EXPERIMENTS ON THE RELATIONSH IP BET WEEN PERDE AND SEY _IR I N TUR KI SH

MA KA M MUSIC

CAN AKKOÇ

The Middle East Technical University (METU)Ankara, Turkey

WILLIAM A. SETHARE S

University of Wisconsin

M. KE MA L KA R AO SMA NO GLU

Yıldız Technical University,Besiktas, _Istanbul, Turkey

‘‘WHEN I WAS A KID, THE ELDERS IN THE VILLAGE COULD

TELL THE MAKAM OF A PIECE JUST BY LISTENING.’’ Whileinterviewing performers, enthusiasts, and experts in tra-ditional Turkish taksims (improvisations), variations ofthis comment were made many times. Some of therespondents claimed to be able to identify the makamof a taksim, but others believed that this ability mightnow be a lost art. This paper documents a series ofexperiments (based on caricaturized or skeletonizedtaksim-like creations) designed to determine if it is pos-sible to identify the makam from purely acousticalfeatures, and, when possible, to determine the relativeimportance of the various audible features that may beused to establish the makam. Two basic classes of fea-tures are investigated: perde (the set of pitches used inthe performance) and seyir (which relates to temporalmotion within the piece, for instance, repetitive or com-mon motives or melodic contour). The experimentsprovide evidence that both kinds of features contributeto the ability to recognize makams. Experiments thatrandomize the order of events show that pitch cues(perde) are often adequate to allow accurate identifica-tion of the makam. In experiments where both pitchand temporal cues are present but conflict (for example,a piece in which the perde is chosen from one makamand the seyir from another), experts often favor thetemporal information.

Received: March 13, 2013, accepted April 5, 2014.

Key words: Turkish makam recognition, AEU system,recognition of scale and key by experts, motif in Turkishmusic, taksim (improvisation)

M AKAM IN TURKISH TRADITIONAL MUSIC

refers to a style in which each makam-typenames a pitch structure (called perde) and/or

specific patterns of motivic/temporal development(called seyir). When hearing a makam performance,a listener will typically have access to more informationthan just the sound: the performer may be known, theparticular piece may be familiar, it may be recognizedfrom a specific place or previous time. Thus the ‘‘elder’’in the ‘‘village’’ of the introductory quote may indeedcorrectly recognize the makam, but this identificationmight stem from extra-musical information and notnecessarily directly related from the acoustic structureof the sound itself. As will be shown in Experiment 1,such extra-musical information is not necessary for cor-rect identification; expert listeners can reliably deter-mine the makam from audible features alone. Thisleads to the second major question that is explored inExperiments 2 through 4: which features of the perfor-mance are key to the ability of an expert listener toidentify the makam? The experiments are structuredso as to investigate the relative importance of the perde(pitches) and the seyir (temporal motion) in the task ofidentifying the makam of a piece.

BACKGROUND

Turkish makam music is primarily an oral traditiontaught on a single instrument using a ney (an end blowncane flute), a kemençe (a bowed stringed instrument),the voice (hanende), or other traditional instrument.Learning typically occurs in a master-apprentice settingthrough extended repetition (mesk). There are (at least)two major kinds of pieces: composed (beste) and impro-vised (taksim). Popular makam music is typically het-erophonic, rhythmic, and performed with percussionaccompaniment; improvised forms are typically soloperformances played with a flowing and relativelyunstructured rhythm. A makam can be viewed asa musical setting with (a) a well-defined underlyingscale of pitches, and (b) a set of conventions that struc-ture the temporal ordering of the pitches into melodiclines.

The standard theoretical explanation for Turkish pitchsets is given by the ‘‘national theory of Turkish Music’’

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322 Can Akkoç, William A. Sethares, & M. Kemal Karaosmanoglu

called the Arel-Ezgi-Uzdilek System (AEU) (Arel, 1968;Ezgi, 1933), which can be viewed as a 24-note set con-structed from Pythagorean commas, and which can beclosely approximated by notes from the 53-tone-equaltempered system (Yarman, 2008). Empirical perde scales(in contrast to scales derived from theoretical considera-tions), have recently been investigated by taking pitchmeasurements on performances from renowned masters(Akkoç, 2002; Bozkurt, Yarman, Karaosmanoglu, &Akkoç, 2009). For example, Figure 1 shows the similar-ities and disparities between the theoretically-derivedscale pitches and those measured in performance.

While there remains controversy about the accuracyand applicability of the AEU classification to makamperformances, both proponents and critics of the AEUsystem agree that it is based primarily on pitch relation-ships. Within the AEU system, more than a hundredmakams have been described and labeled as in Figure 2,which are drawn from Karaosmanoglu et al. (2009). Themusic-theoretical information in Figure 2 is comple-mented by a numerical representation in Appendix Athat is used to quantify the interval-set relationsbetween the various makams. Recent work (Bozkurt,Gedik, Savacı, Karaosmanoglu, & Ozbek, 2010) suggeststhat automated classification of makams can be accom-plished with considerable accuracy using only pitch-histogram information. In terms of the introductoryquote, it is reasonable to posit that it may be possibleto recognize the makam of a piece purely by listeningcarefully to the pitch relationships within the perfor-mance. Since perde is the Turkish word for tones or pitchclusters, we call this the perde hypothesis for makamrecognition.

Others argue that the seyir (a complex of stereotypedmotives, melodic signatures, and latent melodic possi-bilities) associated with each makam is crucial to itsidentity. Akkoç (2008) views seyir as a ‘‘journey betweenpitch clusters forming the underlying scale of the hostmakam.’’ Castellano, Bharucha, and Krumhansl (1984)observe that this is analogous to an Indian rag, which ischaracterized both by its scale and by the manner andorder in which the scale tones are combined. Thus therag in Indian music forms a basis on which melodiccomposition and improvisation may occur. Similarly,the Turkish form exploits sets of scale tones and collec-tions of melodic figures, motives, and patterns that utilizethose scale tones. For example, Beken and Signell (2006,p. 205) state, ‘‘Every instrumentalist chooses from amongconfirming, delaying, and deceptive elements to createa taksim in a given makam. These elements may includegeneral melodic direction, certain intervallic relation-ships, modulations, and most importantly, cadential

points, often coming after stereotyped motives.’’ Similarly,the New Grove Online Dictionary (2013) describes seyiras indicating ‘‘prescribed modulations and the generalshape of phrases, understood as either predominantlyupwards, predominantly downwards, or a combinationof both.’’ The New Grove article on mode credits Kante-mir (1698/2001) with defining a term for melodic progres-sion, and comments that ‘‘the seyir spans a framework oftonal centers’’ that includes the root, the octave above theroot, and other key tones.

Conceiving of seyir as central to the notion of makamsubordinates pitch elements to temporal elements such asmotives, patterns, and melodic contour. A recent study ofrelated Arabic improvisations (Ayari & McAdams, 2003,p. 159) shows ‘‘the melodic reductions of segments ina given maqam reveal the nature of Arabic modes asinvolving not just a tuning system, but also essentialmelodico-rhythmic configurations that are emblematicof the maqam.’’ Confirming this view, our experts wereasked (at the conclusion of the experiments) what theylisten for when trying to determine the makam. A typicalresponse was that of Expert 2 who said, ‘‘I listen forcertain sound patterns, like this (singing) in Ussak or likethis (singing) in Hicaz.’’ Tanrıkorur (2005) states thatmakam encompasses both a pitch structure and (unwrit-ten) rules for melodic progression that must be strictlyobserved by composers, and memorably states thata makam is 20% pitch and 80% seyir. We call thismelodic or motivic notion that emphasizes the temporalaspects of a makam the seyir hypothesis for makamrecognition.

RELATED LITERATURE

The domain of music psychology has only recentlybegun to consider experimental work on the perceptionof Middle Eastern music, and such studies are limited.Ayari and McAdams (2003) consider a segmentationparadigm that contrasts Arab listeners and European

FIGURE 1. This cumulative histogram displays pitch clusters in eight

taksims (improvisations) in the Ussak makam and contrasts these with

the theoretical pitches shown by the tall vertical lines. The horizontal

axis is given in cents with respect to the root at zero, the vertical axis is

the percentage of time spent on each pitch. Shades of gray correspond

to different octaves.

Experiments on the Relationship between Perde and Seyir in Turkish Makam Music 323

listeners, and investigates the ways in which these twogroups partition melodic passages within a makamstructure. Thus they are able to investigate cultural dif-ferences in listening strategies. Our tests are quite dif-ferent since they require identification of the makamdirectly from the audio, a task that those unfamiliar withthe genre are unable to accomplish. Indeed, Ayari &McAdams (2003) observed that some of their Arabmusicians were able to detect and describe modal struc-tures such as the makam of melodic passages. It is thisability, within the context of Turkish makam music, thatis the primary focus of the present paper.

Castellano et al. (1984) define tonality as the ‘‘center-ing of the musical materials around a particular tone,’’and thus tonality provides one way of structuring and

organizing sound materials in music. For example, inWestern music, the tonic is a reference tone associatedwith the musical structure called the key. More generally,the tonic provides a reference point whereby a set ofmusical pitches may be perceived in relationship to thattonic. Bharucha (1984, p. 421) comments that ‘‘consid-erable exposure to pieces of music that are structurallysimilar gives rise to the . . . tonal hierarchy’’ and suggeststhat the temporal ordering of tones may be able toactivate tonal schemas that are held in long-term mem-ory, a view that is at least partly supported by Boltz(1989). In this general sense, Castellano et al. (1984)provide evidence for the tonal perception in classicalIndian music using a probe-tone technique that com-pares the responses of Western and Indian listeners.

FIGURE 2. Twenty-four makams that appear in this paper are represented in the AEU system. Special symbols are used to indicate the root, the

dominant, and the leading tone. Many of the accidentals represent pitches that fall between the cracks of the Western musical scale. Makams may be

characterized as the conjunction of an n-chord and an m-chord (where n + m = 9), for example, a tetra-chord and a penta-chord, as indicated by the

grouping markers that connect the root and the dominant, and the dominant with the upper octave of the root). These samples are drawn from the

software Mus2okur (Karaosmanoglu et al., 2009), which lists basic makams as well as hybrid combinations (or transposed forms) in commonly used

genus patterns. These interval sets are shown numerically in Table A1.

324 Can Akkoç, William A. Sethares, & M. Kemal Karaosmanoglu

In Turkish makam music, the tonic may be identifiedwith the root tone (as in Figure 2) and the hierarchywould include an n-chord and m-chord (for example,a tetra-chord and a penta-chord) as indicated for partic-ular makams by the grouping markers in Figure 2. Thetonal hierarchy is also evidenced by the most importantsatellite tones such as the leading tone and the dominant(in Turkish music, the dominant may be a musical fifth,but it may also be another interval; it is characterized asthe pivot tone that is common to the n- and m-chords).

Using the probe-tone technique of Krumhansl andShepard (1979), Oram and Cuddy (1995) addressedlisteners’ responses to pitch distributional informationin melodic sequences, concluding that more frequenttones (or those with greater total duration) tend to berated as fitting the melodic context better than less fre-quent tones. Both musically trained and untrained sub-jects were responsive to distributional informationwhether the context was a diatonic subset of 12-toneequal temperament or whether it was a nondiatonicsubset, although greater familiarity with tonal materialmade the task somewhat easier. Similarly, using probe-tone studies inspired by the music of Northern India,Castellano et al. (1984) found that the most frequenttones were rated as best fitting the melodic context. Themost common tones in Turkish makam music tend tobe aligned with the most important tones in the pitchhierarchy (the root and the dominant). The melodicmotion tends to be characterized by the establishmentof a pitch center with many small deviations about thatcenter, followed by a motion to another pitch centerwith deviations, and so on. Accordingly, the perceptualrecognition of a makam may be due to the pitch set itself(and the corresponding frequencies of occurrence of thepitches), although it may also be due to the temporalarrangement of the pitches. This dichotomy nicely par-allels the distinction between the perde hypothesis andthe seyir hypothesis that the experiments of this paperare designed to untangle.

OVERVIEW

Experiment 1 establishes that expert listeners canindeed pinpoint the makam from acoustic clues alone(since the sound examples contain no extra-musicalinformation such as performer or location, and are pre-sented with a uniform synthetic timbre). Experiments 2through 4 were then designed in an attempt to distin-guish the perde hypothesis from the seyir hypothesis.A key technical element in these experiments is thegeneration of sound examples where the two aspectsof the makams (perde and seyir) can be separatelycontrolled, combined, and resynthesized. A series of

synthetic taksims (or caricatures) allow precise manipu-lations of the sound, emphasizing and distorting theperde and seyir until they become unrecognizable, so thatpotential outer limits of these two interactive core ele-ments can be ascertained, as much as possible. Construc-tion of the sound examples is described in the stimulussection of each experiment with further technical detailsin the Appendices.

A small number of experts were asked to participatein the experiments. Each is a recognized master of Turk-ish makam music, and brief biographies are presentedin the section on participants. The various experimentswere conducted at intervals of about one week (accord-ing to the availability of the experts). The experts werenot all available simultaneously, so the (roughly) fourweeks of the experiments were staggered over themonths of October and November 2012. From theexpert’s point of view, each experiment is simple. Theyreceived an e-mail (or disk) containing a set of six toeight short sound examples. The duration of the exam-ples is between one and three minutes, depending onthe particular goals of that example. The listener isasked to state what makam (if any) is represented bythe examples. The experts may listen to the examples asmany (or as few) times as they wish, and return theirevaluations by e-mail. The experts were not given anyhints about which makams might be used (so any of theroughly 100 makams conceivably could have appearedin any of the sound examples). After each experiment,the experts were eager to find out more information,and we discussed the sound examples with them inorder to encourage their continued participation. Wedid not disclose details of how the sound examples wereconstructed, and none of the experts had contact witheach other over the duration of the experiments.

Each of the four experiments was designed to test themakam-identification problem in a different way. Inmany cases, the experts agreed in their assessments. Insituations where there was disagreement, it was usuallypossible to look carefully at the way the experiment wasconstructed to reveal plausible reasons for the ambigu-ity. The Discussion and Conclusion section considersthe results of all four experiments together and triesto draw lessons based on all of the experts’ responses.Stripping away all appropriate caveats, the major resultscan be summarized as follows: in the absence of tem-poral cues, pitch cues are often enough to allow accurateidentification of the makam. If both pitch and temporalcues are present but conflict (for example, a piece inwhich the pitches are chosen from one makam and thetemporal information from another), experts oftenresponded most strongly to the temporal cues.

Experiments on the Relationship between Perde and Seyir in Turkish Makam Music 325

Experiment 1: Establishing a Baseline

As commonly performed, a taksim has three sections:an exposition that establishes the host makam, a middlesection that potentially explores other makams, anda recapitulation that restates the host makam, (seeBeken & Signell, 2006). Thus it is not realistic to expectthat every segment within a given performance lies fullywithin the host makam. In 1986, while visiting Worces-ter Polytechnic Institute, the first author asked notedney (an end-blown flute) performer Niyazi Sayın torecord a collection of short ‘‘skeleton’’ taksims thatremained fully within the host makam. The result wasseventeen improvisations in makams Buselik, Eviç,Hicaz, Hicazkar, Huseyni, Isfahan, Mahur, Muhayyer,Neva, Nihavent, Rast, Saba, Segah, Sultaniyegah, Suzi-nak, Ussak, and Yegah. These may be heard in theiroriginal form on the Makam Experiment Website(Sethares, 2014) and form the core of the data usedthroughout these experiments. All of the sound exam-ples from the experiments, as well as intermediate filessuch as the MIDI data files, are also available. NiyaziSayın has also contributed to this work by acting as oneof the experts.

PROCEDURE

In order to create the synthetic taksims for the experi-ments, the seventeen improvisations were analyzedand transformed into MIDI files where they couldbe more easily manipulated. Steps in this transforma-tion are detailed in the stimulus section. The MIDIfiles were then rendered back into audio using a syn-thetic ‘‘bamboo flute’’-like sound that is reminiscent ofthe ney but without the breathy sounds. Six of theseresynthesized taksims were chosen to be the soundexamples for Experiment 1: Hicaz, Isfahan, Muhayyer,Neva, Rast, and Ussak. These six soundfiles wererenamed (so as to hide their origins) and the orderwas randomized (so that the soundfiles, when viewedby computer, would not appear in alphabetical order).They were e-mailed to the experts who were askedone question:

Q: ‘‘What makam, if any, is each piece performed in?’’

The experts were given no hints as to the reason for thequestion (other than a very general ‘‘we are studyingthe makeup of makams and taksims’’) and no hints asto the origin of the pieces. In particular, they were nottold that the ‘‘intended’’ answer would be from amongthe seventeen taksims recorded by Niyazi Sayın ; indeed,there are over 100 different makams catalogued in

standard references (Arel, 1968; Ezgi, 1933), so therange of possible answers is large.

Experiment 1 may appear simple, but it immedi-ately confronts the question of whether experts areable to recognize a makam using auditory clues alone.Moreover, it addresses several issues that are crucialfor successive experiments. To the extent that themakam remains recognizable, it shows that the pro-cess of transforming the original improvisation intoMIDI and then back into sound does no harm. Forexample, it shows that the timbre of the instrumentalvoice is not crucial (since the original is a breathyend-blown flute while the MIDI rendering is a rela-tively simple synthesized flute). It also shows that theremoval of the pitch glides from the original does notharm the recognizability of the makam. It shows thatwhatever errors may occur in the pitch tracking algo-rithms are not crucial. In short, it justifies asking thesame question Q when more substantial changes aremade to the improvisations, justifying the experimen-tal paradigm followed throughout the remainingexperiments.

PARTICIPANTS

The listening tests described in the experiments arequite different from tests with ‘‘naive’’ subjects wherethe aim is to understand the perceptions and abilities ofnormal listeners. In this case, naive listeners (includingmost of the authors) cannot correctly name the makamof a piece by listening to it. Accordingly, it was necessaryto ask experts. Such experts are not easy to find, and soit was not possible to run the experiments on a largenumber of subjects (as would be required for a statisticalanalysis). In some cases, potential experts were deterredfrom participating out of worries that the experimentswere a test of their expertise, or a competition amongstthe various masters of the genre.

The authors were fortunate to find three experts whowere willing to devote time and energy to listening tothe sound examples and answering the (apparently)simple question Q. All three gave their permission tobe named here as participants. Once engaged, theexperts appeared to enjoy the task, and clearly took itseriously. The experts were often confident of theirassessments, although some worried in their e-mailresponses whether they ‘‘got the answers right.’’ Onesaid the experiments of the final test set ‘‘were designedto torture. Everything in them was tinkered with, anddesigned to fool and deceive’’ indicating that the taskswere not always easy.

This section presents basic biographical informationabout the experts.

326 Can Akkoç, William A. Sethares, & M. Kemal Karaosmanoglu

EXPERT 1: N_IYAZ_I SAYIN

Neyzen Niyazi Sayın (1932– ) is a legendary represen-tative of the 5th generation of master musicians follow-ing in the tradition of Hammamizade _Ismail Dede(1778–1846). According to Holtzberg (2008), he isregarded as one of the most important living ney playersin Turkish classical music. His musical geneology can betraced through his teacher, the painter and ney playerHalil Dikmen (1906–1964), who was the student ofAhmet Irsoy (1869–1943), who was the son and studentof Zekai Dede (1825–1897), who was the student ofHammamizade _Ismail Dede. Sayın’s mesk, which Gill-Gurtan (2011) describes as the practice of music trans-mission, is an oral tradition that places him in a longline of masters who perform makam compositions andimprovisations, deal with the culture surrounding themusical performances, engage in arduous training inboth listening and performance, and feel a strong senseof a social identity and responsibility for the preserva-tion and continued transmission of the style.

EXPERT 2: RUH_I AYANG_IL

Ruhi Ayangil (1953– ) started playing Kanun at the ageof 10. He graduated from the Faculty of Law at IstanbulUniversity in 1979 and was a student of _Ihsan Balkır atthe Istanbul Municipal Conservatory where he studiedharmony and orchestration with Cemal Resit Rey.Between 1973 and 1981 he trained and conducted thechorus of Robert College, Istanbul and taught courses inTurkish music. Ayangil’s book ‘‘Learning To Play theKanun,’’ based on Alnar’s technique, provided a basisfor lectures while a member of the faculty at the IstanbulUniversity State Conservatory. In 1988 Ayangil’s Turk-ish Music Orchestra and Chorus made the first record-ing of ‘‘Uyan Ey Gozlerim’’ (Ottoman Sufi Music),compiled by Ali Ufki (1610–1675). Ayangil was awardedthe title of ‘‘artist of the year’’ by the Turkish WritersAssociation for this recording, and he has received sev-eral awards for his research into the roots of Turkishmusic and its evolution. He has now retired as Dean ofthe Faculty of Art and Design, Istanbul Yıldız TechnicalUniversity.

EXPERT 3: NECDET YASAR

Necdet Yasar (1930– ) is a tanbur (lute) player, musicteacher, and a founding member of the Istanbul StateTurkish Music Ensemble. In 1991 he was awarded thetitle ‘‘National Artist’’ by the Turkish government, andSignell (2011) notes that he is a leading tanbur playerwho has performed classical Turkish music throughoutthe world. Yasar was the pupil of Mesut Cemil, son ofthe legendary Tanburı Cemil Bey. According to Aksoy

(2005), Yasar is a master at avoiding stereotyped musicalphrases in his original improvisations, a ‘‘composer ofimprovisations, a poet of the tanbur, who recites maka-mic verses.’’ Yasar was also a primary source in Signell(1986), and an illustrated biography has recently beenpublished (Tokuz, 2009).

STIMULI

The sound examples in Experiment 1 (and throughoutlater experiments) rely on a kind of analysis-resynthesismethod; the audio .wav files in a collection of taksimsare analyzed and transformed into MIDI note-levelrepresentations where the pitch and timing can bestraightforwardly manipulated. The process begins withthe pitch detector of de Cheveigne and Kawahara(2002), which is used to estimate the instantaneouspitch of the original performances at a rate of 100 timesper s. The raw pitch data are converted into estimates ofthe pitch centers and transition probabilities using theExpectation Maximization (EM) algorithm of Welch(2003). These are then used to estimate the note-startand note-end times via the Viterbi (1967) algorithm. Asthese pitch extraction steps are somewhat involved, thesteps are detailed in Appendix B.

The output of the above processes is a set of note-leveldata that are translated into a standard MIDI file. Thesound examples of Experiment 1 are a resynthesis of theanalyzed performances using a flute-like instrumentalsound generated using the Alchemy additive synthesizerby Camel Audio (2013). The sound patch is amplitude-modulated at a slow rate, imitating (somewhat) thevibrato and timbre of the ney, although without thebreathy effect common with the ney. The performanceis quantized to eight notes (per octave) and the specificpitches are determined by the pitches present in theoriginal performances. While this leaves much of themelodic motion intact, it removes pitch glides andmicrotonal ornamentations. The original sound files,the extracted MIDI files, and the resynthesized versionscan all be heard at the Makam Experiment Website(Sethares, 2014).

RESULTS

Experiment 1 consists of six sound examples that areessentially resynthesized versions of the original taksimsfrom the 1986 performances. The taksims chosen forresynthesis are listed in Table 1, along with the responsesof the experts. The specific taksims chosen maintain a bal-ance between those which are more and less common.

All three experts correctly identified four of the syn-thetic taksims precisely (Hicaz, Muhayyer, Rast, andUssak). Isfahan and Neva are comparatively uncommon,

Experiments on the Relationship between Perde and Seyir in Turkish Makam Music 327

and it makes sense that rarer makams would be moredifficult to recognize. Even so, Expert 3 identified Nevacorrectly while Experts 1 and 2 mentioned Neva in con-junction with another more common makam (Ussak andBeyati). To understand this, recall that in ‘‘normal’’ per-formances, a piece will begin on a host makam, modulatethrough other makams, and then resolve back to the host.In Table 1, there are four places where the experts iden-tified more than one makam (those with a slash /). Whenwe asked about this, Expert 2 said that he ‘‘heard echoesof both’’ in the piece, and could not decide which was themost prominent (and so listed both). Figure 2 shows thatNeva and Beyati have the same dominant and tonic, andotherwise differ by a single sharp in the key signature ofthe AEU representation. Similarly, Neva and Ussak differby the same sharp and also have identical dominants andtonics. Moreover, Beyati and Ussak are indistinguishablefrom interval content alone in the classic AEU perspec-tive, as shown in Figure A1. What this shows is thatmakams that are most closely related according to stan-dard theory may be among the most readily confused inlistening tests. Similarly, Isfahan and Ussak are identicalfrom the AEU perspective and are often considered to beamong the makams that are ‘‘most alike.’’ Ederer (per-sonal communication, 2013) observes that there are twokinds of Isfahan: the one used here that might be mis-taken for Ussak or Beyati is formally known as ‘‘BasitIsfahan’’ while younger musicians might be more familiarwith ‘‘Murekkeb Isfahan.’’ The asymmetric confusionbetween Ussak and Isfahan is likely due to the (relative)uncommonness of Isfahan.

These results do not mean that the synthetic taksimsand the original improvisations sound in any sense ‘‘thesame.’’ Rather, it means that the transformations intothe synthetic versions retain the essence of the makamstructure (whatever that may be). This experimentshows that it is possible to recognize the makam froma synthetic version, using only auditory clues. There isno real possibility that such a string of matches couldhave resulted from chance: with over 100 possibilitiesfor each of the sound examples, even getting one correct

in six tries would be highly unlikely. Although we onlyasked the single question (which could in principle beanswered by a single word) the expert’s responses wererarely so succinct. For the most part (in this and insubsequent experiments), the experts indicated thatthey listened to the sound examples several times andin several cases, provided second-by-second analyses ofthe pieces. These would typically end with ‘‘and there-fore I conclude it is in makam X.’’

One way of quantifying the amount of agreementamong subjects is the kappa coefficient (Fleiss, 1971),which can be applied to multiple raters on categoricaldata (Sim & Wright, 2005). The kappa value � ¼ �P�R

1�Rindicates the ‘‘proportion of agreement beyond thatexpected by chance,’’ where �P is the observed agreementand R is the agreement expected by chance alone. � lieson a scale between –1 (complete disagreement) through0 (chance agreement only) to þ1 (complete agreement).A full discussion of the kappa calculation is presented inAppendix C. For Experiment 1, applied to the threeexperts, � lies in the range ð:67; :73Þ, which can beinterpreted as in Table 2 to reflect substantial agreementamong the experts. It should be noted that there is nouniversally accepted interpretation of � values. In ourexperiments, � may be understated because it only takesinto account the categories (the makams) that actuallyappear in one or more responses; the actual difficulty ofthe task is also dependent on the universe of possibleanswers (the 100 or so makams); this would tend tomake � a conservative estimate of the true agreement.Observe that the kappa coefficient does not have a well-accepted notion of statistical significance, and since oursample sizes are quite small, it is probably best to viewthe numbers as suggestions for interpretation ratherthan precise yardsticks.

We report the response of Expert 1 to Experiment 1here for completeness; it should be noted that thisexpert was the original source of the seventeen taksimsfrom 1986. Although he did not consciously recognizeany of the sound examples in this experiment (aftera lapse of more than 25 years), the possibility of the use

TABLE 1. Results for Experiment 1 “Establishing a Baseline”

Makam Expert 1 Expert 2 Expert 3

Hicaz Hicaz Hicaz HicazIsfahan Huseyni Isfahan/Ussak Isfahan/Ussak/

NevaMuhayyer Muhayyer Muhayyer MuhayyerNeva Ussak/Neva Beyati/Neva NevaRast Rast Rast RastUssak Ussak Ussak Ussak

TABLE 2. Interpretation of � values according to Landis and Koch(1977)

� Agreement

< 0 poor0� 0:2 slight0:2� 0:4 fair0:4� 0:6 moderate0:6� 0:8 substantial0:8� 1 almost perfect

328 Can Akkoç, William A. Sethares, & M. Kemal Karaosmanoglu

of extra-acoustic information in the responses cannot beruled out. Accordingly, it may be best to discount Expert1’s responses in this experiment. This caveat does notapply to Experiments 2-4 where the source material wasmanipulated and disguised. (Somewhat paradoxically,recalculating the kappa values with Expert 1 removedraises the value of � slightly.)

Experiment 2: Scrambling Time

Experiment 1 establishes that the host makam canindeed be recognized from auditory features alone; itis possible to ask which features are crucial to this abil-ity. The two primary candidates are the perde hypoth-esis and the seyir hypothesis, and Experiments 2through 4 are aimed at narrowing the possibilities anduncovering the kernel or invariants that lead to recog-nizability of a host makam.

The perde hypothesis posits that makam identifica-tion is crucially dependent on pitch relationships whilethe seyir hypothesis posits that the identification is cru-cially dependent on time ordering. Motifs, sound pat-terns, and melodic contours are inherently ordered;sound X followed by sound Y is fundamentally differentfrom sound Y followed by sound X. This is well studiedin the case of melodies, where rearranging the temporalorder of a melody can leave even a familiar melodyunrecognizable (Deutsch, 1982). In contrast, the set ofpitches present in a piece is invariant with respect totemporal rearrangements. Accordingly, the soundexamples of Experiment 2 rearrange the order of thenotes of the improvisations, leaving the pitchesunchanged. This is done in two different ways: byscrambling segments, and by time reversal.

PROCEDURE AND PARTICIPANTS

Roughly one week elapsed between Experiments 1 and2, and the same expert listeners were again asked ques-tion Q. The timing of each of the experiments wassomewhat different for each expert due to schedulingconstraints. Because the sound files were sent by e-mail(and in one case on CD), the sound examples could notbe ‘‘returned’’ after the experiment was over, and so theexperiments must be considered to be cumulative.When we asked (at the end of all four experiments) ifthe experts had referred back to sound examples fromprevious experiments, all said ‘no.’ Because our subjectsare experts who were donating their time and energy, wedid not feel it was appropriate to answer direct ques-tions with dissembling responses. Accordingly, we sup-plied feedback when asked. Expert 1 was the mostpersistent: asking questions about who was playing,

what instrument was being played, what we had doneto create the sound examples, and what the ‘‘right’’answers were. Expert 2 was considerably more circum-spect, more interested in ‘‘why’’ we were making thesound examples than in ‘‘how,’’ and Expert 3 asked noquestions. Our belief is that our responses supplied nouseful information to influence future decisions, but wecannot say this with complete certainty. In Appendix C,we try to address this quantitatively.

STIMULI

The scrambling-by-segments method relies on theobservation that the original improvisations are builtfrom a number of small segments. These segments cor-respond to the points at which the performer breathes(these were performed on a solo ney) and so providenatural stopping and starting points for the temporalrearrangement. For example, the Hicazkar improvisa-tion was performed in nine small segments. Numberingthe segments sequentially, two resynthesized versionsperformed the segments in the orders 135724689 and183754629. Thus both start and end the same, but movethrough the piece in different orders. This technique isanalogous to the scrambling of melodies presented in(Rabinovitz, 2011).

The second method of rearrangement is time reversal.In these examples, the notes of the improvisation wereperformed backwards: first the final note, then the pen-ultimate note, then the 3rd to last, and so on, all the wayback to the first note. Although there is no musical score,the effect is the same as if the performer played the piecenote-by-note from end to start. (This is not the same asreversing the soundfile, which drastically changes thetimbre of the instrument.) Synthesized versions of Hicaz,Mahur, and Ussak were time reversed in this fashion.

RESULTS

With a single exception, the sound examples of Exper-iment 2 are not simple copies of an original perfor-mance; rather, the sounds are scrambled in time ina nontrivial manner. The two Hicazkar examples arescrambled by section while the three ‘‘Rev’’ examples(short for ‘‘time reversed’’) invert the temporal motionof the piece. The example labeled mahurLinear does notfit this pattern and is, instead, a relatively faithful ren-dering of the original Mahur taksim where the pitcheswere fit with a linear slope (as described in the stimuli ofExperiment 1). This example conceptually belongs withExperiment 1, and all three experts correctly reportedthe makam. (We did not want to ‘‘give away’’ what wewere testing in each set by having all the sound exam-ples created in the same way, so we split the examples

Experiments on the Relationship between Perde and Seyir in Turkish Makam Music 329

among the sound sets: mahurLinear logically belongs inExperiment 1, while the two RastXXX examples fromExperiment 3 logically belong to Experiment 2. Wereport them here as the experiments were conducted.)

There is, as might be expected, more variation in theresponses to the scrambled sound examples. Forinstance, all the experts correctly identified the time-reversed Hicaz (although one perceived it as a transpo-sition of this makam), and all identified Mahur as a com-ponent of the time-reversed Mahur. Two experts alsomentioned Rast in this example: the pitch content ofMahur and Rast differ by one comma flat and onecomma sharp. The final time-reversed example wascorrectly identified by Expert 2 as Ussak, but was heardby Expert 1 as Acemkurdi and by Expert 3 as a transpo-sition of Rast. The scales of Acemkurdi and Ussak differby only one half-flat and in the particular performanceused this note does not occur frequently. While theabove explanation is probably clear to a Western reader,it should be noted that Turkish practitioners may con-ceive the similarity between Acemkurdi and Ussak interms of the root-position cinses of the two makams, (asnoted by Ederer, 2011). In this case, Acemkurdi requiresa Kurdi tetrachord, while the Ussak makam requires anUssak tetrachord. Alternatively, Ussak is often thoughtof as having an ascending character while Acemkurdihas a descending character. Thus these might naturallybe confounded after a time reversal.

Of the two scramblings of Hicazkar, only Expert 1 pin-pointed Hicazkar, and he also heard excursions intoSehnaz. Experts 2 and 3 also heard Sehnaz, but alternatingwith Hicaz. As the names imply, these two are closelyrelated since Hicazkar is formed, according to classicAEU theory, by adding a Hicaz tetrachord (built on perdeneva) to a Hicaz tetrachord (built on perde rast). Perhapsthe most straightforward interpretation of this rests onthe observation that the scales of Sehnaz and Hicazkar(in the AEU representation) are transpositions of eachother. Ederer (personal communication, 2013) notes that‘‘it is possible to perform very simple renditions ofSehnaz and Hicazkar in such a way that it would be hardto tell which was which without also knowing what the

tonic is.’’ Signell (1986) writes about the relationshipsbetween Hicazkar and Sehnaz and gives two extendedexamples (numbers 113 and 114) that demonstrate theextensive similarities and subtle differences. In terms ofthe interval sets, Sehnaz and Hicazkar are rotations ofeach other, as shown in Figure A1. In the exit interview,Expert 2 said that he had recognized the similaritybetween the first and fifth sound examples when answer-ing, and he thought we had used the same twice, ‘‘perhapsto try and trick him.’’ Thus he ensured the answer was thesame for both. The outlier here is the response of Niha-vent, for which we find no obvious explanation.

Calculating the kappa coefficient for this experimentas in Appendix C gives an agreement rating among thethree experts of � in the range ð:26; :34Þ. According toTable 2, this is a ‘‘fair’’ agreement among the experts.Because of the tight relationship between some of themakams used (as mentioned above) and because of thelarge number of possible answers that did not appear,this may understate the agreement.

Experiment 3: Randomizing Events

Another way of removing temporal relationships is viarandomization. In the simplest situation, a histogramcan be used to count how many times each perdeoccurs. A ‘‘new piece’’ can be built by picking notes atrandom with probabilities based on the histogram. Inthe output, notes occur with roughly the same fre-quency as in the original, but in different order. A lessdrastic randomization can be made by considering allpairs of notes and then choosing notes for the new piecebased on the probabilities of the pairs. This would tendto replicate the original time ordering somewhat morefaithfully. Continuing in this fashion, it is possible toconsider triplets (n ¼ 3), quadruplets (n ¼ 4), etc. As nincreases, the randomized output tends to more faithfullyreplicate the original. Said another way, the events in theinput pieces are randomized in such a way so as todestroy long-term temporal structure but to preserveshort-term temporal structure, where ‘‘long’’ and ‘‘short’’are determined by n. A large database is needed in order

TABLE 3. Results for Experiment 2 “Scrambling Time”

Sound Example Expert 1 Expert 2 Expert 3

hicazkar183754629 Hicazkar/Sehnaz Sehnaz/Hicaz Hicaz/SehnazhicazRev Hicaz Hicaz Hicaz transposedmahurLinear Mahur Mahur MahurmahurRev Mahur/Rast Rast/Mahur/Rast Mahurhicazkar135724689 Nihavent Sehnaz/Hicaz SehnazussakRev Acemkurdi Ussak Rast

330 Can Akkoç, William A. Sethares, & M. Kemal Karaosmanoglu

to generate these probabilities; we used the source mate-rial from the ‘‘Turkish Makam Music Symbolic Databasefor Music Information Retrieval’’ (Karaosmanoglu,2012). Details of the procedure used to create the soundexamples with this nth order Markov Chain method arepresented below.

The sound examples of Experiment 3 include n ¼ 1and n ¼ 3 randomizations of the Hicaz and Ussakmakams. The n ¼ 1 sound examples completely destroyall temporal relationships between the notes of the tak-sims while leaving the perdes and the histogram(approximately) intact. If the makams from these exam-ples can still be recognized, this can be consideredstrong evidence for the perde hypothesis. The n ¼ 3sound examples retain some of the temporal motionof the original (in particular, all length-three sequencesin the output must occur somewhere in the input) sothese retain more of the temporal character of the orig-inal taksims. Since these manipulations are made at thesymbolic level (i.e., on the MIDI file) the randomizationdoes not include fast features of the performance suchas ornaments, pitch glides, and other intermittent note-level phenomena.

PROCEDURE AND PARTICIPANTS

The procedures and participants were the same as inExperiments 1–2.

STIMULI

Successive events in musical performances are not inde-pendent. Shannon (1948, p. 8) suggests a way to modelredundancies in text:

. . . one opens a book at random and selects a letter onthe page. This letter is recorded. The book is thenopened to another page, and one reads until this letteris encountered. The succeeding letter is then recorded.Turning to another page, this second letter is searchedfor, and the succeeding letter recorded, etc.

There is nothing about Shannon’s technique that isinherently limited to dealing with text sequences, andnothing that limits the technique to single letters. Animplementation called ‘‘Poem Maker’’ that allows anynumber of sequential letters using text sources drawnfrom the Wolfram library of curated data has been writ-ten by Sethares (2011). With n ¼ 1, the letters are effec-tively chosen randomly from the distribution of letterswithin the text. With n ¼ 2, the letters are chosen fromsuccessive pairs; with n ¼ 3, they are chosen from suc-cessive triplets, etc. The probabilities of clusters of lettersare defined implicitly by the choice of the source text.

By considering a piece of music as a sequence ofsymbols, Shannon’s book can be replaced by a suitablecorpus of music. The Turkish makam database SymbTr(Karaosmanoglu, 2012) provides a suitable collectionof pieces classified by makam. Accordingly, the text-based ‘‘Poem Maker’’ was translated into a MIDI-basedsequence generator. Instead of generating text based onn-term probabilities, the MIDI generator createssequences of notes where n-note patterns occur withprobabilities specified by the source collection. Thusfor n ¼ 1, individual notes occur with the same prob-abilities as in the makams of the SymbTr database. Forn ¼ 2, pairs of notes occur with the same probabilitiesas in the database, etc. The randomized synthetic tak-sims of Experiment 3 were generated in this manner,and then realized using the same simulated-ney soundas in Experiment 1.

RESULTS

Experiment 3 again consists of two ‘‘kinds’’ of soundexamples. Logically, the two rastXXX examples belongwith the scrambling examples from Experiment 2. Thenew technique is embodied in the examples with the‘‘Rand’’ suffix, which indicates that these were createdusing the Markov chain randomization techniquedescribed above.

Tura (1988) comments that Rast is the root of allmakams, so it might be anticipated that it would beamong the easiest to recognize, even in scrambled form.Indeed, all three of the experts identified the scram-blings of the Rast makam, although Expert 2 identifieda more complex structure that lies ‘‘on a Rast scale withplenty of Segah, most like Sazkar’’ (we have abbreviatedthis in the table). In terms of interval sets, Sazkar andRehavi are both the same as Rast, as shown in FigureA1. Hence this answer is quite reasonable.

The Hicaz and Ussak makams were randomizedaccording to the Markov chain method with n ¼ 1 andn ¼ 3, where n is the length (or memory) of the chain.The n ¼ 1 examples have no memory (pedantically,a memory of one note) and are effectively the same asif one generated notes at random from probabilities

TABLE 4. Results for Experiment 3 “Randomizing Events”

Sound Example Expert 1 Expert 2 Expert 3

rast13572468 Rast Sazkar RasthicazRand3 Hicaz Hicaz HicazussakRand1 Beyati Beyati/Acemkurdi Nonerast17654328 Rast Rast RasthicazRand1 Hicaz Hicaz HicazussakRand3 Ussak Huseyni None

Experiments on the Relationship between Perde and Seyir in Turkish Makam Music 331

dictated by the histogram. The n ¼ 3 examples havea memory of triplets, that is, one-, two-, and three-note sequences will occur with the same probabilitiesas in the original database. Both Hicaz randomizationswere correctly identified by all three experts. The Ussakrandomization with n ¼ 1 was identified as Beyati bytwo of the experts. This is easy to understand since theUssak and Beyati makams have the same set of pitches;indeed, some authors such as (Arel, 1968) do not con-sider these to be distinct makams. In terms of the intervalsets of Figure A1, the distance between Ussak and Beyatiis zero. Signell (1986) makes the argument that they differprimarily in melodic direction: that Ussak is an ascend-ing form (tonic-dominant-tonic) while Beyati is anascending-descending form (dominant, lingers, thento tonic). Such directional motions are annihilated bythe randomization. Expert 2 heard the n ¼ 3 Ussakrandomization as Huseyni, which is again a closelyrelated makam. This is the same confusion found inExperiment 1 and may be understood by observing thatthe single sharp difference occurs on a relatively raretone.

Perhaps the most interesting responses in Experiment 3were provided by Expert 3 to the two randomized Ussakmakams, who wrote ‘‘piece wanders over pitches with nomakam structure detected.’’ This is the only case whereany of the experts took advantage of the ‘‘if any’’ clause inthe question Q. Although the amount of randomizationwas the same, apparently the ‘‘wandering’’ in the Ussakexamples was more pronounced than the wandering inHicaz. For at least one of the experts, the sound manip-ulations had annihilated the makam structure.

Expert 2 commented that the n ¼ 3 randomizedexamples ‘‘sound like an overture.’’ An overture typi-cally contains many small snippets of the pieces that areto come; the n ¼ 3 randomizations contain many small(3-note) snippets from the database from which theparameters of the Markov chain are drawn. Thus Expert2 was likely hearing many of the small motifs inheritedfrom the SymbTr database (Karaosmanoglu, 2012).

To calculate the kappa value for the agreementbetween the three experts requires handling the ‘‘nomakam’’ response of Expert 3. If this is interpreted asanother category of response, the kappa value lies in therange ð:45; :62Þ as shown in Table C1. These values maybe interpreted as in Table 2 as ‘‘substantial agreement’’for the sound examples of this experiment.

Experiment 4: Cross-Makam Generation

The sound examples for Experiment 4 are constructedto help determine which hypothesis (perde or seyir) isstronger. The examples are formed by merging two ofthe taksims, grafting the perdes of one makam onto theseyir of a second (and vice versa). For instance, thesound example labeled perHusSeyMah uses the perdesof the Huseyni makam along with the seyir of theMahur makam. Similarly, the sound example labeledperMahSeyHus uses the perdes of the Mahur makamalong with the seyir of the Huseyni makam.

Such cross-generated sound examples do not havea single ‘‘correct’’ answer. Listeners may choose themakam represented by the pitch structure (providingsupport for the perde hypotheses), they may choose themakam represented by the temporal structure (provid-ing support for the seyir hypotheses), or they mayrespond with some other makam. The latter case mayindicate that the crossing procedure has destroyed thenature of the makam, that the sound example wasinherently ambiguous, or perhaps that crossing of cer-tain pairs of makams may imply a third. Such situationsmay be challenging to interpret.

PROCEDURE AND PARTICIPANTS

The procedures and participants were the same as inExperiments 1-3.

STIMULI

The sound stimuli for Experiment 4 are constructed bygrafting the pitch profile of one makam onto the

TABLE 5. Results for Experiment 4: “Cross-Makam Generation”

Sound Example Expert 1 Expert 2 Expert 3

1 perMuhSeyUss Ussak Ussak Rast2 perHusSeyMah Similar to Neva Ussak Rast3 perNihSeyYeg Kurdilihicazkar Kurdi Muhayyer4 perMahSeyHus Huseyni Huseyni Huseyni5 perUssSeyMuh Muhayyer Muhayyer Muhayyer6 perYegSeyNih Rast Rast None7 perNihSeySuz Nihavent Nihavent ends in Nihavent8 perSuzSeyNih Suzinak Suzinak/Rast Rast

332 Can Akkoç, William A. Sethares, & M. Kemal Karaosmanoglu

temporal profile of another. The basic source material isthe original corpus of 17 makams, each of which issubjected to the analysis of Appendix B. Two makamsA and B are chosen for each example, and a one-to-onemapping is constructed that replaces each note ofa makam with the corresponding note from the other.For instance, in the first sound example, the pitches/perdes from Muhayyer are mapped onto the temporalmotion of the Ussak makam and the result is called‘‘perMuhSeyUss’’ in the first line of Table 5. The com-plete procedure is described in detail in Appendix D.

RESULTS

Experts 1 and 2 heard sound examples 1, 4, and 5 asdictated by the temporal motion, in support of the seyirhypothesis. Both also heard sound examples 7 and 8 asdictated by the pitch content, in support of the perdehypothesis. Expert 3 agreed on the importance of theseyir in sound examples 4 and 5 and replied that soundexample 7 ‘‘goes through a bunch of mixed (confusing)melodies and concludes in Nihavent makam,’’ thusagreeing (in the end) with the others in support of theperde hypothesis. In contrast, the responses to soundexamples 2, 3, and 6 apparently show little agreementwith either of our prior expectations. There was no over-lap in the answers of the three experts about the per-ceived makam of sound examples 2 and 3. While Experts1 and 2 perceived Rast in example 6, Expert 3 declaredsound example 6 to be in no recognizable makam.

To shed light on the results of this experiment, wefocus on three issues. First, what distinguishes examples1, 4, and 5 (where the experts agree with the seyirhypothesis) from examples 7 and 8 (where the expertsagree with the perde hypothesis)? Second, what distin-guishes examples 1, 4, 5, 7, and 8 (where the expertsmostly agree) from sound examples 2, 3, and 6 (wherethe experts mostly disagree)? Finally, what distinguishessound examples 2 and 3 (where the experts completelydisagree) from sound example 6 (where two agree andone hears no makam at all)?

One way to understand the difference between thesound examples where the seyir hypothesis dominates(1, 4, 5) and the sound examples where the perdehypothesis dominates (7, 8) is that in the former thepitch changes are mild while the tonic-dominant rela-tionship is different, while in the latter the pitch differ-ences are large and the tonic-dominant relationships arethe same. For example, from the point of view of inter-val content, Ussak and Muhayyer (of examples 1 and 5)are quite similar. Figure 2 shows the key signature ofUssak and Muhayyer as differing by just one sharp, andFigure A1 displays this difference in the interval sets in

the lightest shade of grey. This is not the way a Turkishpractitioner would describe these relationships. Ederer(personal communication, 2013) comments that thescalar material of the Ussak makam consists of an Ussaktetrachord on dugah conjoined with a Nihavent penta-chord on neva, while the Muhayyer makam consists ofan Ussak pentachord on dugah conjoined with a Buseliktetrachord on huseyni.

On the other hand, the tonic-dominant relation inUssak is a fourth while that in Muhayyer is a fifth. Incontrast, Nihavent and Suzinak (of examples 7 and 8)have almost no relationship in terms of perdes (the darkgrey coloring in Figure A1 indicates a large difference ininterval set) while the dominant-tonic relationship isidentical (a fourth). Moreover, agreement among theexperts in example 8 may be greater than is obviousfrom a glance at Table 5 since Rast (the outlier responseof Expert 3) is closely related to Suzinak (Figure 2 dis-plays the key signatures as differing by just one flat).Example 4 fits a similar pattern, since both Huseyni andMahur differ greatly in interval content but have thesame dominant-tonic relationship (a fifth). There aretwo common threads that run through these cases. First,the seyir hypothesis tends to dominate when the inter-val sets are close; the perde hypothesis tends to domi-nate when the pitch sets are significantly different.Second, when the dominant-tonic interval is the same,the responses tend to support the perde hypothesis;when the dominant-tonic interval differs, the responsestend to support the seyir hypothesis.

While the experts are in considerable agreement inthe above five sound examples, they appear to be inconsiderable disagreement in the other three. For exam-ple, there are six different makams cited by the threeexperts in examples 2 and 3. As we will argue, thisdisagreement is more apparent than real. Expert 1 citesNeva for example 2 and Kurdilihicazkar for example 3.Figure A1 shows that the interval sets of Neva andHuseyni are identical, and that the interval sets for Kur-dilihicazkar and Nihavent are identical. Since Huseyniand Nihavent are the expected answer under the perdehypothesis, Expert 1’s answers both support the perdehypothesis, under the assumption that rotations of theinterval set of a makam are identified. Similarly, Expert2 chose Kurdi for example 3 (which has the same inter-val content as Nihavent) and Ussak for example 2(which has a key signature that is exactly one sharpdifferent from Huseyni, as shown in Figure 2). ThusExpert 2’s responses also support the perde hypothesisunder the assumption that nearby makams (in the senseof key signatures) may be identified. Similarly, Expert3’s response of Muhayyer can be understood as further

Experiments on the Relationship between Perde and Seyir in Turkish Makam Music 333

support for the perde hypothesis because its key signa-ture is one sharp different from Kurdi. Of these sixresponses, the only one that is not interpretable in thismanner is Expert 3’s choice of Rast. Thus five of the sixresponses in examples 2 and 3 can be viewed as supportfor the perde hypothesis, under the assumptions thatmakams with nearby key signatures (no more than oneaccidental difference) and those which are rotations ofthe interval set are identified.

In example 6, two of the experts responded with Rastand one responded that the example had no discerniblemakam structures. There are three possible explanations.It may be a result of the strong leading-tone: Yegah,Nihavent, and Rast all have a leading tone that is closeto the root (Nihavent and Rast have the F# to G relation-ship while Yegah and Rast have the same pitch set, dif-fering only by a modal transposition). On the other hand,Yegah and Rast have almost identical pitch sets that differby only one note (the low C# in Yegah). This C# does notoccur frequently in the particular Nihavent taksim.Meanwhile, Nihavent and Rast have the same root-dominant structure (which may again be interpreted asan aspect of temporal motion and seyir), which is distinctfrom the root-dominant structure in Yegah. Thus Rastmay be viewed as a combination or hybrid of Yegah andNihavent with the pitch set drawn from Yegah and theseyir drawn from Nihavent. Appendix G of Ederer (2011)offers a third alternative based on the complex historicalrelationships between Yegah and Rast. Overall, soundexample 6 remains somewhat enigmatic.

Interpreting the ‘‘no makam’’ response as a category ofresponse, the kappa value for this experiment lies in therange ð:41; :42Þ as shown in Table C1. This may be inter-preted as in Table 2 as ‘‘moderate agreement’’ among theexperts for the sound examples of this experiment.

Discussions and Conclusions

When we first contemplated these experiments, wefeared that even experts might not be able to name theintended makams, leaving us with a dilemma; wouldthis mean that the experts failed to identify the makam,or would it mean that the process of creating theresynthesized sound examples had destroyed theessence of the makam? Fortunately, in the majority ofexamples, the experts concurred with our intendedmakams and with each other. This gave us confidencethat the sound resynthesis techniques were transparent(at least from the point-of-view of makam recognition).The answer to the question as to the identifiability of themakam from purely acoustical data is unequivocal: yes,expert listeners can accomplish this task.

The bulk of the experiments were then designed touncover the acoustic cues that the experts might use toachieve this feat of cognition, centering on the two centralhypotheses of a pitch/perde-based recognition and a tem-poral/seyir-based recognition. The results of Experiments2 and 3 show that pitch relationships alone (i.e., the scale)can account for the recognition of makams in many cases.Whether the notes of the improvisation are scrambled orrandomized, the experts were often able to identify theintended makam. When they ‘‘missed,’’ it was often easyto see why: makams with similar interval sets are easy toconfound. Had we stopped the experiments at this point,we would have concluded (in agreement with a simpleinterpretation of the AEU theory) that recognition ofmakams is primarily a pitch-based activity; we would havebeen pleased to report that the auditory pitch acuity of theexperts was fine enough to distinguish many makamsfrom their pitch content alone.

But the testimony of performers and authorities onTurkish music (including our experts) suggests that tem-poral information ought to be significant. We were notable to design an experiment that isolates the seyirhypothesis (as Experiments 2 and 3 isolate the perdehypothesis). But we were able to conduct Experiment 4,which tests the relative importance of the two hypotheses.In many cases, the seyir-based recognition dominates theperde-based recognition. Thus, although pitch relation-ships alone can be used to identify the makam, when bothpitch information and temporal information are presentand conflict, listeners tend to choose the makam repre-sented by the temporal information (e.g., sound examples1, 4, and 5 of Experiment 4), especially when the intervalsets of the makams are close. In cases where the pitches arevery different (sound examples 7 and 8 of Experiment 4),the perdes may still dominate. While one or the other ofthese phenomena may dominate in any given experiment,it should be understood that in normal listening, perdeand seyir work together to define the makam.

Makam recognition is a highly complex cognitive pro-cess. When there is only pitch information available (asin the contrived sound examples of Experiments 2 and3), it is often enough to identify the makam. However,when temporal information is present, and the perdestructures happen to be ‘‘close,’’ the temporal informa-tion may be the preferred vehicle for makam recognition.Some of the cases where the expert’s answers differedfrom our prior expectations may provide clues to rela-tionships between makams. For example, sound exam-ples 2 and 6 of Experiment 4 suggest that when makamsA and B are combined (choosing the perdes of A and theseyir of B), the proper response may be neither A nor B,but a third makam C which is related to the two input

334 Can Akkoç, William A. Sethares, & M. Kemal Karaosmanoglu

makams by a balance of both pitch and temporal simi-larities. Further experiments, designed specifically to testsuch relationships, could be conducted with the aim ofuncovering a ‘‘distance’’ function that might measure thesimilarities and differences between makams based onpitch and temporal structures.

Castellano et al. (1984) consider the features of tonalorganization that may become internalized throughexperience in the context of Indian rags. We did notextend our experiments to Western listeners because itwould be difficult for those without experience to dis-tinguish one makam from another, and clearly impos-sible to name them. It would be interesting to conductprobe-tone experiments analogous to those of Krum-hansl and Shepard (1979) using the tonal material ofTurkish makams. These would require an expandedpalette of pitches to include at least the 24 tones of theAEU system, although they might also benefit from thefull 53-tone set of commas and/or the inclusion of12-tone equal tempered pitches, which might be signif-icant for listeners who also have significant exposure toWestern idioms. In order to bypass the need to choosewhat pitches to use (and indeed, to bypass the need tochoose a music-theoretic system on which to base theexperiments) we have analyzed specific musical perfor-mances and derived the pitch sets used in the experi-ments directly from those performances. The accuracyof the pitch extraction is on the order of one cent, and sois finer than any common theoretical system.

There are many examples throughout a variety ofmusical cultures where small pitch changes are usedas expressive elements in performance; these are oftenconsidered to be ornamental inflections about some setof nominal pitches. Ayari and McAdams (2003) reportthat for many Arab listeners, small comma-sized varia-tions may signal a change in the identity of the makam.The experiments in this paper confirm that a commachange (such as those that distinguish the variousmakams) may carry important information about theform and organization of the piece, at least in the realmof the taksims of Turkish makam music. Such differ-ences in form (i.e., the various makams) can often beperceived and identified by experts.

Oram and Cuddy (1995) observe that a listener’ssensitivity to pitch-distributional information maybe important in developing listening strategies foratonal music. This may equally hold when listeningto an unfamiliar musical style (such as a Westernerlistening to makam music) where the form of tonalityis different. Extending this one step further, it is alsoplausible that an expert may use pitch distributionalinformation when other, more familiar information

(such as temporal order) is unavailable. For example,in the scrambling experiments, where the order ofpitches were randomized and temporal cues destroyed,the experts may have adjusted their listening strategies.When those temporal cues were returned in Experi-ment 4, it is plausible that their listening strategiesreadjusted to focus on the most pertinent information.(Bharucha, 1984) comments that the tonal hierarchymay be evoked either by the relative durations of tonesin a piece or by activation of long term memory.

Deutsch (1984) comments on Castellano et al. (1984)and asks, in the context of Western music, if key assign-ments tend to be made on the basis of pitch collectionsalone, or if the order of the notes is also significant. Thisprovides a simple experimental paradigm where theinteractions between tonal perceptions and temporalordering of events can be studied. Deutsch constructsan example where identical sets of notes imply differentkeys depending the order in which they are played, andstates that ‘‘we are dealing with an elaborate bootstrap-ping operation . . . so that ultimately both a key anda sequential representation are arrived at by the listener’’(p. 418). This is consistent with our conclusion thata makam may be identified from pitch informationalone but that when sequential information is present,it may also exert a significant influence. Indeed, in cer-tain cases (such as the makams along the diagonals inFigure A1) the pitch sets of two makams are identicaland the sequential presentation is crucial. The results ofExperiment 4 attempt to address the relative importanceof the sequential and the pitch information.

In linguistics, the saying that ‘‘native speakers do notmake grammatical errors’’ (Andersson & Trudgill, 1990)can be interpreted to mean that language is a social con-struct where the limits of usage are governed by the speak-ers of that language. In musical discourse, while there is no‘‘native speaker,’’ experts do spend years learning, training,and performing in a style that is governed by their prac-tice. Our intention is not to idolize such experts (althoughwe do have great esteem for their abilities) but to use theirresponses to understand the limits of the makam style andthe limits of human perception. In the experiments, thesimplest situation is when the experts agree with ourintended makam. When the experts agree with each other(but disagree with our intended makam), this indicatesthat we designed the experiment poorly or misunderstoodsome aspect of the sound example. When the expertsdisagree among themselves, it is possible that one has‘‘made a mistake’’ perhaps through inattentive listeningor happenstance, but our first presumption is that theydisagree because they are attending to different aspects ofthe experimental stimulus. In such cases, we have tried to

Experiments on the Relationship between Perde and Seyir in Turkish Makam Music 335

pinpoint plausible explanations for such disagreements. Itis also possible that certain combinations are fundamen-tally ambiguous.

Seyir and perde are core elements of makam music,and they function as central features in makam iden-tification. The experiments presented above for thepurpose of exploring the interactions between thedynamic elements of seyir (temporal information) andthe static elements of perde (pitch information) inTurkish makam music reveal some of the intricateacoustic features needed for makam recognition,pointing to a combined seyir-perde architectureunderlying the makams. The experiments rely ona back-door approach that explores the inner workingsof the seyir-perde mechanisms by investigating whatdoes and does not work, by finding the limits of whatexpert listeners do (and do not) hear as proper makamstructure. This was achieved by the creation of synthetictaksims which deliberately distort and caricaturize ele-ments of seyir and perde in the hopes of approachingthe essential ‘‘kernel’’ of makam-ness. This same kind ofapproach (of designing experiments to concretely andunambiguously uncover the abilities of expert listeners)may be applied to related issues. For instance, interviewssuggest that the performance of a makam ought to bemore than a mere collection of stereotypical motives; if

so, what are these audible and measurable quantities, andhow can they be demonstrated or falsified?

Acknowledgements

The authors would like to thank the experts Niyazi Sayın,Ruhi Ayangil, and Necdet Yasar, without whom this studywould not have been possible. Others who were helpful orsupportive of this work include Ozan Yarman, GulçinYahya Kaçar, Ugur Keçecioglu, Eric Ederer, and the parti-cipants of the workshop Turk Musikisinde _Icraya DayalıNazariyat Modeli Arayısları in November 2012 at ODTU.Ali Yasar was key in our interactions with Necdet Yasarthroughout the experiments and Ugur Keçecioglu helpedwith the logistics in Istanbul. Mehmet Polat helped deci-pher some of the musical riddles caused by the experts’responses. The authors are grateful to the Institute forApplied Mathematics at the Middle East Technical Univer-sity in Ankara for support throughout a sabbatical visit bythe second author. Preliminary presentations of the workin this paper were made at Baskent University and atODTU in Nov. 2012, and at McGill University in Jan. 2013.

Correspondence concerning this article should beaddressed to Can Akkoç, Institute of Applied Mathe-matics, The Middle East Technical University, Ankara,Turkey. E-mail: can1936@gmail.com

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Appendix

A. Measuring the Distance Between Makams inPitch Space

One way of characterizing the pitch content ofmakams is via the set of successive intervals thatoccur in the scale. Table A1 shows the interval sets

for the 24 makams of Figure 2. Intervals are mea-sured in terms of the Holdrian comma, an interval of1/53 of an octave (22.6 cents) (Touma, 1996). Forexample, in the Ussak makam, the interval betweenthe root and the second tone is 7 commas, betweenthe second and third tones is 6 commas, etc. Because

Experiments on the Relationship between Perde and Seyir in Turkish Makam Music 337

the scales repeat at the octave, each row of the tablesums to 53.

In the standard AEU theory, commas are restricted tomultiples of 4, 5, 8, 9, 12 and 13. Bozkurt, et al. (2009)and Akkoç (2002) show that in practice, commas of size6 and 7 also occur, and Table A1 adopts these values. Forexample, in the standard AEU theory, the interval set forthe Saba makam would be 8, 5, 5, 13, 4, 9, 9. Suchdifferences arise from inconsistencies between theoryand practice and may be subject to controversy.

The interval sets can be used to describe a metric inmany ways. Perhaps the simplest is to calculate the sumof the absolute values of the L1-distance jjx � yjj1 wherex and y are interval sets. Somewhat more meaningfulfrom a musical perspective is to consider all rotations(circular shifts) of the interval sets. Let RiðxÞ be a circularshift of the interval vector x by i positions to the right.Then

dðx; yÞ ¼ minijjRiðxÞ � yjj1 ðA1Þ

is the value of the smallest of the L1-differences betweenthe interval set y and all possible rotations of the intervalset x. This effectively identifies those scales which areidentical but for transposition. In a Western context,

Eq. A1 would identify scales such as C-Major, D-Dorian, and E-Phrygian (etc.) that contain the sameinterval-set but start on a different note. From a math-ematical perspective, observe that dðx; yÞ ¼ dðy; xÞ forall x and y. Identifying all scales x and y for whichdðx; yÞ ¼ 0 into an equivalence class makes Eq. A1a metric on the space of interval sets.

Figure A1 shows the distances dðx; yÞ between all themakams of Figure 2 as measured by Eq. A1. In thefigure, white represents zero distance. For example,Ussak, Beyati, and Isfahan contain the same set of inter-vals, indicating the close relationship between thesescales. Black represents the largest distance; for themakams of Table A1, this is between the pair Sehnaz/Hicazkar and the triplet Ussak/Beyati/Isfahan, whichhas a numerical value of 18. Gray values represent inter-mediate distances. In order to more clearly displaymakams with similar interval sets, the order of presen-tation has been rearranged according to a k-means clus-tering algorithm. The effect of this reordering can be

Acemkurdi Kurdilihicazkar

Mahur Nihavent

Kurdi Buselik Beyati

Isfahan Uşşak

Hicazkar Sehnaz

Huseyni Muhayyer

Neva Suzinak

Hicaz Rast

Rehavi Sazkar Yegah

Evic Sultaniyegah

Segah Saba

Ace

mku

rdi

Kur

dilih

icaz

kar

Mah

ur

Nih

aven

t K

urdi

B

usel

ik

Bey

ati

Isfa

han

Uşş

ak

Hic

azka

r Se

hnaz

H

usey

ni

Muh

ayye

r N

eva

Suzi

nak

Hic

az

Ras

t R

ehav

i Sa

zkar

Ye

gah

Evic

Su

ltani

yega

h Se

gah

Saba

FIGURE A1. The distance d(x,y) as calculated by Eq. A1 for all the

makam pairs in Table A1. White represents zero distance, black

represents the largest distance in the set, and shades of gray indicate

intermediate values. White blocks along the diagonal show sets of

makams with identical interval sets, and include Beyati /Isfahan/

Ussak, Hicazkar/Sehnaz, Hüseyni/Muhayyer/Neva, Suzinak/Hicaz, and

Rast/Rahavi/Sazkâr. The largest group, at the top left, contains

Acemkürdi /Mahur/ Kürdilihicazkar /Nihavent/ Kürdi /Buselik, all of

which are constructed from the same interval set (allowing for

rotation). Makams with closely related (but not identical) interval sets

are indicated in light grey.

TABLE A1. Interval sets of the 24 makams of Figure 2 can berepresented as integer multiples of the Holdrian comma. Data aredrawn from (Karaosmanoglu et al., 2009). These scales are shownin musical notation in Figure 2.

Acemkurdi 4 9 9 9 4 9 9Beyati 7 6 9 9 4 9 9Buselik 9 4 9 9 4 9 9Eviç 5 9 8 9 5 9 8Hicaz 5 12 5 9 8 5 9Hicazkar 5 12 5 9 5 12 5Huseyni 7 6 9 9 7 6 9Isfahan 7 6 9 9 4 9 9Kurdi 4 9 9 9 4 9 9Kurdilihicazkar 4 9 9 9 4 9 9Mahur 9 9 4 9 9 9 4Muhayyer 7 6 9 9 7 6 9Neva 7 6 9 9 7 6 9Nihavent 9 4 9 9 4 9 9Rast 9 8 5 9 9 8 5Rehavi 9 8 5 9 9 8 5Saba 7 6 6 12 4 9 9Sazkar 9 8 5 9 9 8 5Segah 5 9 8 9 5 13 4Sultaniyegah 9 4 9 9 4 13 5Suzinak 9 8 5 9 5 12 5Sehnaz 5 12 5 9 5 12 5Ussak 7 6 9 9 4 9 9Yegah 9 8 5 9 7 6 9

338 Can Akkoç, William A. Sethares, & M. Kemal Karaosmanoglu

seen in the white squares that sit along the main diag-onal; the Sehnaz/Hicazkar group and the Ussak/Beyati /Isfahan groups are clearly delineated, as are severalother sets of makams with identical interval sets underthe metric given by Eq. A1.

B. Analysis-Resynthesis Method of GeneratingSound Stimuli

This appendix details the common steps that underlythe synthetic taksims used in the experiments. The over-all approach is a method that relies on a computer-based analysis of the original corpus of 17 taksims. Foreach taksim, a set of instantaneous pitch measurementsis made using the open source program Tarsos (Six &Cornelis, 2011). This implements the YIN pitch detec-tion algorithm (de Cheveigne & Kawahara, 2002) and isused to estimate the instantaneous pitch of the originalperformance at a rate of 100 times per s. The raw pitchdata are converted into estimates of the pitch centersand transition probabilities using the Expectation Max-imization (EM) algorithm (Welch, 2003). Effectively,this transforms the 100 times per s data to a small col-lection of eight pitches (per octave) and correspondingtransition probabilities, which indicate the likelihoodthat any given pitch will transition to any other givenpitch throughout the analyzed piece. These probabili-ties, together with the raw pitch measurements, are thenused to estimate the note start and end times via theViterbi (1967) algorithm. This reduces the raw pitchdata to a set of ‘‘note-level’’ data that can be transformedinto a MIDI file. Since the pitches of the notes do not alllie on the pitches of the Western 12-tone equal tem-pered scale (as is the default in a MIDI representation),each note is coded as a pitch value along with a pitch-bend value. Together, these allow the sounded MIDInotes to have a repeatable pitch accuracy of better thanone cent.

The model presumes eight pitches (or pitch clusters)per octave, as is common in Turkish makams. The cen-ters of these clusters are denoted s1; s2; . . . ; sm. These areunknown, and the EM algorithm is used to estimate thestates of the underlying Markov chain fXig and thetransition probabilities

�ij ¼ PðXlþ1 ¼ sjjXl ¼ siÞ; i; j ¼ 1; 2; . . . ;m: ðB1Þ

Suppose there are n observations y1; y2; . . . ; yn whereyi ¼ Xi þ ni and where ni conditioned on Xi ¼ sl isindependent of both fX1;X2; . . . ;Xi�1g andfn1; n2; . . . ; ni�1g, and is Gaussian with mean �l andvariance �2

l . In Figure B1, the points yi form the clouds

of small dots; they tend to cluster around certain perdecenters that are the pitches si used in the performance.For notational convenience, define �l ¼ ð�l; �

2l Þ,

l ¼ 1; 2; . . . ;m. Conditioned on Xi ¼ sl, yi is Gaussianwith mean sl þ �l and variance �2

l , and the probabilitydensity is

f ðy : �lÞ ¼expð�ðy � �l � slÞ2=2�2

l Þffiffiffiffiffiffiffiffiffiffi2��2

l

p : ðB2Þ

The EM algorithm updates the estimates of the param-eter values �ij and �i for i; j ¼ 1; 2; . . . m by computingthe ‘‘forward’’ probabilities

ajð1Þ ¼ ujð1Þf ðy1 : �jÞ; j ¼ 1; 2; . . . ;m

ajðiÞ ¼Xm

k¼1

akði� 1Þ�kj f ðyi : �jÞ;

j ¼ 1; 2; . . . ;m i ¼ 2; . . . ; n

ðB3Þ

(which can be initialized to ujð1Þ ¼ 1=m, j ¼ 1; 2; . . . ;m) and the ‘‘backward’’ probabilities

bjðnÞ ¼ 1; j ¼ 1; 2; . . . ;m

bjðiÞ ¼Xm

k¼1

�jk f ðyiþ1 : �kÞbkðiþ 1Þ;

j ¼ 1; 2; . . . ;m and i ¼ n� 1; n� 2; . . . ; 1:

ðB4Þ

The likelihood L ¼Pm

j¼1 ajðnÞ increases at each itera-tion. Updated estimates of the parameters are

–200

0

pitc

h (c

ents

)

time

200

400

600

800

FIGURE B1. A six-second segment from the Ussak taksim. The cloud of

small points are the instantaneous pitches as detected by the Tarsos-

YIN procedure. The solid horizontal lines are the perde centers as

detected by the EM-Viterbi method, which can be exported directly

into MIDI. The EM step detects the scale values (in this case, seven

pitches at —212, —3.5, 158, 276, 495.5, 713, and 880 cents as well the

probabilities of transition, which are not shown). The Viterbi step finds

the most probable path (the best set of horizontal lines) to maximize the

likelihood throughout the complete performance.

Experiments on the Relationship between Perde and Seyir in Turkish Makam Music 339

��jk ¼Pn

i¼2 �jkðiÞPni¼2

Pml¼1 �jl ið Þ j; k ¼ 1; 2; . . . ;m

��j ¼Pn

i¼1 ujðiÞyiPni¼1 uj ið Þ j ¼ 1; 2; . . . ;m

�2�j ¼

Pni¼1 ujðiÞðyi � ��j Þ

2

Pni¼1 ujðiÞ

j ¼ 1; 2; . . . ;m

ðB5Þ

where

ujðiÞ ¼ajðiÞbjðiÞ

Lj ¼ 1; 2; . . . ;m i ¼ 1; 2; . . . ; n

vjkðiÞ ¼�jk f ðyi : �kÞajði� 1ÞbkðiÞ

Lj; k ¼ 1; 2; . . . ;m i ¼ 2; . . . ; n:

ðB6Þ

The iterations may be initialized with �ij ¼ 1=m for alli; j ¼ 1; 2; . . . ;m and �i ¼ 0. The most probable pathis the sequence of states that maximizes the likelihood.Let ðnÞ ¼ max

x1;...;xn

PðX1 ¼ x1;X2 ¼ x2; . . . ;Xn ¼ xn; y1;

y2; . . . ; ynjparametersÞ; jðkÞ ¼ maxx1;...;xk�1

PðX1 ¼ x1; . . . ;

Xk�1 ¼ xk�1;Xk ¼ sj; y1; . . . ; ykjparametersÞ; and letmjðkÞ be the argument x1; x2; . . . ; xk�1 at which themaximum of jðkÞ occurs. This is the most probablepath to be in state sj at time k, given the observationsup to time k. Initializing jð1Þ ¼ 1

m f ðy1 : �jÞ forj ¼ 1; 2; . . . ;m and pjð1Þ ¼ mjð1Þ ¼ , this can becomputed by the iteration:

jðkþ 1Þ ¼ ðmaxiiðkÞ�ijÞf ðykþ1 : �jÞ

j ¼ 1; 2 . . . ;m k ¼ 1; 2; . . . ; n� 1

pjðkþ 1Þ ¼ arg maxiiðkÞ�ij

j ¼ 1; 2 . . . ;m k ¼ 1; 2; . . . ; n� 1

mjðkþ 1Þ ¼ ½mpjðkþ1ÞðkÞ; spjðkþ1Þ�:

ðB7Þ

The most probable path is then constructed from theViterbi backtracking procedure. Since jðnÞ is known forj ¼ 1; 2; . . . ; n, let pn ¼ arg maxj jðnÞ. The most prob-able path

fmpnðnÞ; spng ð8Þ

represents an approximation to the perde centers ofthe performance. This is the ‘‘best’’ (in the maximumlikelihood sense) set of ‘‘notes’’ (the horizontal lines inFigure B1) to approximate the instantaneous pitch mea-surements (the small dots). While this method of pitch

extraction may seem complicated, it does not requirea large number of free parameters (such as thresholdsand filter-lengths) that are dependent on the details ofthe timbre of the sounds being analyzed (Bozkurt et al.,2010). The only parameters that must be chosen areinitial values for the scale steps si; these can be conve-niently chosen from the peaks of the histogram of theobservations yi.

C. Calculation of Fleiss’ Kappa

The kappa coefficient (Fleiss, 1971) can be applied tomultiple raters on categorical data. The kappa value

� ¼�P � R1� R

ðC1Þ

indicates the amount of agreement beyond that expectedby chance, where �P is the observed agreement and R isthe agreement expected by chance alone. These are cal-culated as shown in Equations C2 and C3 below.

Let N be the number of sound examples in the exper-iment, M the number of raters (experts), K the numberof categories (makams), and mn;k the number of expertswho chose the kth makam in response to the nth soundexample. The proportion of all assignments to the kthmakam is

pk ¼1

NM

XN

n¼1

mn;k:

SinceP

k mn;k ¼ M, the pk’s sum to unity, i.e.,Pk pk ¼ 1. If the experts chose makams at random,

the average agreement would be

R ¼XK

k¼1

p2k: ðC2Þ

The amount of agreement observed among the Mexperts in the nth sound example is calculated from theproportion of agreeing pairs out of all the MðM � 1Þpossible pairs. This is

Pn ¼1

MðM � 1ÞXK

k¼1

mn;kðmn;k � 1Þ;

which are averaged to give

�P ¼ 1N

XN

n¼1

Pn: ðC3Þ

Equations C2 and C3 are then combined to give the � ofC1. � values may be interpreted as in Table 2, although it

340 Can Akkoç, William A. Sethares, & M. Kemal Karaosmanoglu

is important to understand that with the small numberof sound examples, there is no plausible way to measurethe statistical significance of these values.

In calculating the � values for the makam tests, somedecisions are required in the interpretation of theresponses. For example, some of the experts gave morethan one answer: should the � value be calculated basedon the first/primary answer alone or should theresponse be ‘‘split into two’’ with each being weighted(and if so, what weighting should be applied)? Anotherissue occurs when two makams have the same intervalcontent; for example, whether Beyati and Ussak, whichhave identical interval sets, should be considered agree-ment or disagreement. Since each such variation maygive a slightly different value, we report a range ofvalues. In particular, �1 uses only the first/primaryanswer of each expert, �2 weights all multiple responsesequally, and �3 considers makams with identical inter-val sets to be ‘‘the same response.’’ For example, inExperiment 1, N ¼ 6 sound examples and M ¼ 3experts. With K ¼ 8 different makams in the responses,�1 ¼ :67; with K ¼ 8, �2 ¼ :71; with K ¼ 7, �3 ¼ :73.Accordingly, we report the range of values� 2 ð:67; 0:73Þ. A list of the parameters used in the �calculations is given in Table C1.

Because the sound examples in each experiment werenot all based on the same kinds of sound manipulations,we also calculate the �-values for a set of pseudo-experi-ments which analyze the results of the sound exampleswith all equivalent sound modifications analyzedtogether (instead of analyzed in the groupings in whichthey were presented to the experts). These are:

1. Pseudo-experiment 1: all the data from Experiment1 plus the mahurLinear sound example from Exper-iment 2.

2. Pseudo-experiment 2: data from Experiment 2(with mahurLinear removed), plus the RastXXXXexamples from Experiment 3.

3. Pseudo-experiment 3: data from Experiment 3(with RastXXXX examples removed).

The recalculated kappa values for these revised experi-ments are shown in the bottom half of Table C1. Theranges change somewhat: from (.67, .73) for Experiment1 to (.72, .76) for Pseudo-experiment 1, from (.26, .34)for Experiment 2 to (.29, .36) for Pseudo-experiment 2,and from (.45, .62) for Experiment 3 to (.30, .39) forPseudo-experiment 3. Experiment 4 is unaffected by thisre-grouping strategy. In terms of the agreement shown(as in Table 2), the only change is that Pseudo-experiment 3 has ‘‘fair’’ agreement while Experiment 3has ‘‘moderate’’ agreement. This may indicate someinfluence of learning or influence from side informationgleaned from conversations between the experiments.On the other hand, it should be intuitively clear that therandomized scramblings of Pseudo-experiment 3 pose atleast as difficult a task as the more modest scramblings ofPseudo-experiment 2. This intuition is more consistentwith the overlapping �-ranges of Pseudo-experiments 2and 3 than with the increase in �-ranges from Experi-ments 2 to 3.

D. Generation of Cross-Makam Sound Stimuli

This appendix details the technique used to create thesound stimuli for Experiment 4 in which each soundexample is constructed using the pitch profile of onemakam and the temporal profile of another. The basicsource material is the original corpus of 17 makams,each of which is subjected to the analysis of AppendixB. For each sound example, two makams are chosen,which are labeled A and B.

The most probable path for makam A is given by Eq.B8 as a sequence of frequency/time triples

ðf1; t1; e1Þ; ðf2; t2; e2Þ; . . . ; ðfnA ; tnA ; enAÞ ðD1Þ

TABLE C1. Details of the calculation of the � parameters for thefour experiments and the three pseudo-experiments (see text). Thenumber of experts M is three in all cases.

Experiment N K �

1 6 8 �1 ¼ 0:6711 6 8 �2 ¼ 0:7141 6 7 �3 ¼ 0:7352 6 7 �1 ¼ 0:3452 6 7 �2 ¼ 0:2632 6 5 �3 ¼ 0:3193 6 7 �1 ¼ 0:5003 6 8 �2 ¼ 0:4473 6 5 �3 ¼ 0:6224 8 10 �1 ¼ 0:4244 8 10 �2 ¼ 0:4244 8 6 �3 ¼ 0:411

Pseudo-experiment

1 7 9 �1 ¼ 0:7251 7 7 �2 ¼ 0:7551 7 9 �3 ¼ 0:7622 7 9 �1 ¼ 0:2982 7 8 �2 ¼ 0:2952 7 5 �3 ¼ 0:3593 4 5 �1 ¼ 0:3873 4 5 �2 ¼ 0:3043 4 4 �3 ¼ 0:361

Experiments on the Relationship between Perde and Seyir in Turkish Makam Music 341

where nA is the total number of pitch events (notes) inthe performance, the start and end times ti and ei are inseconds (accurate to about 0.01 s), and the fundamentalfrequencies fi are in Hz. The Viterbi procedure leadingto Eq. B8 ensures that the fi are quantized to a smallnumber of values (eight per octave) which are the scalesteps sj

1; sj2; . . . ; sj

8 where

j ¼1 octave above root0 octave of the root�1 octave below root

8<: :

Similarly, the most probable path for makam B is

ðf1; t1; e1Þ; ðf2; t2; e2Þ; . . . ; ðfnA ; tnB ; enBÞ ðD2Þ

where nB is the total number of notes in performance Band frequency is again quantized by Eq. B8 to the scalesteps sj

1; sj2; . . . ; sj

8.In any given performance, not all scale steps may

appear in all octaves. For example, there may be nooccurrences of scale pitch s1

2 in makam A even thoughthere are occurrences of the corresponding pitch inmakam B. Since the goal is to create a mapping betweens and s, missing terms can be ‘‘filled-in’’ using occur-rences of the same scale step in other octaves. Thus themissing s1

2 would be set equal to 2s02. The mapping

between the two makams assigns the root note s01 of

makam A to the root note s01 of makam B, the second

scale step s02 of makam A to the second scale step s0

2, etc,until all have been assigned and there is a one-to-one

correspondence between the pitch sets used in the twomakams.

Somewhat more formally, let m be the number of(possibly filled-in) scale steps and relabel the s toremove the octave notation so that the sj

i are relabeledwith a single subscript �1; �2; . . . ; �m. Similarly, relabelthe sj

i as �1; �2; . . . ; �m. Let g be the map which takes �k

to �k and g�1 be its inverse, that is, �k ¼ gð�kÞ and�k ¼ g�1ð�kÞ for k ¼ 1; 2; . . . ;m.

The output sequences are created by applying the twomappings g and g�1 to the performances as extracted inEquations D1 and D2. For instance, each of the ele-ments fi in 1 corresponds to one of the �k, which ismapped by g to �k. With a slight abuse of notation,denote this element gðfiÞ � gð�kÞ ¼ �k, and thesequence becomes

ðgðf1Þ; t1; e1Þ; ðgðf2Þ; t2; e2Þ; . . . ; ðgðfnAÞ; tnA ; enAÞ; ðD3Þ

which consists of nA pitches from makam B, each ofwhich is associated with a start and end time specifiedby makam A. This sequence is then translated intoa MIDI representation (where the frequencies are spec-ified by MIDI note-number and pitch-bend) and thensynthesized into audio using the same sounds as in theprevious sound stimuli. The resulting sound examplecontains the perdes/pitches from makam B (i.e., thepitches gð�kÞ performed with the timing/temporalinformation from makam A (i.e., at timest1; t2; . . . ; tnA ). Similarly, the sequence

TABLE D1. Example of cross-makam generation of Ussak and Muhayyer. All frequencies are given in Hz.

Ussak MuhayyerComment Fundamental Scale Scale Fundamental

Frequencies Step Label Label Step Frequencies Comment

lead 199.14 s�17 �1 �1 s�1

7 202.30 leadroot 225.97 s0

1 �2 �2 s01 226.71 root

242.32 s02 �3 �3 s0

2 243.74263.78 s0

3 �4 �4 s03 264.06

dom 297.76 s04 �5 �5 s0

4 298.71342.26 s0

5 �6 �6 s05 343.95 dom

352.02 s06 �7 �7 s0

6 367.01lead 398.28 s0

7 �8 �8 s07 404.59 lead

octave 451.94 s11 �9 �9 s1

1 453.43 octave* 484.64 s1

2 �10 �10 s12 487.48

527.56 s13 �11 �11 s1

3 528.13dom* 595.52 s1

4 �12 �12 s14 597.43

* 684.52 s15 �13 �13 s1

5 687.91 dom* 704.04 s1

6 �14 �14 s16 734.02

342 Can Akkoç, William A. Sethares, & M. Kemal Karaosmanoglu

ðg�1ðf1Þ; t1; e1Þ; ðg�1ðf2Þ; t2; e2Þ; . . . ; ðg�1ðfnBÞ; tnB ; enBÞðD4Þ

consists of nB pitches from makam A which are associ-ated with starting and ending times ti and ei from makamB. When translated into MIDI and then into sound, thiscontains the perdes/pitches from makam A with thetiming/temporal information from makam B.

To show the procedure concretely, consider the firstsound example which combines elements of Ussak andMuhayyer. The procedure of Appendix B applied to theUssak makam results in a sequence defined by Eq. D1containing nA ¼ 105 note events, each with a specifiedpitch, start time, and end time. There are 10 distinctpitches (those without asterisks in first column) with fun-damental frequencies that appear in the second column ofTable D1. The same procedure applied to the Muhayyermakam results in a sequence given by Eq. D2 containingnB ¼ 183 note events with the 14 different fundamentalfrequencies listed in the seventh column of Table D1.

Corresponding to the frequencies are the scale steps sji

and sji and the relabeling of the corresponding �k and

�k. The comments show important notes in the scales:the leading tone, root, and dominant. For Ussak andMuhayyer, these align closely; the major difference is

the location of the dominant. (These labels play no rolein the construction of the sound examples, they areintended to aid in the interpretation of the results.) Thefour asterisks in the leftmost column indicate the fournotes that appear in the performance of the Muhayyermakam that are missing from the Ussak performance. Inorder to have a one-to-one mapping between the scalesteps of the two makams, it was necessary to fill-in thesevalues as described above. This is why (for instance) s1

4 isexactly twice s0

4. The mappings g and g�1 can be readdirectly from the rows of the table, and constructing thesound examples D3 and D4 is now a matter of substitut-ing the desired values into the sequences. The othersound examples are constructed similarly.

Thus each of the synthesized sound examples con-tains certain aspects derived from makam A and otheraspects derived from makam B. In the example, thepitch structure of makam A (Ussak) is grafted ontothe temporal structure of makam B (Muhayyer); thesequence of pitches and their timings is determinedby the Muhayyer, but the exact pitches that occur aredetermined by the Ussak. We state this concisely(although somewhat inaccurately) by saying that theexample contains ‘‘perdes from Ussak’’ and the ‘‘seyirfrom Muhayyer.’’

Experiments on the Relationship between Perde and Seyir in Turkish Makam Music 343