practicality in dmitri tymoczko

8/10/2019 Practicality in Dmitri Tymoczko

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Practicality in Dmitri Tymoczko's Graphs

Today's music industry is made up, for the most part, by performers, composers and non-musicians who deal with managerial aspects of what the rest of them require !usic theoristsha"e the #oy of disco"ery what the others seems to o"erlook, not that it is any consequence oflaziness or obli"ion but rather that their area of e$pertise doesn't apply the insistent demandfor the music's e$istence % draw a thin line between composers and theorists partly because of how they are percei"ed by the rest of the industry, most ob"iously by their output, not in theamount but who their output reaches & composer's finished product can be heard by anyone

#ust as a theorists product can be e$amined by anyone f course, the aural element is muchmore palatable to a wider audience than understanding a gamut of foreign equations andterminology

"..it is possible that with extensive training ordinary listeners can sensitize themselves to the sequences structure.."

Dmitri Tymoczko is one of those indi"iduals who has dug deep to disco"er new formations(eing able to defending what composers ha"e gi"en us is an integral part of composing and

performing !usic of the future is influenced by studying music of the past %n Tymoczko'sresearch the details go far to #ustify his ideas but to often these ideas seem to be e$aggerated%'m in no intellectual position to brush off Tymoczko's findings on grounds that there are toomany e$ceptions or that details don't matter !y hope is that by applying these tactics to somefamiliar pieces in my standard repertoire % can better understand the conte$t of where hisconstraints and graphs can impro"e my understanding of a musical genre, set of works or )atthe "ery least* an indi"idual piece of music

&s Tymoczko leads us through a redisco"ery of what is already known he first presents a powerful statement whose only purpose is to completely confuse us, then he has theopportunity to slowly rebuilding the concept %n our state of ignorance e$amples are pulledfrom many different breeds, such as his reference of a +lementi sonata and some Debussywhen detailing his PT%+ system e are in no position to slow our rebuilding process byquestioning the significance of his methods and how they relate to the entire collection ofthose composers' music The e$amples compliment his current argument well but may pro"eunable to stand up to their claims when more is to be pro"ed

e are taken through a maze of models and instances of the PT%+ application and itsimportance of simplifying chords we encounter The pitch-class philosophy is not a comple$item to iterate The lengths he goes to spell out the different ways to interpret distance seemswasteful uckily, if in the earlier chapters of his book % ha"e missed the boat captained byDmitri at least % ha"e his pardon . it is possible to understand the gist of later chapters e"enwhile remaining somewhat fuzzy about the technical material in +hapters /01 .

Pitch 2pace "s Pitch-+lass


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3oice eading is taken to a whole new le"el by Tymoczko &gain, the process remains thesame while our understanding of it is o"ershadowed by the elaborate attempt at e$posing newideas Trained musicians can already see these chordal relationships that the PT%+ systemrepresents ur theory 454 courses con"eyed "oice leading well enough to trust (ach,+lementi, 6aydn and !ozart &s we witness in the following century we can see a slow

progression of creati"ity and risk taking of 47th century composers e had music thatforeshadowed agner such as the e$perimentation by (eetho"en in his late career, eber and

iszt Tymoczko's "oice leading theories are so forgi"ing in that they allow a melody to #ustify any harmonic progression %t's hard to conceptualize a ma#or chord being anythingmore than ma#or Tymoczko lays out e"er relationship between standard chords in terms ofsemi-tones and then retraces his steps claiming that more is to be seen in between thenotes The pitch-class system ultimately remo"es one problem we encounter when condensinga chord for the purpose of identifying it8 which pitch will be the constant as the other "oicesare mo"ed to an appropriate octa"e within a 4/ semi-tone space near the constant note arger gaps within the newly arranged chord can be quickly eliminated by repositioning notes, one ata time, from one end of the chord to the other until the smallest number of semitones e$istsThe same can be done to the neighboring chords to see if the "oice-leading is effecti"e

"Thus when we say that an object is a major chord, we are neglecting an enormous number of musical details, leaving behind something that is very abstract an ordered sequence ofcloc!wise distances around the pitch class circle.#

The phrase .chord progression. seems to be equi"alent to cursing when Tymoczko uses it 6is portrayal is that we don't see the mo"ement in the "oices from chord to chord 6is pitch-classwheel does present a new "isual for following a particular "oice but forces us to completelyturn off our ears !usicians using the pitch-class system )that has already been set place by

pre"ious theorists, like 6oward 6ansen* know to use it only for brief isolation of a "oices path Tymoczko's pitch space graph )or line* is less in"asi"e to our sensiti"ity toward "oicemotion 6ere there is an equally as simply layout with a "oice's path easy to distinct from itscolleagues 6is wording is so bold that you'd think he is defending a new standard fornotation e'"e always been able to mo"e from chord to chord in multiple ways, is he reallythe first one to point out the shortest path9 :o one wishes to use a pitch system that forces usto ignore "oice leading and settle for a .tunnel "ision. approach to chord analysis %n the caseof most other theories there is no need to lea"e out a reference to pitch on some sort of"ertical gauge unless eliminating doubling on the staff pro"es to be far too cumbersome -2piral piano

(ut back to the PT%+ system; Tonal music illustrates a state of aural homeostasis8 adhere

to the guidelines and you'll fit right in The procedures e$plained in $ %eometry of &usic arequite broad 2o often Tymoczko walks us through a chord to chord modification showing ourcurrent staff notation side-by-side to the graphs of the newly introduced pitch space and pitch-class systems and then halts the discussion before relating any con"incing element of scienceThis book is all about using the math to #ustify "oice-leading paths but there is a significantlack of mathematical equations The application of a combination of permutation, in"ersionsand the others operations can create endless potential in harmonic progression but the details


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are missing that should include specific equations for creating the desired mo"ementTymoczko anticipated public connection to his book would be much impro"ed if a companionmanual containing these equations e$isted %t is unclear where the math and science arein"ol"ed in the PT%+ symmetries

Tymoczko insinuates that "oice leading is incorrectly taught in regard to the size of the "oice-leading %n a search for


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tempered instrument with twel"e pitches and then looking at how the octa"e is di"ided on thestaff (y comparing wa"e length and our diatonic scale system we are decei"ed %n fact, whenunderstood through this process, augmented chords become the nearly e"en triads and ma#ortriads are perfectly e"en This makes more sense on paper before applying it to an instrument%n the three dimensional chord theory, this replaces the augmented cubes with ma#or cubes(y di"iding the scale like Tymoczko we ha"e not created greater or fewer possibilities forharmonic progression but #ust changed where the central a$is appears 6e prefers the methodin his book because it applies so fairly to the (rahms Piano Cuartet he presents %f mysuggestions were e$plored the outer limits of the three dimensional tiles would be well suitedfor the baroque and classical styles

%f ma#or chords act as the focal point then this three-dimensional space would translate easilyinto representing mo"ement between scales )more appropriately modes* &s we mo"e fromthe cube that represents the + ma#or scale one note is altered There are si$ options closelyrelated to the scale and then three for the one following %f working with baroque or classicalstyles few scales will be utilized but, as Tymoczko e$plains, (rahms, 2hostako"ich andDebussy will use many e$otic scales :o matter the way the octa"e is di"ided, chords withdoubled notes will still be found on the walls of the diagram, strongly suggesting that the

piece of music at hand is not tonal %f a composer were applying this system to a new piece ofmusic written in the late romantic style he would find it useful in finding desired "oiceleading on a chord-to-chord basis or at most the motion o"er a small phrase

% appreciate math@s presence in music and % use it as often as needed The circle of fifths is anin"aluable tool for training and reading music by referencing the distance from one note to thene$t rather than resetting the brain for e"ery change The significance of using small distancesfor "oice leading and harmonic progression is reawakened by the in-depth application ofTymoczko@s symmetries (y bewildering and then con"incing the reader that these findingsare original encourages more credit than is due Pitch space and three-dimensional diagramsassist in the redisco"ery of what we already ha"e understood ith the help of other theoristssuch as ulian 6ook

not enough math A$cuses it as science

ulian 6ook, Eoger 2cruton

riginal but e$aggerated


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Ee"iew of Dmitri Tymoczko, & Geometry of !usicB 6armony and +ounterpoint in theA$tended +ommon Practice ) $ford Fni"ersity Press, /544* ulian 6ook httpB www mtosmt org issues mto 44 4> H mto 44 4> H hook html

Dmitri Tymoczko -6andouts 1 and /5httpB dmitri mycpanel princeton edu files pdfs !F245Ihandouts pdf

2cruton The 2pace of !usic / review of The Geometry of !usic httpB www roger-scruton com work-in-progress 47-books J7-the-space-of-music html
http://www.mtosmt.org/issues/mto.11.17.3/mto.11.17.3.hook.html#AUTHORNOTE1http://www.mtosmt.org/issues/mto.11.17.3/mto.11.17.3.hook.html#AUTHORNOTE1http://www.mtosmt.org/issues/mto.11.17.3/mto.11.17.3.hook.htmlhttp://dmitri.mycpanel.princeton.edu/files/pdfs/MUS105handouts.pdfhttp://dmitri.tymoczko.com/geometry-of-music.htmlhttp://www.mtosmt.org/issues/mto.11.17.3/mto.11.17.3.hook.htmlhttp://dmitri.mycpanel.princeton.edu/files/pdfs/MUS105handouts.pdfhttp://dmitri.tymoczko.com/geometry-of-music.htmlhttp://www.mtosmt.org/issues/mto.11.17.3/mto.11.17.3.hook.html#AUTHORNOTE1

practicality in dmitri tymoczko

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