also aesthetic and emotional responses:

“the sense made of phenomena is always a construction . . each of the

individuals finds in the material and thereby gives existence to aspects that

simply does not exist for the other. For the person who attends the metric aspects

of rhythm, figures [in the sense of figural knowledge] remain unrecognised; for

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the person who attends to figures, the classification of events according to their

shared duration remains inscrutable” (Bamberger 1991: 29)

Figural knowledge, or sometimes functional, refers to that kind of global, continuous

apprehension of the musical phenomenon that gives instantaneous access to a holistic

representation of the music. Our cognition keeps track simultaneously of all music

parameters, assigning each surface event a function inside a figural representation that is

highly dependent on the surrounding context, “events within a figure are contextually

bound” (Upitis 1987: 41). Usually a minor alteration in a single dimension, or the tiniest

attempt to break down this functional relation into its different constituents, is enough to

alter or lose altogether the musical identity of the figure.

Formal knowledge or sometimes metrical, stands for a kind of music apprehension that is

completely different. It is concerned with those aspects of the musical stimulus than can be

counted, measured, classified, mostly in terms of proportional durations and frequency

ratios, and is put to play when a conventional representation of music, as in SMN, is needed.

Figural apprehension is the kind of knowledge involved in several different responses to

music - aesthetic, emotional, kinaesthetic - that involve some kind of meaning. The transit

from a figural mode to a formal one may be conceived in relative terms: any time that we

integrate a formal concept in a context, we are moving up in the hierarchy and giving rise to

a figural concept. Where structural components are involved, it could be said that figural

knowledge allows the access to a higher level hierarchy that shapes the meaning of

individual events, and viceversa, to formalise in the context of this work means to access to a

lower level in a hierarchical representation of music. However, it is not that the figural and

formal modes are mutually exclusive, nor can we imagine each one of them in a pure form.

While most of the times both figural and formal modes alternatively contribute to music

cognition, their contribution may be considered asymmetrical. If a “purely” figural approach

is in a sense limited because it has a restricted access to formal knowledge, this fact does not

diminish its musical value. On the contrary, a purely formal approach is limited in a more

important way, since no formal knowledge is musical, without the meaning added by the

figural dimension. Presumably a musically literate musician can switch from one mode of

perception to the other at will, though I suspect that there is always a mismatch between both

modes; our figural perceptions always staying beyond what we are able to formalise; we

always ‘know more than we can tell’.

The figural - formal transaction

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The teaching of notation - certainly a complex formalization - consists in allowing the

learner to perform a fluid interplay between both modes. At the very beginning the learner

needs to switch from his/her figural representation to a formal one, a process that we call the

figural - formal transaction. The crucial point is how to integrate both dimensions in the

learner’s representation: one is intuitive, continuous and holistic, the other is rational,

discrete and analytical. When we are perceiving in a figural mode we do not hear each note

in the music, but rather “a non-linear relationship [exists] between the notes in the score and

what people hear when they listen to a performance of it” (Cook 1994: 79). The

formalization needed for notation follows exactly the opposite way: it replaces a figural

experience with a formal description, “a meaningful continuity with a meaningless

particularity” (Cole 1974, cited by Terry 1994: 104). It is this wholeness what renders so

difficult to determine exactly all the processes involved in the figural experience of music,

but certainly grouping, beat and meter abstraction, perception of regularities like pattern

alternation or repetition, segmentation, and awareness of tension-relaxation schemas can be

considered kinds of figural apprehension. One central contention of this work is that when

we “rescue” our students from that undifferentiated sea of music, when we guide the first

transactions between their figural and formal knowledge, if we fail in establishing the right

first link between both modes of representation it probably will never be easily and naturally

restored. Or otherwise, it will be restored just by some exceptional individuals who are able

to find their way alone in that tempestuous sea2.

Pedagogical implications: modelling the learner’s cognition

The formalization required for SMN necessarily needs some kind of categorisation of this

figural perceptions - to make discrete something that is naturally continuos -, and

categorisation in turn involves a finite number of categories within a given continuous

dimension. If we assume that possible figural hearings are infinite and formal

representations are finite, we conclude with the very obvious assertion that two or more

figural representations may have, depending on the level of analysis, a common formal

representation; and also the opposite, that a formal representation - no matter how detailed it

may be - will have more than only one functional representation3. This is so because the

figural experience is holistic and will be automatically affected by the context. A higher

hierarchical organisation can always be preserved with a theoretically infinite number of

surface (low level) features. Conversely, a formal construct may preserve its integrity while

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its figural function may be affected by an infinite number of contextual, higher level frames

of interpretation. In Example 1 are exemplified two cases of formalizations coupled with

different figural interpretations. In both cases the figural interpretation involves the

consideration of a context operating at a level higher than the one at which the formalization

operates.

What puzzles the learner in his/her first contacts with SMN is the finite, relatively limited

number of concrete means of notation (musical figures) - a characteristic inherent to any

symbolisation - and the consequent infinite number of musical “faces” that that symbols may

adopt in different contexts:

“mistake[s] can be traced to a mismatch between internal mental representation

and conventional descriptions, [and so] it is useful to help students confront

these differences. In this instance, that would mean helping students to move

back and forth between metric and figural hearings and between metric and

figural descriptions of a rhythm or melody” (Bamberger 1991: 66-7).

The usual strategy of the ear training pedagogy is to present as many examples of formal

configurations as possible, each one tied to a unique figural representation. This one-to-one

relationship obscures the listener’s active role in the process of construction of these figural

meanings from a neutral notation, and consequently the student achieves, at best, a figural -

formal transaction that is rigid and inflexible. He/she finds it difficult to distinguish one

mode of representation from the other, and has problems to differentiate among the aspects

of his/her figural experience that can be reflected by notation and those that notes cannot

portray, no matter the degree of detail in the score’s specifications.

This dialogue between the specifications present in the notation and the sense that the

learner makes of it is of crucial importance and must be carefully aided. It could be said that

the role of the teacher is to model the learner’s cognition by helping to disentangle both

kinds of representations while allowing a fluid interplay between them. As few as a single

error, only a small mismatch between this two dimensions, may be catastrophic for any

further learning. The didactic strategy proposed here is in a sense opposed to the traditional

one: it consists in presenting the learner with as many different figural representations as

possible that a single formal representation can stand for.

To learn what is already known

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How can extant psychological studies inform an ear training pedagogy guided by the

conceptual framework outlined so far? One assumption of this approach to the teaching of

notation is that formal knowledge can only be constructed from figural knowledge. In this

conception the figural mode is not an imperfect or preliminary form of knowledge but a

foundation and in turn also a goal of the formal one. If we found that every member of a

culture is able to construct a figural representation of the music, that would imply that every

person within the range of standard perceptual and cognitive abilities should be able to learn

to read and write music.

Cultured adults process automatically enormous amounts of musical information. The

exposure to the music of the culture, together with innate cognitive machinery to structure

the environment, originates an ‘implicit knowledge’ that can be found in most people. This

ability consists mainly in grouping musical sounds and in giving them meaning inside a

culture-driven pattern (cf. Dowling 1999). This musical competence is relevant here because

it seems to involve similar processes in both musicians and no musicians. If we turn to

experiments concerned with some of the different processes involved - like grouping (cf.

Deliège 1987), the perception of tensing-relaxing patterns (cf. Bigand 1993) and of

underlying hierarchic structures (cf. Serafine, Glassman and Overbeeke 1989) - we find that

naive listeners indeed show a performance very similar to that of musicians. It seems that

musical training does not affect substantially the ability of normal adults to respond to the

figural aspects of the music, but rather that “music perception is fundamentally similar in

listeners with varying degrees of sophistication” (Trehub, Schellenberg & Hill 1997: 104).

There is also enough evidence to assume that the processes involved in this music

competence develop gradually from the pre-natal stage (cf. Lecanuet 1996) and through

childhood as a result of normal exposure to music. Infants group auditory information

according to Gestalt principles of proximity and similarity in ways similar to those used by

adults (Demany 1982; Fassbender 1993; Thorpe and Trehub 1989; Thorpe, Trehub &

Morrongiello 1988), can discriminate between different rhythmic and melodic patterns

(Chang and Trehub 1977a-b), and are sensitive to phrase structure (Krumhansl & Jusczyc

1990; Jusczyc & Krumhansl 1993). These and other cognitive processes involved in the

figural apprehension of music - like the understanding of tonal closure and harmonic

relationships - develop steadily through childhood and “are generally well in place in human

cognition by the age of 10 or 11 years” (Serafine 1988: 224).

This challenges the traditional conception of the aural training pedagogy that treats the

learner as if his/her first contact with the music took place at the conservatory classroom. If

the music theory teacher assumes a valuable pre-existing musical knowledge in the learner,

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the process of formalization will consist simply in learning “what he/she already knows”

(Bamberger 1991: 259). The transition from figural to formal will consist simply in putting

names to “things” that the novice already perceives and notices. In that sense the job of the

teacher is not to teach but just to show.

When a person listens to a given piece she recognises - understands - several

characteristics of the music in a straightforward manner. The cruder, most basic

formalization of that understanding is the discrimination between that precise piece and

another, even if she could not rationalise the difference. In that case she “knows more than

she can tell”. In a very direct way that situation of the novice learner differs only in degree

from the experience that any musician knows: to listen to some sounds or music passage, to

perceive and understand the function, the “meaning”, but not being able to write it down or

to play it in the piano: “that sounds like a cadence but I don’t know exactly which the chords

or the inversions are”. Musicians and aural training teachers, no matter their audio-analytic

sophistication, continuously are faced with passages, chords, musical relations that they

“understand”, but are not able to formalise.

But if the average listener can indeed make all the subtle discriminations involved in the

“musical” apprehension of sounds, why is it that not everybody can learn to formalise this

knowledge in the form of SMN? I argue that when people fail to understand the basis of

music notation it is because aural training didactics fails when coming to formalise their pre-

existing musical knowledge: the “units of perception” do not match the “units of

description” (cf. Bamberger 1991: 8).

One of the central contentions of this work is that with the adequate teaching almost

every musically cultured adult should be able to learn the basics of music reading and

writing. We only need to find means in which the learner could profit from what he/she

already knows. If they do not find bonds between their percepts and the formalizations

required for notation the music teacher will simply be, as the saying goes, “answering

questions that the learners have never asked themselves” and that knowledge will never

become operative. I propose that the best way to establish links between figural and formal

percepts in music is to draw on the extant figural knowledge of the learner and to exploit any

previously acquired abilities in general auditory pattern processing. In the following section

I present some brief comments and suggestions of how a didactic approach to the teaching of

rhythm could take into account that premises.

A DIDACTIC APPROACH TO RHYTHMIC TEACHING

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The key didactic issue is to find out the kind of formal description of rhythm that the

novice can more easily access, the one that is closer to his/her figural description. The

crucial question for the aural training teacher is how to lead the learner’s rhythmic

processing beyond the basic cognitive mechanisms like regularity extraction and

segmentation into groups (cf. Drake 1998). What is the next step that the learner should take

towards a formalization of his/her perceptions of uniformity and change in the rhythmic

flow? At this point the usual focus in ear training courses is to start from the metric aspects

of rhythm. Traditional pedagogy has assumed that, given that everyone can perceive an

underlying beat, they can easily use it as a temporal ruler to measure the length of events

that group over the pulsed field. But, as we have seen, that is an “after the fact” reasoning

that assumes a metrical “skill” inexistent in the learner. I argue that the next stage in the

formalization of rhythmic perception should rely not on the metric aspects of groups of

events, but on the functional relations among them. Now let’s examine what are the

functional relations in a group than can be more easily formalised (I use the word functional

instead of figural because it reflects more accurately the idea of relatedness of one event to

other, or others, in a group).

Speech and music prosody

The grouping of events - a functional perception - takes place in the framework of “a

regular pattern of strong and weak beats to which he [the listener] relates the actual musical

sounds” (Lerdahl & Jackendoff 1983: 12) called metrical hierarchy. It seems evident that the

first novices’ attempts at the formalization of rhythmic groups should be more conveniently

done at a single level of the metrical hierarchy and without loading on long term memory,

that is, weak beats grouped around strong ones, and precisely speech prosody offers an

example of that kind of grouping. Since most music in the Western tradition can be

interpreted in terms of figural units that can be described in prosodic terms, I propose that

the figural-formal transaction should start by the formalization of rhythmic groups in terms

of prosodic units.

Prosody is the overall acoustical profile of a spoken/chanted utterance that results from

the organisation of weak discrete elements - syllables - around stressed ones; the term stress

designates perceptual salience achieved by any mean like dynamic changes, lengthening of

sounds, and pause, etc. In speech comprehension language prosody plays a paramount role

(cf. Cutler, Dahan & Donselaar 1997, Pynte 1998), and the same is true for music. We can

imagine the musical parallel in the case when we chant a melody in a monotone, at half way

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between speech and singing. In the absence of accurate melodic or rhythmic information, we

can still keep track of its structure relying solely in the information carried by the prosodic

profile of the output: almost every music can be reproduced, or mimicked, with variable

degrees of precision by the human vocal apparatus.

Both speech utterances and music involve the perception of auditory patterns in the

framework of sequential and hierarchical cognitive processing, where continuous sound

strings are analysed into discrete phonemes or notes. For language and music reading the

opposite way is followed: a symbol string is decoded to produce a spoken/sung/performed

output. This continuous strings of syllables or sounds, as they unfold in time, are structured

around metrical stresses that determine the prosodic profile of the phrase. The similar nature

of constituents marking in speech and music (cf. Carlson, Friberg, Frydén, Granström. &

Sundberg, 1989) indeed suggests the existence of some shared cognitive mechanisms for

grouping in language and music (cf. Pinker 1997: 535, Fassbender 1996: 80)4.

The first didactic work with prosody must start with the distinction between stressed and

unstressed events in a sound string. This is not a trivial point, since we have seen that in the

multidimensionality of the listener’s experience it may be difficult to keep track of the

salience of events along a single dimension. But the formal processing of speech sentences -

a well learned process in most schooled adults - constitutes a clear example of the grouping

of events (syllables) along a single temporal dimension. The syllable is the basic rhythmic

unit of Spanish, and the prosodic profile of an utterance is shaped by the way in which weak

syllables group around stressed ones. One of the most characteristic features of the spoken

language is that all the syllables in a rhythmic group, whether stressed or unstressed, tend to

follow each other at more or less evenly spaced intervals of time5. The identification of

stressed syllables in words and sentences may be used as a common cognitive framework for

the processing of musical events. By splitting words into syllables, and imposing a steady

beat, we can bring easily our students to the perception of the prosodic profile of an

utterance, and to transfer it to SMN. In a typical didactic sequence we can ask the student:

to recite a sentence following a steady beat and assigning one syllable to each beat

to find the stressed syllables that organise the meter

to place bars before the stressed syllables, and finally

to transfer to music notation the metrical structure of the utterance - establishing a

correspondence between strong and weak syllables and strong and weak musical beats - by

replacing the syllables by any conventional music symbol (Example 2).

Once the metrical structure is established, the further identification and description of

prosodic constituents follows. Each prosodic unit, or foot, is organised around a metrical

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stress. The formalization of this feet in the learner’s representation must consist in the

distinction between the different ways in which syllables/events organise around this stress.

Since the same metrical structure allows several prosodic interpretations, depending on the

grouping, by interchanging different words to match a given metrical structure, the different

groups/feet that unstressed syllables/events may form around metrical stresses can be made

evident for the learner (Example 3)6.

In a typical analytic-reading activity the learner will be asked to search for all the possible

different figural interpretations, that is, all possible prosodic feet that could be formed,

following the rule that each of them must contain one, and no more than one, metrical stress

(or head). In that way, for instance, a 4 bar rhythmic phrase will present 4 different groups,

each “wrapped” around a head. The feet can be kept similar among themselves, within the

possibilities of the phrase structure, or different feet may be combined (Examples 4 and 5).

The concept of duration

People is not very good at comparing durations because the formal operation involved in

comparison of temporal lengths is strongly influenced by the figural organisation of the

events (i.e., the detection of the lengthenings of events between groups are “harder to detect

and identify than similar lengthenings in other positions within the group” [Drake 1998: 18;

cf. also Fitzgibbons, Pollatsek & Thomas 1974]). Usually a notated duration stands not for

the metrical length of an event, but mainly for the rate of attacks between events that in turn

will determine its figural grouping. From experimental data and musical experience it is well

known that “musically calibrated durations [are not] the fundamental processing units of

rhythm” (Serafine 1988: 60). Indeed notational figures used in rhythmic SMN are very

limited even at specifying relative durations: a crude arithmetic relation of twice as much, or

half, does not reflect the timing of even the simplest tune when it is performed musically.

More important, a tune can be perfectly recognised when the absolute durations of the events

are changed (as with changing articulations) provided that the attack points are preserved. A

primary role of rhythmic notation is not to specify the exact relative durations of events, but

rather the relative time spans between attacks, leaving the performer an “enormous latitude

[for] . . . the manner (legato-staccato) of filling them with sounds” (Monahan 1993: 127).

Even when absolute durations have an important role in determining grouping behaviour,

that comes as a mere consequence, or by-product, of the change in the rate of attacks (cf.

Povel & Okkerman 1981).

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In spite of this, most music syllabus approach the issue of durations from the stand point

of the durations of events. In conservatory courses all music figures (crochets, quavers,

semiquavers, etc.) are “taught” fairly quickly - usually in the first year of formal training (cf.

Musumeci 1998b) - relying in the common sense assumption that for teaching relative

durations as those represented by rhythmic notation, one needs at least two different

durations to compare between each other. But what that conceptions promote is the close

(and erroneous) association - in the learners representation of the event - of the different

dimensions of event attack point and event duration. In the teaching of notation the

distinction between this two dimensions must be carefully aided. If it is not so, the learner

will not understand what a notational figure - i. e. a quaver - stands for (it is usual to be

asked by first year students “how long exactly is a quarter note”).

It is for that reason that I propose to avoid the concept of figures’ duration at the

beginning of rhythmic notation teaching. In the examples presented so far it should be noted

that the syllables/quavers stand for isochronous beats in which events are attacked, with not

special concern with its duration. However, when chanting a rhythmic phrase students are

encouraged to perform so many subtle deviations in absolute and relative durations as

necessary for achieving the “sense” of the phrase. When chanting “like speaking” all

variations in timing (as well as in loudness, pause and pitch like in speech prosody) are

performed intuitively under the illusion of beat’s isochrony. By eliminating the factor of

figure’s durations the learner can concentrate in the “important differences between notes

that look the same on the page” (Bamberger 1991: 39). The simple figural percepts that arise

from different groupings at a single level (Example 6) - like if the quaver marked * can be

thought of as “forward looking” or “backward looking” - are basic and underlie all further

perceptual organisation involving different rates in the attacks of events, and in consequence

their formalization must precede the work with the different proportional durations

represented by the whole range of conventional musical figures.

But rhythmic teaching must also go on to help the grasping of that groupings that do

depend in gross variations in the rate of appearance of events, like the relations expressed by

conventional figures. This relations are indeed very few and simple: patterns composed of a

few events with attack points holding relations multiples of two and three, and further

rhythmic complexity is achieved through a hierarchical arrangement of these basic

“rhythmic contours” (Monahan 1993: 127). In traditional aural-training settings the

confusion between absolute and relative duration is perpetuated by means of the explicit

taxonomy of contents, that presents as different several groupings-of-figures that have in fact

a common figural-grouping when transposed to another metrical hierarchy (i.e., the groups

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half note - two crochets and crochet - two quavers are metrically (formally) different but

figurally identical.

The conflict arising from this ambiguity surely is one of the factors responsible for the

mismatch between novices’ figural and formal representations mentioned in previous

sections. I argue that the formalization of these hierarchical transpositions should come only

after the basic relationships of rhythmic contours have been grasped at a single metric level.

By introducing whole-beat rests to our ‘elemental’ prosodic phrases we can convey a whole

range of time-span proportions without the burden of introducing different durational

symbols. Since the goal is not to teach relations among figures but among time spans, this

method allows the learner to grasp the concept of duration as an abstract relation between

time spans, rather than a property of figures themselves. A whole range of rhythmic contours

can be conveyed without using more than just one metrical level (Example 7). Only after the

formalization of this rhythmic contours is that the “transposition” to other hierarchical levels

symbolised by the different range of durational figures makes sense.

A COGNITIVE PEDAGOGY OF AURAL TRAINING

The kind of training proposed so far has not the traditional goal of just teaching to read

rhythmic notation, but rather that the student should become an analyst of the notation to

find which factors will lead his/her cognition to reverse the process of formalization and

give rise to figural concepts. In a former section I argued that traditional teaching presents

formal descriptions (notations) tied to single figural interpretations, usually forgetting that

the sense made of music is not determined completely by the score, but rather is govern by

several factors with variable strengths and that may be in concordance or in conflict. Each

passage of music may have different preferred hearings - or figural interpretations. Lerdahl

and Jackendoff (1983) formalised the interplay of these factors in a set of preference rules

that establish “not inflexible decisions about structure, but relative preferences among a

number of logically possible analysis” (p. 42). It is paramount to show the learner how this

several preferred hearings originate from a single formal representation.

I consider a useful pedagogic tool for aural training classes to encourage the identification

of all “logically possible analysis” - in terms of prosodic feet - that may be performed over a

rhythmic surface. The simplest rhythmic phrase may be a source of enlightenment regarding

exactly what characteristics of musical understanding are reflected by conventional notation

and what others are ignored (Example 8).

13

By constructing and deconstructing the different figural representations corresponding to

different preferred hearings learners may gain a conscious access to the factors that govern

the formation of that representations. This factors, like Gestalt principles of temporal

proximity, similarity, and good continuation, and abstract concepts like balance between

phrases, symmetry, and motivic repetition, must be made evident to the students from the

beginning of teaching. This elemental, crudely stated, “well formedness rules” are perfectly

accessible to the music novice and constitute a basic premise for all further learning. The

educative power of the concept of preferences among competing organising principles

cannot be overestimated. Such concept does not play an accessory role in music reading but

on the contrary, good music reading consists in evaluating in real time the odds of each

different musical figure to arise from the current notation. This ability to foreseen the

chances of alternative groupings must not be considered just one more didactic devise to

gain proficiency in note reading but a fundamental component of musical understanding.

From this standpoint the ambiguity inherent to music notation represents not a marginal

effect of an inefficient system, but rather the space left for a “cognitive” interpreter.

Rhythmic complexity in most music is achieved by competing simple preferences at

multiple levels. But, regrettably, the prevailing didactic approach to rhythmic training in

conservatories and music schools indeed reflects a noteworthy lack of contact with the

principles of structural organisation that are at the heart of “musical intuitions”. I argument

that this lack of musicality is the consequence of confounding structural complexity with

sheer difficulty, confusion that in turn reveals a profound ignorance of the ways in which

human cognition “composes” and in turn interprets music pieces. If it is possible “to explain

artistically interesting aspects of musical structure in terms of principles that account for

simpler musical phenomena” (Lerdahl & Jackendoff 1983: 2-3), that imply that artistic

music teaching should always remain close to that simpler phenomena: “structural simples”

(Bamberger 1991) like Gestalt principles, temporal symmetry or balance, alternation

between stability and tension, and so forth.

CONCLUDING REMARKS

Aural training pedagogues must take into account what is now widely accepted in music

cognition literature: that artistic content - or musical meaning - is not an unexplainable

achievement of humans, but rather the output of very refined cognitive processes that are

common to the species and that are revealed by the widespread receptive music competence

14

of people. What that implies is that formal music learning - involving SMN or not - is

accessible to any person with standard cognitive abilities and exposure to music. The lack of

“ear” can be seen only as the failure to develop spontaneously the links between the inborn

and acquired cognitive processes underlying musical understanding and a formal system of

description. Keeping this in mind would reverse the charge of responsibility for learning that

we found in typical music settings, where the success of the learner mainly depends on his

ability, or talent, to pick up the musical knowledge provided by the teacher. A failure to do

so is considered most of the time as beyond the reach of music pedagogy. On the contrary, a

“cognitive teaching” would be attentive to the way in which learners make sense of the

musical phenomenon, and their success would heavily depend on how that implicit

knowledge is didactically developed - transformed from figural into formal - by the teacher.

What can be done to improve the communication between pedagogues and

psychologists?, and who can do it? Within the great diversity of lines and approaches, it

could be said that researchers in perception have done their job well. They have been

improving their methods, technologies and - more important - their theoretical frameworks

steadily during the last three decades, and there is a growing concern with achieving a

musical significance in their works. Perhaps music educators would be grateful if music

psychologists focused more on the evolutive aspects of the phenomena that they investigate,

and indeed it is very rare to find in the academic papers a explicit reference to the

transference of their findings to music pedagogy. But with regard to the teaching profession,

I am inclined to think that after all psychological findings are there waiting for music

educators to make sense of them. If somehow these findings may be too many for the

professional teacher to handle, it seems useful to outline a framework - articulating

pragmatic and theoretical concerns - inside which it could be assessed the relevance of the

psychological data for pedagogic ends. This work is an attempt to foreseen how that kind of

synthetic framework could enrich professional music teaching.

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18

Example 1

FORMALIZATION DIFFERENT FIGURAL INTERPRETATIONS

three events stress context

three heights articulation context

Example 2Es - ta ca - si - ta tie - ne ven - ta - nas

| | | | | | | | | | a steady beat

Es - ta ca - si - ta tie - ne ven - ta - nas

| | | | | | | | | |

Es - ta ca - si - ta tie - ne ven - ta - nas

| | | | | | | | | |

Example 3Es - ta ca - si - ta tie - ne ven - ta - nas

1 |________| |_______________| |_________| |________________|

Un ju - ga - dor ca yó des - ma - ya - do

2 |___| |________________| |_________| |______________________|

Ár - bo - les al - tos pó - da - los to - dos

3 |________________| |_________| |_________________| |__________|

Example 4

|_______| |_________| |_________| |____________|

|_________| |_________| |_________| |_________|

|____________| |_________| |_________| |_______|

|_______________| |________| |_______| |____|

Example 5

|_______| |___________| |_______| |____________|

|_________| |_______| |___________| |__________|

|____________| |____| |______________| |________|

Example 6 *

|____| |_______|

|_| |__________|

Example 7

= or

=

Example 8

1 The teaching of notation as a hard and fast rule for decoding a score, specially for instrumental reading, perhaps enables the musician to perform some very complex tasks from an orchestral stand, but if acquired at the expense of other music cognitive abilities - as it usually happens - it turns the music reader into a merely mechanistic “note reader”. The score should not be considered a mere prescription of the notes to be played or sang, but rather a description of the music that needs the interpretation of human cognition. The word description involves an active participation of the performer - or singer - who makes his/her own abstract representation of the music from the myriad of symbols in the score.

2 This figural - formal transaction is also paramount for instrumental performance. For a performer it is very important to keep in mind the figural aspect of music notation, because when reading a score he/she will have to reverse the process: a performance is the enactment of figural designs. When a poor sight reader reads a score for the first time, he/she is performing formal operations like counting, labelling, etc. Later the automation of this behaviour will help he/she to achieve a musical rendition, that will consist in the integration of that surface features in successively higher level arrangements, from motives and phrases to the whole piece (cf. Clarke 1988). A good sight reader who can make musical sense of a score the first time he/she reads it is in a sense performing the transaction formal - figural at a better rate. He/she is accessing alternatively, in quick succession, to different hierarchical levels of knowledge.

3 This procedure is at the core of any attempt to describe and analyse music. Its limitation is at the same time its strength. Any attempt to describe music needs a symbol system, discrete and finite (be it SMN or not) that could stand for, or represent, infinite musical relations. ¿Could a notation be devised with an increased number of categories? ¿Could a system be developed where, for instance, a specific pitch - that has a unique formal representation in SMN - may have many formal representations depending on its figural function within the musical context? In view of the success of Western written music to be transmitted by notation, we may at first think that the number of categories used for formalization in SMN has been optimal, but of course this is an issue like the chicken-and-egg argument.

4 It has been proposed that motherese - the infant-directed speech - exhibits universal prosodic features that are not only brought about by cultural tradition and education but also by genetic predisposition (Papousek 1987). The fact that “there is considerable similarity across languages in the prosodic correlates of utterance position” (Cutler et al. 1997: 159) suggests that the proverbial “universality” of musical language may lie in its prosody-dependence.

5 “The subjective perception of isochrony between spoken sounds correspond[s] . . . neither to equal interonset intervals, nor to equal durations of the sounds and/or silences between them, but to equal intervals between internal points of the syllables which play the role of ‘gravity centres’. . . isochrony in any language is not determined by acoustical properties of speech but by the isochrony illusion of the perceiver” (Gérard & Auxiette 1992: 101). Spanish speakers tend to assign a regular beat to each syllable, a type of timing that is called “syllable-timed”, in contrast to English language that is “stress-timed”, that is, not all the syllables but only the stressed ones tend to be evenly spaced in time. In syllable-timed languages “the metric organisation of music can be paralleled with the eurythmic principle in speech: in the two domains, small cells . . . are signalled by accents and concatenated in longer strings” (Gérard & Auxiette 1992: 100).

6 Words are specially relevant for this purpose because in Spanish each polysyllabic word is a foot with a nucleus (the accented syllable) and different unaccented components that may act as upbeats (co - ra - zón), afterbeats (tém - pa - no) or a combination of both (ca - lien - te).

|_| |___________| |__________| |___________|

|_____| |__________| |__________| |_______|