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STATE CONSERVATORY OF TURKISH MUSIC * TECHNICAL UNIVERSITY OF ISTANBUL“Issues Surrounding the Conflict between Theory and Practice in Turkish Musicand Potential Resolutions”, conference (by invitation) to be held in Istanbul,

3-6 March 2008

Constructing a Theory of Turkish MusicBased on Practice by Traditional Masters

Dr. Can Akkoç1

Institue of Applied Mathematics (IAM), The Middle East Technical University (METU),Ankara, Türkiye (Turkey)

Abstract: The plausibility of constructing a theoreticalmodel for Turkish Music, based on direct pitch measurementstaken from performances by indisputable masters is discussedwithin the framework of current sound technology. The intentis to set the stage for building a practice-basedtheoretical habitat capable of spawning models that canrepresent the music with optimal accuracy and applicability.As the sound structures in Turkish Music are uncovered bypitch measurements and statistical analyses over a massivedatabase, it appears, theoretical models presentingreasonable compromises between accuracy and practice may bewithin reach.

The `Universal` Scale

Pitch measurements on performances by indisputable mastersof Traditional Turkish Music have presented maqam scales inthe form of pitch clusters2, referred to as “perde”s in theTurkish lexicon, rather than single pitches, as in the 12t-

1 E-mail: can1936@gmail.com , written correspondence may be sent to ODTÜ, Uygulamalı Matematik Enstitüsü, Ankara, Türkiye (TURKEY).

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ET deterministic scale in Western music. Sampleimprovisations used in this study were taken fromtraditional masters with a very special request for stayingwithin the declared maqam for the entire piece, and notstraying into neighboring maqams, common practice in TurkishMaqam Music, so that characteristic musical patterns for thehost maqam could be determined without contamination throughseepage from other maqams. Furthermore, since these masterswere trained in the traditional meşk3 system, it is ourthinking and hope that the structure of the perdes making upthe underlying non-deterministic scales for various maqamsshaped4 in their musical memory were not influenced heavily,if at all, by theoretical models coming down the centuries,thus devoid of the conflict addressed in this article.

Given these circumstances and the associated assumptions, itappears reasonable to attempt construction of a theoreticalmodel for Turkish Maqam Music based entirely on pitch

2 [1] C. Akkoç, Non-Deterministic Scales Used in Traditional Turkish Music, Journal of New Music Research, Vol.31, No.4, December 2002, pp.285-293 (in English). [2] Kemal Karaosmanoğlu ve Can Akkoç, Türk Musikisinde İcra-Teori Birliğini Sağlama Yolunda bir Girişim, (Müz-Dak 10. Sempozyumunda Sunulan Bildiri; T.C. Kültür Bakanlığı yayını) Folklor Derlemeleri ve Müzik Araştırmaları, İstanbul Teknik Üniversitesi Türk Musikisi Devlet Konservatuvarı Mezunları Derneği, İstanbul, Türkiye, 3-5 Aralık 2003 (inTurkish).

3 [transliteration~meshk] In this grueling master-apprentice type learning mode music is passed on by endless repetitions involving reciting/performing/disecting/etc. compositions, melody and rythm, from traditional composers, ultimately followed by attempts, under the watchful eyes and never ending criticisms of the master, on improvisations in various maqams. Improvs are considered to be the pinnacle of musical practice in traditional Turkish music.4 As a typical example, Neyzen Niyazi SAYIN, featured in this article, is a legendary representative of the 5th generation of master musicians after the great Hammamizade İsmail Dede (1778-1846). Because of the meşksystem he was brought up with, we believe, Niyazi SAYIN’s musical memoryembodies acoustic details of the perdes, going all the way back to the Great Dede, presenting an incredible treasure of musical information andknow how.

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measurements from recorded/live performances of the mastersthat will not clash with practice.

Observations on the acoustic structures of perdes for alimited number5 of sample improvisations can be summarizedas follows:

Pitch clusters pertaining to the main perdes for agiven maqam presented pitch distributions that weresteep and compact compared with those of minor perdesplaying a secondary role in the maqam structure (Figure1) 6.

Minor perdes, on the other hand, displayed pitchdistributions that were wide spread, scattered,sometimes showing local clustering underneath the maindistribution (Figure 1).

Pitch distributions pertaining to certain minor perdesappear to be changing personalities or character, in thestatistical sense, depending upon their role in theunderlying scale of the maqam they are used in. As anexample, statistical structure7 of the perde Çargah, asit appears in the underlying scale for the Uşşak maqam8

(Figure 2), presents a totally different picture whenviewed in the underlying scale of the Sabã maqam(Figure 3).

5 Samples referenced in this article were taken from one particular master, Neyzen Niyazi SAYIN, at a certain day and time. Statistically they bear no significance in drawing inferences on the perdes. However, the intent in this article is not to present a complete perde structure for Turkish music. Instead, we try to set the parameters needed for ultimately getting to the said acoustic structure of the perdes in all maqams. 6 For all figures: Coordinates along the horizontal axis are musical distances, measured in cents, from the tonic, while vertical coordinatesrepresent the durations, in % of the entire piece, of the individual pitches used in the improvisation.7 General shape, range (width), compactness, etc. 8 Per the, so called, Arel-Ezgi system, a theoretical model currently used in schools of music.

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Figure 1. Pitch cluster at perde “Dugah” is, relatively speaking, steep and compact, while the perde in the “Kurdi_dik Kurdi” zone is wide and scattered. Both are legitimate perdes of the Uşşak maqam.

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Figure 2. Perde “Cargah” is 18 cents wide when used in the underlying scale for the Uşşak maqam, and has the shape shown in the histogram.

Figure 3. Perde “Cargah”, as it appears in the scale of the Sabã maqam, is now8 cents wide and has the distinct shape observed in the histogram. One could speculate that the perde Cargah is being pressured from the right by the “nim Hicaz-Hicaz” group, which is a major perde for the host makam, and does not havemuch room to spread(?).

Conclusions and Suggestions [universal scale]

In order to construct a universal scale of statisticalsignificance for Turkish music, sufficient number ofreliable samples need to be processed. Sample pieces9

9 We suggest that samples be sought that were not contaminated by motifs or fragments belonging to other maqams, as would be the case if the performer had been wandering around visiting neighboring maqams. This, we realize is a tall order. Requesting a pure improvisation from a master musician that does not delve into other maqams could be viewed asabsurd, almost like handcuffing the performer. However, if the master could be communicated that the proposition is entirely for purposes of

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representing different maqams collected into a massivedatabase, categorized and analyzed statistically afterstandard smoothing procedures, then followed by musicalanalysis targeting the maqam structures, probably calls fora major project of grotesque proportions. Such analysisshould also include statistical character determination ofeach perde appearing in more than one maqam.

Theoretical Model [universal scale]

There appears to be a pressing need for the development of atheoretical model capable of accomodating mathematicalprofiles of all perdes used in Turkish music for all maqams.Creators of such a model are going to be burdened, amongothers, with the following crucial problem: Given, theuniversal scale is formed by a sequence of pitch clusters,rather than discrete pitches, as in deterministic systems,what sort of mathematical representation would besatisfactory?

If a deterministic system is attempted, as widely acceptedin musicological circles globally, which particular pitch isgoing to be selected from each cluster to characterize thelocation of the clusters? Furthermore, some clusters presentsmaller accumulations, clustrettes, under the umbrella of awide and scattered cluster recognized as a single perde inpractice? Are such clustrettes going to be accounted for inthe deterministic system in any form or shape?

This inconvenient issue could be swept under the rug by aHamparsum10 type fuzzy tuning model, where the score laysout the road map for the journey between pitch clusters, andsays nothing about individual pitches to be selected fromacademic research, it may be received favorably.

10 Hamparsum Limonciyan (1768-1839) was an Armenian Ottoman composer of Armenian church music and Turkish classical music and musical theorist who developed the Hamparsum notation system. The system was the main music notation for Turkish classical music until modern times and is still used by the Armenian Apostolic Church.

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each cluster visited during the performance. It is expectedthat the meşk system will fill in the gaps. This, however,could be viewed as a major deterrent for beginners today whomay not have the dervish patience in their souls, needed tosurvive such a challenging and grueling experience.

Given the bleak picture skethed here, and until such time astochastic tuning system can be conceived, a deterministicsystem of adequate resolution, capable of accomodating theprofiles of pitch clusters to mimic the maqam structure withreasonable accuracy and compromise would be ourrecommendation at this point in time.

An alternative approach that might prove to be effective, inparticular for training beginning students in schools ofmusic, would be to construct a multi-level theoretical modelwith several layers of sophistication. However, the perdestructure, intrinsic to Turkish music should never beignored, even at the least sophisticated level. It may beplausible to build a cascade of models starting with aquasi-deterministic system, ultimately leading to a fullstochastic model11 for the master classes.

The Seyir12 Issue/Problem

We strongly believe the genetic structure, so to speak, ofTurkish Maqam Music lies heavily in the seyir issue. If sucha conjecture carries any merit, then the most urgenttheoretical issue would be to get to the bottom of thismusical structure. On the other hand, there are strong

11 It is conjectured that the seyir issue (discussed below) is going to bean integral part of the said stochastic model since the actual pitches to be selected from the perdes are thought to be dictated by where the music has been for the past several steps (short term memory) before getting to a given cluster. 12 A term of Arabic origin “sayr~path” used in Turkish lexicon for the melody line, or the path the melody follows.

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indications13 that this might be a formidable task, if not amission impossible.

If seyir is viewed, in the abstract, as a “sequence ofpitches” the melody line follows, then the seyir problem canbe formulated as constructing mathematical characterizationsfor all admissible seyirs14 for every maqam in Turkish MaqamMusic.

Durations of pitches in the seyir sequence is anothercritical parameter that demands special consideration. Infact, the sequence of durations of pitches may turn out tobe the centerpiece of the seyir problem down the road15. Inglissandos the durations are short and brief, whereas inslow moving passages they are longer and more persistent.

Most authors of theoretical works in Turkish musicinvariably suggest generic recepies for seyir in the maqamat16

discussed in their book. On the other hand, one sometimesruns into recordings or live performances of masters wherethe said recipes are violated just about every step of theway, and the seyir is still acceptable for the maqam onhand. In fact, such out of the box seyirs are sometimes viewedas a stroke of a genius, with lasting influences on thegenerations to follow.

Seyir over Pitch Clusters

From a different animated perspective, seyir can also beviewed as a journey between pitch clusters forming the

13 For Western music the only study we are aware of, resembling somewhatthe seyir problem in Turkish Maqam Music, is Dmitri Tymoczko’s work at Princeton University, referenced at the Internet address <music.princeton.edu/~dmitri>.14 It is conjectured that the set of all admissible seyirs for a given maqam is a countably infinite set. Then its complement, the set of all inadmissible seyirs, would also be a countably infinite set. 15 This statement is sheer speculation on our part at this point. Our apologies for such a bold venture.16 Plural form for maqam.

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underlying scale of the host maqam. The itinerary for thesaid journey -- which clusters are going to be visited inwhich sequential order, and how long will each visitationlast(?) -- is believed to be determined by the inspirationalmood/mode of the composer for formal compositions, and ofthe individual performer in free improvisations.

However, such itineraries can never be totally random walks.On the contrary, certain flow patterns, no matter how fuzzy theysometimes might get, pertaining to the host maqam must beobserved. The meşk system, after all, can be viewed as asetting where the master transmits such wealth of stochasticpatterns to the apprentice, with possibly some room allowedfor fuzziness at a higher level to stimulate the futuremaster’s creative faculties.

This introduction immediately brings up a crucial question:Given, the perdes in the underlying scale are made up ofpitch clusters17, how does a performer decide exactly whichparticular pitches should be selected from each cluster asthe music weaves its way between the perdes?

This question could be neutralized and swept under the rug bysuggesting that the meşk system has evolved precisely toaddress this extremely critical issue. An aspiringapprentice accumulates and assimilates such stochasticpatterns after an almost never ending ordeal under constantrepetitions. Yet, in this article we are interested ingetting down to the genetic code of this matter inmathematical terms, no matter how fuzzy things might get.

What we have been able to conceive so far in the way of athinking model is that of a “short term memory”18, plausiblyembedded in pitch sequences forming the melody line. This17 Such stochastic structures are not necessarily unique to Turkish music. A theoretician in the West, Willam A. Sethares, suggests “Similarobservations have also been made concerning Western performances.” in his book “Tuning, Timbre, Spectrum, Scale”, Springer, 2nd Edition, 2005,page 71.

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model suggests that, what directs the flow of music to a particular pitchwithin a given cluster, about to be visited, is the sequence of pitches selected justbefore getting to that cluster.

We strongly believe, the genetic code for such musicalphenomena, if this turns out to be the case, is embeddedentirely in the seyir problem and will begin unravel itselfif and when the admissible set of seyirs are completelycharacterized for the maqamat in Turkish Maqam Music.

Conclusions and Suggestions [seyir]

Although the problem, as posed and partially formulatedhere, appears to be a tall order for the author, newmathematics coming down the pipeline during the past fewdecades, particularly those intended for infrastructuringthe computers, might generate a stimulating setting for amathematical resolution to the seyir problem.

A few examples of such mathematics would be hidden Markovmodels, machine learning, neural networks, Kohonen maps(self organizing maps_SOM), Farey series, symbolic dynamics,formal languages, and data mining techniques.

The search and the expedition continues. However, the onlyprogress report we are able to present at this time, in termsof concrete results, is none other than that of the five blind18 When the manuscript for the article referenced above in footnote #2 (Akkoç) was reviewed, one of the referees was reported to have commented, “I consider especially useful the finding of two different tunings: the micro and the macro level "grand space". The suggestion that micro level is strongly connected to the concept of the short term memory gives good possibilities to connect the study of scale systems tocognitive processes. Actually, the term "cognitive reference point" could be easily related to the finding of sound clusters, that were called in the paper as "anchor notes". For the future steps I believe that the author would benefit a lot if she/he would have time to be morefamiliar with the main concepts and approaches in cognitive psychology of music.”

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men and the elephant. We are sorry for not being able to endthis report in a more positive note.

Can Akkoç