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Journal of Experimental Psychology: General . „ u , C?Pyri8ht 1984 by the

1984, Vol. 113, No. 3, 394-412 American Psychological Association, Inc.

Tonal Hierarchies in the Music of North India

Mary A. Castellano J. J. BharuchaCornell University Dartmouth College

Carol L. KrumhanslCornell University

SUMMARY

Cross-culturally, most music is tonal in the sense that one particular tone, called thetonic, provides a focus around which the other tones are organized. The specific orga-nizational structures around the tonic show considerable diversity. Previous studies ofthe perceptual response to Western tonal music have shown that listeners familiar withthis musical tradition have internalized a great deal about its underlying organization.Krumhansl and Shepard (1979) developed a probe tone method for quantifying theperceived hierarchy of stability of tones. When applied to Western tonal contexts, themeasured hierarchies were found to be consistent with music-theoretic accounts.

In the present study, the probe tone method was used to quantify the perceived hierarchyof tones of North Indian music. Indian music is tonal and has many features in commonwith Western music. One of the most significant differences is that the primary meansof expressing tonality in Indian music is through melody, whereas in Western music itis through harmony (the use of chords). Indian music is based on a standard set ofmelodic forms (called rags), which are themselves built on a large set of scales (thats).The tones within a rag are thought to be organized in a hierarchy of importance.

Probe tone ratings were given by Indian and Western listeners in the context of 10North Indian rags. These ratings confirmed the predicted hierarchical ordering. Bothgroups of listeners gave the highest ratings to the tonic and the fifth degree of the scale.These tones are considered by Indian music theorists to be structurally significant, asthey are immovable tones around which the scale system is constructed, and they aresounded continuously in the drone. Relatively high ratings were also given to the vaditone, which is designated for each rag and is given emphasis in the melody. The ratingsof both groups of listeners generally reflected the pattern of tone durations in the musicalcontexts. This result suggests that the distribution of tones in music is a psychologicallyeffective means of conveying the tonal hierarchy to listeners whether they are familiarwith the musical tradition. Beyond this, only the Indian listeners were sensitive to thescales (thats) underlying the rags. For Indian listeners, multidimensional scaling of thecorrelations between the rating profiles recovered the theoretical representation of scalesdescribed by theorists of Indian music. Thus, the empirically measured tonal hierarchyinduced by the rag contexts generates structure at the level of the underlying scales orthats, but its internalization apparently requires more extensive experience with musicbased on that scale system than that provided by the experimental context. There waslittle evidence that Western listeners assimilated the pitch materials to the major andminor diatonic system of Western music.

394

TONAL HIERARCHIES IN INDIAN MUSIC 395

Music can be described in terms of a num-ber of basic attributes: melody, harmony,rhythm, timbre, and musical form. Acrosscultures, there are marked differences in theemphasis given to these various dimensions.For example, much of the structural com-plexity of Western music is rooted in harmony,whereas in the music of North India, the focusof complexity is on melody and rhythm. Eth-nomusicologists describe the striking varietyof organizational schemes that have developedfor each aspect of the structured sound ma-terials of music. One organizational principlefound quite generally, however, is tonality.Tonality is the centering of the musical ma-terials around one particular tone, called thetonic or tonal center. The tonic is given em-phasis in the music through a variety of means.From a psychological point of view, it functionsas a reference point for the set of musicalpitches as a whole (Krumhansl, 1979), suchthat the listener perceives each sounded ele-ment in its relation to the tonic. The tonic,thus, plays a central role in the process throughwhich the listener assimilates the sounded ele-ments and derives a sense of the underlyingorganization.

This general description of tonality appliesto most music employing variations in pitch,but the particular manner in which tonalityis expressed takes a variety of forms. In tra-ditional Western music, the choice of the tonicimplies a particular set of scale pitches, butthe primary means of establishing tonality isharmonic, that is, through the use of particularcombinations of tones as chords, which maybe realized as tones sounded simultaneouslyor implied by successive tones. Out of thisharmonic practice has developed a structural

- This research was supported by National Science Foun-dation Grant BNS-81-03570 to Carol L. Krumhansl, whocompleted the manuscript as a Fellow at the Center forAdvanced Study in the Behavioral Sciences, with supportfrom National Science Foundation Grant BNS-76-22943.

The authors are grateful for the helpful comments ofMartin Hatch, Elizabeth Bharucha, Ray Jackendoff, Ed-ward Kessler, Diana Deutsch, W. Jay Dowling, and FredLerdahl.

Requests for reprints should be sent to Carol L. Krum-hansl, Department of Psychology, Cornell University, Ith-aca, New York 14853, or to J. J. Bharucha, Departmentof Psychology, Dartmouth College, Hanover, New Hamp-shire 03755.

level that relates the different keys, or tonalcenters, to one another. These interkey rela-tionships are musically instantiated as mod-ulations, or changes, between keys within acomposition. Music theory provides systematicaccounts of interkey distance and the com-positional methods for achieving the shift fromone tonal center to another (see, e.g., Piston,1978; Schoenberg, 1954/1969).

Music-theoretic descriptions of Indian mu-sic (Jairazbhoy, 1971) also refer to relationsbetween different tonal organizations, repre-sented by a large array of scales, called thdts.(When using Hindi words in this article, a barover an a indicates that the a is pronouncedas in ma; an a with no bar is to be pronouncedlike a u as in cut.) On these thats are builtcharacteristic clusters of melodic features,called rags. A rag specifies a set of melodicfeatures to be used in a musical performance,features that are thought to embody a uniqueaffective quality. Among these characteristicfeatures are a catch phrase (pakar), and per-haps a typical ascending (aroh) and descending(avroh) line. "A rag does not exist in any pre-cise form . . . but is a complex of latent me-lodic possibilities" (Jairazbhoy, 1971, p. 32).Classification systems for the rags have in-cluded ethnological origins, geographic asso-ciations, the time of day the rag is to be per-formed, the nature and number of tones, andsimilarities in melodic patterns. The classifi-cation system most analogous to the Westernsystem of musical keys, however, is one inwhich the rags are ascribed to a system ofthats, or parent scales, which are presumed tobear specific relations to one another.

Unlike traditional Western music, whichpredominantly employs just two scales, majorand minor, Indian music draws its pitch ma-terials from a greatly expanded set of hepta-tonic scales, called thats. Explicit represen-tations provided by music theorists, often ofa geometrical nature, show the degree of re-latedness between these scales (Jairazbhoy,1971). These relations are not expressed di-rectly in Indian music as modulations, whichrarely occur, nor are they derivative of theharmonic functions of chords, which do notappear in Indian music. Yet, Indian musictheorists have suggested that rags might beorganized around a system of underlying scalesin a way that is analogous to the key relations

396 M. CASTELLANO, J. BHARUCHA, AND C. itRUMHANSL

in Western music. We present here an empir-ical study of the psychological basis for thisclassification system and consider possiblecommonalities with the psychological repre-sentation of Western tonal organization.

Empirical Studies of Tonal Organization

A primary motivation for the empirical in-vestigation of the psychological response tomusic is the development of a systematic de-scription of musical structure that is informedfrom a psychological point of view and thatprovides a suitable descriptive framework formusic of diverse styles. For the most part,quantitative analysis of musical structure cross-culturally has been limited to measurementsof tuning systems, that is, the frequencies ofthe musical pitches. Although such investi-gations provide a way of comparing certainphysical properties, such as interval sizes, theyhave limited utility as a means of studyingperceptual and cognitive factors. An alternativeapproach is to devise methods for measuringattributes that may be primarily, or perhapsentirely, psychological in character.

A method for assessing the psychologicalresponse to one aspect of musical structure,tonal organization, is the probe tone method(Krumhansl & Kessler, 1982; Krumhansl &Shepard, 1979). In previous studies, thismethod has been applied to traditional West-ern music. The present study extends it to themusic of North India. The objective is toquantify the hierarchy of stability or structuralsignificance induced by a tonal context on theset of musical tones. As described by Westernmusic theorists, a tonal context establishes ahierarchical ordering on the set of 12 pitchesin each octave. The tone that dominates inthe hierarchy is the tonic. Following the tonicin the hierarchy are the other tones that areclosely related to the tonic; in Western music,these are the third and fifth tones of the scale,the tones that together with the tonic form thetonic triad chord. The other scale tones occupythe next lower levels of hierarchy, and thenonscale (nondiatonic) tones occupy the lowestlevels.

To obtain a quantitative measure of thishierarchy, subjects in the earlier experimentswere presented with a context (a scale, tonictriad chord, or chord cadence) that quite un-

ambiguously established either a major or mi-nor key. This context was then followed by asingle probe tone, 1 of the 12 possible (chro-matic) tones in an octave; the listener's taskwas to rate how well the final probe tone fitwith the preceding context in a musical sense.The results recovered the patterns expectedfrom the qualitative music-theoretic accountjust outlined.

Krumhansl and Kessler (1982) demon-strated that a highly regular and interpretablespatial representation of the relations betweenkeys could be derived from the quantified tonalhierarchy. To obtain a measure of the psy-chological proximity of any two keys, theirrespective rating profiles were correlated. Highcorrelations correspond to keys that induce asimilar hierarchical ordering on the set of mu-sical tones, indicating a close relation betweenthe two keys. Low correlations correspond todistantly related keys. These correlations,computed for each possible pair of keys, werethen analyzed using multidimensional scaling.In the resulting configuration, the points forthe 24 major and minor keys were located onthe surface of a torus in four dimensions. Onthis surface, there was one circle of fifths formajor keys and one for minor keys; these werealigned to represent the parallel and relativerelations between major and minor keys. Theresults accorded well with music-theoreticdescriptions of key structure, containingSchoenberg's (1954/1969) maps of musicalkeys, in local regions.

Krumhansl and Kessler (1982) also notedthat keys closely positioned in the spatial rep-resentation share harmonically significantchords. That is, structure at the level of keysor tonal centers reflects the fact that musicalchords frequently play roles in more than onekey. This raises the possibility that the obtaineddescription of key structure may not be a con-sequence solely of the information summa-rized in the quantified tonal hierarchy but maybe based wholly or in part on the harmonicfunctions of chords in Western music. An al-ternative or additional factor that may con-tribute to perceived key proximity is the rel-ative frequency of modulations between dif-ferent keys. Modulations in music occur mostfrequently between keys that are closely po-sitioned in the spatial representation.

In Western music, these three factors—tonal


hierarchy, harmonic functions of chords, andmodulation frequency—are so closely inter-related that it is difficult to assess their relativecontributions. Krumhansl and Kessler (1982)assigned the primary contribution to the tonalhierarchy itself. However, key structure canalso be derived from measures of perceivedchord relations (Bharucha & Krumhansl,1983; Krumhansl, Bharucha, & Castellano,1982; Krumhansl, Bharucha, & Kessler, 1982).In addition, there are suggestions that key dis-tance may be closely linked to modulationsand transpositions, that is, changes of key.Krumhansl and Kessler (1982) showed thatmodulations between distant keys are moredifficult to assimilate than are those betweenclosely related keys. Cuddy, Cohen, and Miller(1979) and Bartlett and Dowling (1980) foundeffects of key distance on recognition of trans-posed melodies, Together, these studies pointto three interdependent factors as contributingto key structure in traditional Western music.Therefore, Indian music, which lacks bothmodulations and harmonic chord functions,provides an interesting comparison case inwhich the contribution of the tonal hierarchycan be assessed independently of the other twofactors.

Tonal Hierarchies in Indian Music

Like traditional Western music, Indian mu-sic is organized around a single tone, the tonic,which is called Sa. In practice, different pitchesmay serve as the tonic, but in most theoreticalaccounts the tonic is set by convention to bethe tone C. Sa (C) serves as the starting pointof the scale and is the most stable of the scaletones. The fifth scale tone, Pa (G), is consideredthe next most stable (except in the few scalesthat exclude it). In both Western and Indianmusic, tones in, the melody are usually per-ceived as anchored to the most stable tones,primarily the tonic. This anchoring is achievedby a variety of means: by using stable tonesmore frequently than less stable tones, byplacing stable tones in metrically strong po-sitions and at beginnings and endings ofphrases, by following unstable tones with stabletones in the form of a resolution, and by usingtones from established musical scales. In In-dian music an additional mechanism, a drone,is used to explicitly anchor the melody line to

the tonic. A drone is the continuous soundingof the tonic, Sa (C), and usually the fifth scaletone, Pa (G). The only Western counterpartto the drone is the pedal point, a tone heldfor a long duration, normally in the bass, whileother voices carry changing harmonies.Whereas the Western pedal point is typicallyused for the duration of a few measures orphrases, the Indian drone is present throughouta performance.

Jairazbhoy (1971) asserts that it is the rel-ative dissonance of certain tones with respectto the drone that induces a need for resolutionto one of the drone tones or to a tone consonantwith the drone. According to Jairazbhoy, thisdissonance accounts for both the need to relateeach tone independently to the tonic and theneed to resolve unstable tones to the stabletones that follow them. The grounding of eachtone to the tonic is reflected in the fact thatmodulation rarely occurs because the originaltonic is sounded continuously.

In addition to the degree of consonance, thehierarchy of stability would also be expectedto reflect the particular selection of tones thatconstitutes the scale underlying the musicalcontext. Indian music employs a large set ofscales, and the intervals contained in the scalesprovide a distinctive flavor for the rags builton them. In addition, certain rags deviate fromtheir underlying scale by the addition or dele-tion of one or more tones, and these deviationsin tuning are said to contribute to the uniquecharacter of the rag. The effect of consonanceand dissonance may therefore be modified bythe contribution of the particular tonal ma-terials employed in the musical context.

For each rag, two other tones, called thevadi and samvadi, play important roles. Onlyfor a few rags are Sa (C) or Pa (G) designatedas the vadi or the samvadi, because the prom-inence of Sa and Pa is common to most rags,whereas the vadi and samvadi are unique toindividual rags. There are no clear definitionsof these two tones. However, Bhatkhande (citedin Jairazbhoy, 1972, p. 66) defines the vadi as"that note which compared to the other notesin the rag, is sounded most often with clarity,"and Danielou (1968, pp. 61-62) describes itas the "predominant note from which all vari-ations begin and on which they end: it is alwaysaccentuated and bears long pauses." The sam-vadi is said to be the second most sounded

398 M. CASTELLANO, J. BHARUCHA, AND C. KRUMHANSL

note, assisting the vadi in the creation of amood. Ideally, the samvadi should be separatedfrom the vadi by an interval of a fifth. In ac-tuality, the employment of the vadi and sam-vadi is somewhat ambiguous, and their char-acteristics are still a matter of debate by musictheorists (e.g., Jairazbhoy, 1972).

To summarize, Indian music theory suggeststhat a number of factors may influence theordering of tones in the tonal hierarchy. Thetonic, which is sounded as the primary drone,would be expected to dominate in this hier-archy. A relatively high position may also beexpected to be given to the secondary drone,which is usually the fifth tone of the scale. Thedesignated vadi and samvadi may also be per-ceived as prominent compared with the re-maining scale tones. Finally, the set of tonesin the underlying scale would be expected tohold generally higher positions in the hierarchythan the tones not in the scale.

Circle of Thats

The term that refers to the scales, each con-sisting of seven tones, on which rags are built.The names of the seven degrees of the that(Sa, Re, Ga, Ma, Pa, Dha, Ni) bear an exactcorrespondence to the Solfege syllables (Do,Re, Mi, Fa, Sol, La, Ti), in that they stand forthe notes of the major diatonic scale. One that,Bilaval, is identical to the major scale. In otherthats, one or more of the scale degrees is flator sharp, that is, raised or lowered by a halfstep. Sa (C) and Pa (G), the first and fifth scaledegrees, are considered immovable and arenever altered in any of the scales. The re-maining five that tones may be altered, eachin one direction only. Re (D), Ga (E), Dha(A), and Ni (B) may be lowered by a half step,and Ma (F) may be raised by a half step. Thealtered scale degrees are denoted Re t, Ga t,Ma#, Dhat, and NH, respectively. Any com-bination of the five movable tones may be used,giving rise to a set of 32 possible seven-tonescales. In South Indian music, fewer restric-tions are placed on the pitch direction in whichthe movable tones may be altered, giving riseto 72 scales, of which the 32 North Indianscales are a subset.

Although these 32 scales provide the frame-work for the classification of all rags in NorthIndian music, Bhatkhande (cited in Jairaz-

CIRCLE OF THA'TS

KALYAN

BILAVAL

KHAMA'J

KAFI

ASAVRI

Figure 1. The circle of thats illustrating inter-that distance.(Nine of the 10 thats on the circle are members of Bhatk-hande's classification system. No. 7 is not currently usedin North Indian music. That Bhairav occupies a positioninside the circle.)

bhoy, 1971) classifies nearly all the rags under10 of thje 32 thats. Nine of these thats fall onwhat is called the circle of thats, shown inFigure 1. The tones contained in the thats areshown in musical notation in Figure 2 and aredesignated by their letter names in Table 1.Although there are 10 thats around this circle,1 (No. 7) is not currently used. The 10th thatin Bhatkhande's system of classification isBhairav, which, as is shown in Figure 1, oc-cupies a position inside the circle of thats. Onthe circle, each that shares all but one tonewith its neighboring thats. In this respect, thecircle of thats is similar to the circle of fifths,which expresses the relations among the majorkeys and among the minor keys in Westernmusic. It should be emphasized, however, thatthe circle of thats represents the relationsamong scales that all have the same tonic tone,unlike the circle of fifths in which the scale ofeach key is based on a different tonic. More-over, certain thats consist of a set of tones notshared by any major or minor Western scale.

Figure 2 illustrates a theoretical accountgiven by Jairazbhoy (1971) for the circle ofthats. This account examines the thats for thepresence of an augmented fourth (an interval

TONAL HIERARCHIES IN INDIAN MUSIC

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Figure 2. Jairazbhoy's theoretical model for the circle o£ thats based on a systematic progression formedby "correcting" the diminished or augmented fourths of thats.


Table 1Rags Used in the Experiment

Rag Parent that That tones Vadi Samvadi Tuning

BhairavYamanBilavalKhamajKafiAsavriBhairviTodiPurviMarva

BhairavKalyanBilavalKhamajKafiBhairviBhairviTodiMarvaMarva

(C, D|,,E, F, G, Al.B)(C, D, E, F#, G, A, B)(C, D, E, F, G, A, B) .(C, D, E, F, G, A, Bl)(C, D, El., F, G, A, Bl)(C, Dl.E'l , F,G, AI .BI)(C, Dl, El, F, G, Al, B»(C, Dt .El , F#,G, A I, B)(C, D I, E, FW, G, A, B)(C, D I; E, FW, G, A, B)

AlEAEGA lCAlEE

DlBEBCDlFElBA

Same as thatSame as thatB missingB addedSame as thatSame as thatD and F# addedSame as thatF addedG missing

of three whole steps formed by four successivescale tones) or a diminished fourth (an intervalof two whole steps formed by four successivescale tones). For example, in the Kalyan that,there is one augmented fourth formed by Sa(C) and Ma# (FW). If one-"corrects" this aug-mented fourth by lowering the Ma# by a halfstep to Ma (F), one obtains the next that, Bi-laval, around the circle. However, this intro-duces another augmented fourth between Ma(F) and Ni (B) that, when altered, producesthe next that around the circle. This processcontinues to account for the succession of thatsuntil the Bhairvi that is reached. At this point,the process cannot be continued further, be-cause this would mean lowering Pa (G) a halfstep, which would violate the fundamentalpremise that Pa is immovable, that is, that itcannot be raised or lowered. The enharmon-ically equivalent tone, Ma# (FW), is introducedinstead, giving the that labeled A7 (not in cur-rent usage). However, this introduces a di-minished fourth between Ma# (F#) and Ni [,(B t), which is corrected in the next step aroundthe circle by raising the Nit (Bl.) to Ni (B),giving the Todi that. This in turn introducesa diminished fourth between Ni (B) and Ga \>(El>), which is then changed to Ga (E), givingthe next that, Purvi. This process of succes-sively raising the upper tone of the diminishedfourth continues until finally the first that,Kalyan, is reached.

This theoretical account generates the cir-cular configuration called the circle of thats,which plays a central role in Bhatkhande'sclassification system of rags. The circle of thatsshares certain structural features with the circleof fifths, namely that successive scales overlap

in all but one scale pitch. Indeed, thats Kalyanthrough Bhairvi correspond in their scalepitches to the Western keys of G, C, F, B|>,E[>, and A|> major, respectively. They differ,however, in that the Indian thats are all basedon a fixed tonic, Sa (C), whereas each majorkey has a different tonic. The remaining thats,A7 through Marva, do not correspond to theset of scale pitches of any major or minor keyin that they contain distinctively differentcomponent intervals.

North Indian Rags

The concept of a rag has no counterpart inWestern music. There exist several hundredrags, with distinctive melodic figures. Thus, arag is characterized not only by its scale butalso by the manner in which it combines thetones. Jairazbhoy (1971, p. 28) describes a ragas the "melodic basis for composition and im-provisation." Music-theoretic descriptions ofIndian music refer extensively to the emotionalcontent of rags and even assign qualities tothe individual tones out of which they are con-structed. Although our present focus is on fac-tors governing pitch organization, considerableweight is given in Indian music theory to theaffective dimension also (Bose, 1960; Danie-lou, 1968; Jairazbhoy, 1971;Kaufmann, 1968;Neuman, 1980).

A musical performance consists of theexpression of a rag set to a particular metricpattern (tal). A musical performance typicallybegins with an exposition of the characteristicmelodic features of the rag, the specific deliveryof which is improvised by the performer. Thisexposition, called the dldp, is metrically free,


seeming to consolidate the rag before the talis introduced by the drummer. When the talis first introduced, following the alap, the me-lodic line usually follows a set composition(gat) that is based on the rag. As soon as thetal is consolidated, the performer may departfrom the set composition, using it only as abasis for improvisation. The set compositiongenerally has at least two sections, the sthdyiand the antrd. The sthayi is played mostly inthe lower and middle pitch registers and oftenfocuses on the vadi, whereas the antra is playedin the middle and upper pitch registers andoften focuses on the samvadi.

Experimental Design

Ten North Indian rags in common usagewere chosen as stimulus materials for the ex-periment. Table 1 presents the names of therags and their underlying thats, vadis, sam-vadis, and tunings (notes added or deleted fromthe thats) as given by Danielou (1968). These10 rags are classified under eight of the parentthats. It should be noted that some of the ragshave names that do not correspond to thenames of the underlying thats. In certain casesthe name of the rag is the same as the nameof some other that. This may reflect inconsis-tencies in the classification scheme, historicalchanges, or geographical differences. In anycase, we adopt Danielou's (1968) classification.To facilitate interpretation of the results pre-sented later, Figure 3 shows the 10 rags em-ployed in the study arranged according to thepresumed relations among the designated un-derlying scales.

The block of trials for each rag began withthe sounding of the sthayi section of the fixedcomposition played twice to establish the rag.Each experimental trial began with a brieftheme (roop), which incorporates the char-acteristic features of the composition andtherefore of the rag on which it is based. Figure4 shows in musical notation the sthayi andtheme from rag Yaman (Danielou, 1968).Musical examples can be heard on the recordaccompanying Jairazbhoy (1971) and otherrecordings of classical North Indian music.Using the probe tone method, the theme con-text on each experimental trial was followedby a single pitch, 1 of the 12 tones in an octaverange. The listener was asked to rate how well

RAGS ON THE CIRCLE OF THATS

BIL.3VAU

KHAMAJ

Figure 3. The 10 rags used in the experiment placed onthe circle of thats. (Each rag is located in the position ofits parent that.)

the final tone fit with the preceding contextin a musical sense. The listeners were dividedinto two groups based on their experience withIndian music.

Method

Subjects. Sixteen subjects were offered $4 for partic-ipating in one experimental session lasting 2 hr. Therewere two groups of 8 subjects. One group consisted oflisteners with considerable exposure to Indian music, 6 ofwhom were recruited from the India Student Association.Subjects in this group had been exposed to North Indianclassical music, beginning at an average age of 12 yearsold. Six played an Indian instrument, averaging 4 yearsof formal training. The 8 subjects listened to Indian musicfor an average of 3 hr per week and listened to Westernmusic for an average of 10 hr per week. Subjects in theother group had minimal exposure to and no formal in-struction in Indian music. Seven of these subjects playeda Western instrument, averaging 6 years of formal training.These 8 subjects listened to Western music 18 hr per week.Only 1 of these listeners reported having listened to Indianmusic.

Apparatus. The stimuli were synthesized digitally bya DMX-1000 (Digital Music Systems, Inc.) signal-pro-cessing computer under the control of a PDF-11/24 com-puter. Recordings were made on Maxell UD 35-90 tapesusing a Sony TC-388-4 tape recorder. The tapes were playedat 7 in. per s (19 cm per s) through an Ampex AA-620loudspeaker at approximately 65 dB sound pressure level.


Stimulus materials. Equal tempered tuning, based onan A(4) of 440 Hz, was used. Each tone consisted of afundamental and six higher harmonics with the followingamplitude ratios: 1, 1/3, 1, 1/3, 1, 1/3, 1. The amplitudeenvelope consisted of a 10-ms onset gradient followed bya linear decay to zero, thus simulating a plucked instrumentsuch as the sarod. Frequency modulation (Chowning, 1973)was used to simulate the sound of the C and G dronetones, with a ratio of 7:5 between modulator and carrierfrequencies and a modulation index of 10 (Digital MusicSystems, Inc., 1981).

The sthayi and theme for each rag were taken fromDanielou (1968). There were 10 blocks of trials, each rep-resenting 1 of the 10 rags shown in Table 1. Each blockof trials began with two successive presentations of thesthayi. The Duration of the sthayis averaged 65.75 s, witha range of 37.80-93.03 s. Following the sthayi, subjectswere presented with 14 experimental trials. Each trial con-sisted of a theme, followed by a 1-s pause, and then followedby a probe tone that was sounded for 1 s. The durationof the themes averaged 19.44 s, ranging from 10.80 s to

39.36 s. The same theme was used for the block of 14consecutive trials. The first 2 trials of each block were forpractice. In the other 12 trials, the 12 probe tones fromthe chromatic scale were paired with the theme in randomorder. The drone, consisting of the Sa (C) and Pa (G), wassounded during the sthayi and theme but not during theprobe tone. A 5-s interval between trials allowed subjectsto record their responses. Blocks were presented in differentrandom orders to different subjects,

Procedure. Subjects were instructed to judge how welleach probe tone fit with the preceding theme in a musicalsense. The ratings were made on a 7-point scale ranging(ram fits poorly (1) to fits well (7). Responses were indicatedby circling the appropriate number on the response sheet.

Results

Rating profiles. The listeners rated each ofthe 12 tones of the chromatic scale in the con-text of each of the 10 rags listed in Table 1.

YAM AN

STHAYI

THEME

Figure 4. Musical transcription of the sthayi and theme (roop) of rag Yaman.


This produced rating profiles for the 10 rags,which are plotted in Figure 5, averaged overall 16 subjects. The profiles for Indian andWestern listeners were quite similar; for in-dividual rags, the intergroup correlations av-eraged .871 and were significant (p < .01) foreach of the 10 rags. Consequently, the profilesshown in Figure 5 are those for the two groupscombined. Differences between the two groupsare described later.

Tonal hierarchies. A number of statisticaltests were performed to determine whether theratings from the experiment conformed to thepredicted tonal hierarchy. The series of testscan best be described with respect to Figure6, where each branch corresponds to a testperformed. The figure shows the average ratinggiven to the tones in each of the following sets:non-mat tones, that tones, Sa (C), Pa (G), vadi,

samvadi, and the remaining tHat tones. In theseanalyses, the ratings given to the tones in eachset were computed for each subject, averagedover the 10 rag contexts. The first test com-pared the ratings for that and non-that tones,finding a significant preference for that overnon-that tones, f(l, 15) = 129.16, p < .01.The non-that tones were then eliminated, andthe next analysis compared Sa (C) with theother that tones, showing a preference for Sa(C), the tonic, over the other that tones, F(\,15) = 39.30, p < .01. Sa (C) was then elim-inated and the next test showed a significantpreference for Pa (G) over the remaining thattones, F(l, 15) = 42.97, p < .01. After Pa (G)was eliminated, the next analysis showed asignificant preference for the vadi over the re-maining tones, F(l, 15) = 18.41, p < .01.However, once the vadi was eliminated, no

BHAIRAV

C C* D D* E F F* G C* A A* B

YAMAN

C C* D D* E F F* G C* A A* B

BILAVAL

C C* 0 D* E F F* G C* A A* B

KHAMAJ

C C* D D' E F F* C C* A A' B

KAFI

C C* D 0* E F F* G G* A A* 8

ASAVRI

C C#D D#E F F#G G* A A* B

BHAIRVI

C C* 0 0* E F F# G G* A A* B

TOD I

C C#0 0*E F F#G G#A A# B

PURVI

C C* D 0* E F F* G G* A A* B

MARVA

C C' D D* E F F* G G* A A* B

Figure 5. The obtained rating profiles for 10 rags. (Each profile consists of the ratings, averaged over 16subjects, given to the 12 chromatic scale tones in the context of each of the rags.)


preference was found for the samvadi over theremaining that tones. It should be noted thatthe tests for vadi and samvadi eliminated thedata for those rags in which either was Sa (C)or Pa (G).

The same series of tests was performed sep-arately for the Indian and Western subjects,with virtually identical levels of statistical sig-nificance. The results of all listeners generallyconformed to the predicted tonal hierarchy.There was a definite preference for that tonesover non-mat tones, and within the set of thattones, Sa (C), Pa (G), and the vadi receivedparticularly high ratings.

Tone duration. In order to assess the extentto which the rating given to a tone is a functionof the relative amount of time the tone issounded in the rag context compared withother tones, the duration of each of the 12chromatic tones in each rag theme was tab-ulated. The durations of the 2 tones in thedrone were not included in this measure. Theseduration values were correlated with the ratingprofiles. The correlations for the 10 rags av-eraged .820, and all were significant (p < .01).The same analysis performed separately forIndian and Western listeners showed no dif-ference between the two groups; for Indian

PROBE TONE RATING

3 4 . -5

ALL 12 TONES

NON-THAT THA"T

SA

PA

OTHERS VADI

OTHERS II SAMVADI

Figure 6. Tree diagram to illustrate the hierarchical ordering imposed by the rag contexts. (Each branchshows the average rating given to a tone or'to a set of tones.)


listeners, the average correlation was .828; forWestern listeners, .805.

That membership. In order to evaluate theeffect of whether the probe4one is a memberof the parent that of the rag, a variable rep-resenting that membership was constructed.Each probe tone was scored 1 if it was con-tained in the parent that of the rag, and 0 ifit was not. These values were correlated withthe rating profiles from the experiment. Thecorrelations averaged .821 for the 10 rags, andall were significant (p < .01). The strength ofthe eifect of that membership, however, dif-fered for the two groups of subjects. Thatmembership had a stronger and more consis-tent effect for the Indian listeners, with an av-erage correlation of .832 between the thatmembership variable and the rating profiles;the corresponding average was .740 for theWestern listeners, and these two values differedsignificantly, F(\, 9) = 6.40, p < .05. Thus,the ratings of the Indian listeners reflectedmore strongly whether the probe tone wascontained in the parent that of the rag thandid the ratings of the Western listeners.

Tone duration and that membership. Theprevious analyses showed that higher ratingswere generally given to tones that are soundedfor relatively long durations in the rag themeand tones that are in the parent that of therag. These variables are, of course, related;tones heard in the theme are for the most partmembers of the underlying that. An analysisof the tone duration and that membershipvariables showed these variables correlatedwith each other. The average correlation overthe 10 thats was .691, and in all cases, thecorrelation was significant (p < .05). However,these variables are not identical, so a multiplecorrelation was performed to assess their rel-ative contributions. This multiple correlationpredicts the rating profile for each rag fromthe two variables, tone duration and thatmembership.

For all 16 subjects, the average multiple R =.905, p < .01, with both tone duration andthat membership contributing to the multiplecorrelation. The t(9) values, for the regressionweights averaged 2.84 and 2.40 for tone du-ration and that membership, respectively (bom/K < .05). However, when the same analysiswas performed separately for Indian andWestern listeners, differences were found. For

Indian listeners, the average multiple R = .907,and significant contributions to the regressionswere made by both tone duration, t(9) = 2.76,p < .05, and that membership, t(9) = 2.73,p < .05. In contrast, the average multiple cor-relation for Western listeners was somewhatlower, R = .857, and although the tone du-rations contributed significantly, t(9) = 2.37,p < .05, that membership did not, t(9) = 1.70,ns. Thus, tone duration and that membershiptogether accounted quite well for the patternsfound in the rating profiles of the Indian lis-teners. For Western listeners, the ratings relatedsystematically to the pattern of the tone du-rations but not to that membership.

Effect of tuning. In five of the rags, thetuning (i.e., the actual set of tones used in therag) differs from its parent that by the additionor deletion of one or two tones. For example,rag Bilaval is missing Ni (B), even though itis included in its parent that, Bilaval. All to-gether, six tones differ between the tuning ofthe rag and its underlying that. In five of thesix cases, the Indian listeners' ratings corre-sponded more accurately to the tuning thandid the ratings of the Western listeners. If thetuning included a tone absent from the that,the Indian listeners gave the tone a higher rat-ing than did the Western listeners; conversely,if the tuning omitted a tone contained in thethat, the Indian listeners gave it a lower ratingthan did the Western listeners. This indicatesthat the Indian listeners were more sensitiveto deviations in the rag tuning from the parentthat than were the Western listeners.

Major and minor key profiles. To assessthe similarity of the rating profiles for the ragsto those for major and minor keys, the presentresults were compared with the profiles formajor and minor Western diatonic scales fromour earlier experiment (Krumhansl & Kessler,1982). The C major and C minor profiles wereused because these keys share the same tonicas the rag contexts of the present experiment.Using the average data for all 16 subjects, theprofile for each rag was correlated with bothmajor and minor key contexts of the earlierexperiment. The correlations with C majoraveraged .616 and varied considerably. Thehighest correlation, .934, was with rag Bilaval,whose parent scale is identical to C major; thelowest correlation, .181, was with rag Todi.The correlations with C minor averaged .489;


the highest correlation with any of the rag pro-files, .842, was the Kafi, the tones of whichare included in (the various forms of) the Cminor scale; the lowest correlation, .249, waswith the rag Purvi. The same analysis per-formed separately for Indian and Western lis-teners showed similar patterns; the correlationswith major keys (averaging .587 and .609 forIndian and Western listeners, respectively) andwith minor keys (averaging .456 and .499 forIndian and Western listeners, respectively)showed a very slight but nonsignificant ten-dency for the responses of Western listenersto produce ratings more like Western majorand minor keys.

Because of the strong commonalities be-tween Western and Indian rating profiles, theanalysis just presented may not be optimal foruncovering differences between the groups asthey correspond to major and minor Westernkeys. A more sensitive test would be to cor-relate the differences between the ratings forthe two groups with the major and minor pro-files. When this analysis was performed, thecorrelations of the differences between Westernand Indian ratings with the major key profileaveraged .192 across the 10 rags. A t test wasperformed to see whether these correlationswere significantly different from 0, with theresulting value, J(9) = 4.77, p < .01. The cor-relations of the differences with the minor keyprofile averaged .219; t(9) = 5.49, p < .01.Thus, there was a consistent tendency for thedifferences between the Western and Indianlisteners' ratings to be related to C major andC minor. It should be noted, however, that thisaccounted for only about 4% of the varianceof the difference between the ratings for thetwo groups.

Inter-rag correlations. To obtain a measureof similarity between rags, their correspondingrating profiles were correlated. If two rags arebased on parent thats that have similar tonalhierarchies, the correlation between their rat-ing profiles would be high. Conversely, if tworags are based on parent thats with dissimilartonal hierarchies, the correlation between theirrating profiles would be low. Figure 7 (top)shows the rating profiles for rags Yaman andBilaval superimposed. These two rags havesimilar profiles, producing a correlation of.775. Figure 7 (bottom) shows the rating pro-files for rags Yaman and Bhairvi; their profiles

YAMAN

BIL7VAL

C C# D D# E F F# G G# A A# B

YAMAN

BHAIRVI

C C# D D# E F# G G# A A* B

Figure 7. The probe tone ratings for rag Yaman super-imposed onto the ratings for rag Bilgval (top) and ontothe ratings for rag Bhairvi (bottom) to illustrate relativelysimilar and dissimilar rating profiles.

are dissimilar, producing a correlation of—.081. Correlations were computed for allpairs of rags for all listeners combined, andwere computed separately for the Indian lis-teners and the Western listeners.

Multidimensional scaling of inter-rag cor-relations. The inter-rag correlations produceda matrix of values indicating the degree ofsimilarity or dissimilarity between each pairof rags. These were analyzed \ using multidi-mensional scaling (Kruskal, 1964; Shepard,1962a, 1962b). The particular program usedwas MDSCAL (Kruskal, 1968). The results forIndian and Western listeners are shown sep-arately, because the differences between thegroups were perhaps most apparent in thescaling solutions.

The solution obtained in two dimensionsfor the Indian listeners, with a stress value of.060 (using Stress Formula 1), is shown at thetop of Figure 8. These results showed a markedsimilarity to the pattern predicted by Jairaz-bhoy's circle of thats, with Bhairav locatednear the center of the configuration and theother rags arranged around the circle in thepredicted order. Notice that rags Purvi and


Marva, which are both based on the parentthat Marva, are represented by points in vir-tually identical positions. Similarly, rags Asavriand Bhairvi, both based on parent that Bhairvi,are represented by points in the same location.Two other rags, Bilaval and Khamaj, also oc-cupy essentially the same position in the scalingsolution. This can be understood by consid-ering the tunings of the two rags. Althoughthey are classified under two different parent

INDIAN SUBJECTS

YAHANPURVI

KHAMAJBILAVA

BHAIRAV

VAU

KAFI

TOOl BHAIRVI

WESTERN SUBJECTS

thats, their tunings are almost identical. Theircommon tones are Sa (C), Re (D), Ga (E), Ma(F), Pa (G) and Dha (A); they differ only inthe seventh degree of the scale. The tuning ofBilaval contains neither Ni (B) nor Nil. (Bt),whereas the tuning of Khamaj contains both.

To substantiate the similarity between thisscaling solution and the theoretical circle ofmats (Jairazbhoy, 1971) shown in Figure 3,the two spatial configurations were comparedusing the program CMH2 (Cliff, 1966). Thisprogram rotates, translates, and expands orcontracts the scaling solution of the data tobest fit a specified configuration, in this casethe theoretical circle of thats. The resultinggoodness of fit measure was .953, indicatingthat the scaling solution of the data from theIndian listeners recovered the predicted circleof thats to a good degree of approximation.

The two-dimensional scaling solution for thegroup of Western listeners is shown at the bot-tom of Figure 8. The stress value was .089. Inaddition to having a somewhat higher stressvalue, this solution matched the theoreticalcircle of thats less exactly than did that of theIndian listeners. The measure of goodness offit of this solution to the theoretical circle ofthats was only .650; rags Purvi and MarVawere misplaced with respect to rag Yaman,and rags sharing the same parent that werenot spatially identified. Thus, the rating pro-files given by Western listeners recovered lesswell the predicted relations between the thatsunderlying the rags used in the experiment.

YAMAN PURVI

BILA-VAL MARVA

KHAMAJ

BHAIRAV

TOOIKAFI

BHAIRVI

Figure 8. The two-dimensional scaling solution of the in-tercorrelations between the 10 rag rating profiles for Indiansubjects (top) and for Western subjects (bottom).

Discussion

Cross-cultural research in cognition is oftenmotivated by the attempt to classify phenom-ena as either universal or culturally relative.In few cases can this distinction be establishedunequivocally, either because of the complexintertwining of innate factors with cognitivestructures acquired through experience or forlack of a rigorous methodology for cross-cul-tural research. There are additional reasonsmore specific to the present experiment to becautious of conclusions concerning universal-ity. First, the subjects were presented with mu-sical segments that are rich in information;the responses of both Indian and Western lis-teners would be expected to reflect to somedegree the information readily accessible from


the particular segments of music heard in theexperiment.

Second, certain structural features areshared by Indian and Western music. Theseshared features, noted in the beginning of thisarticle, include the establishment of a tonictone as a primary point of reference, the sec-ondary importance of the tone a fifth abovethe tonic, the approximate equivalence of thetuning systems, and the use of basic scalesconsisting of seven tones in each octave range.Despite important and theoretically interestingdifferences between these musical systems, thecommonalities would be expected to inducecertain similarities in the patterns of responsesobserved in the experiment.

Third, the Indian listeners who participatedwere currently residing in the United Statesand have had considerable exposure to Westernmusic in addition to their training in Indianmusic. Consequently, their responses mighthave been influenced to some extent by theirexperience with Western music. Although theparticular selection of Indian listeners mightnot have been ideal, it should be noted thatthe influence of Western music is currentlyquite strong in the popular music of India, andit would be difficult to obtain a subject pop-ulation totally unfamiliar with Western tonalstructure. A more important point in this con-nection, however, is that music-theoretic de-scriptions of Indian music provide hypothesesabout the pattern of results expected if thelisteners are in fact sensitive to the structuresof Indian music. The results conform closelyto these expectations, and moreover, inter-pretable differences are found between the re-sults for Indian listeners and those for Westernlisteners who have had minimal exposure toIndian music.

Thus, the motivation for the present ex-periment is not to uncover universalities inmusic perception and cognition. We are, how-ever, concerned with the effect of previous ex-perience with a musical tradition on the lis-tener's response to the musical materials usedin the experiment. Comparisons between thetwo groups of listeners provide informationabout two questions. The first question is thefollowing: What features of tonal organizationbecome internalized through experience?Tonal organization is expressed in a variety ofways cross-culturally. Certain features of this

organization are explicit in the music. Othersmay require greater exposure if they are tobecome abstracted and internalized. Patternscontained in the results of Indian listenersabove and beyond the patterns contained inthe results of the Western listeners would beinterpreted as the product of more extendedexposure to Indian music.

The second question concerns the descrip-tion of the experience of a listener unfamiliarwith the conventions of a particular musicaltradition. For the Western listeners, whatstructural features of the music are apparent?For listeners trained in Western music but un-familiar with Indian music, certain organi-zational principles may be immediately ap-prehended, either through sensitivity to thepatterns contained in the sounded elementsor through analogies with the organizationalprinciples of Western music. The responses ofthe Western listeners, then, can be used tounderstand the kinds of perceptual processesthat a listener who is naive to a particularmusical tradition brings to bear on the ap-prehension of its underlying organization.

Another reason for undertaking the presentstudy was to provide a test of the general ap-plicability of the methods developed and pre-viously applied exclusively to Western music.Cross-cultural comparisons of music are dif-ficult owing to the extremely diverse formsthat music takes. Attempts to develop an ab-stract, descriptive terminology general enoughto encompass music of these diverse styles aresubject to biases as to which features are tobe considered important. Owing to their fa-miliarity with particular traditions, analystsmay give undue emphasis to certain featuresand may ignore others. Moreover, such anal-yses cannot ensure that the features incor-porated in the theoretical system are, in fact,psychologically salient. Although the musicmay follow certain constraints or conventions,these may not be perceptually or cognitivelyrealized even for a listener familiar with thetradition.

The alternative approach taken here is toemploy a methodology that allows us to de-termine which features are, for the listener,psychologically important. The form that thedata take permits the application of certainanalytic techniques, facilitating comparisonsacross different musical systems and across


different groups of listeners. In addition, inthe cases of Western and Indian music, theresults map onto a construct described by mu-sic theorists, the hierarchy of tonal functions,which serves as a source of validation for theexperimental methodology.

Tonal hierarchies: Sa, Pa, and the vadi.Tonal hierarchies described by music theoristsare based on careful analyses of the employ-ment of tones within the musical literature.Tones said to dominate in these hierarchiesare given emphasis in the music through avariety of means common to Western and In-dian music. In Indian music, the special rolesof the tonic, Sa (C), and of the fifth degree ofthe scale, Pa (G), are also made explicitthrough their constant sounding in the drone.These tones are also considered significant be-cause they are fixed or immovable; hence, theinterval of a perfect fifth above the tonic is aconstant feature of most Indian rags. In thepresent experiment, both Indian and Westernlisteners were sensitive to these structural in-variants. The highest rating overall was givento the tonic, and the next highest rating, tothe fifth tone of the scale.

Other tones considered structurally signif-icant in North Indian music are the vadi andsamvadi. The vadi is given emphasis in thesthayi, the section played at the beginning ofeach block of trials in the experiment. As ex-pected, the ratings of both Indian and Westernlisteners reflected a sensitivity to the specialfunction of this tone; its rating was on theaverage higher than the other that tones ex-clusive of Sa (C) and Pa (G). The samvadi isof secondary importance and is not necessarilyfeatured in the sthayi. In the experiment, nei-ther group Of listeners rated this tone higherthan the other that tones, on the average. Gen-erally, however, the results confirmed predic-tions from Indian music theory concerningthe tonal hierarchies.

Effect of tone duration. To explore the effectof the relative durations of the musical toneson the probe tone ratings, we correlated thesetwo variables. For each rag, we computed thetotal duration of each of the 12 chromatictones in the theme and correlated these valueswith the rating profile for that rag. The highlysignificant correlations indicated a strong effectof tone duration on the listener's judgments;tones given high ratings were sounded for rel-

atively long durations in the context. This fac-tor was equally strong for Indian and Westernlisteners. By employing contexts that are richin structure, the present study has pointed totone duration as a dominant factor controllingthe perception of tonal hierarchies.

A similar effect of tone duration seems toapply to Western tonal music. Hughes (1977)

, did a tone duration analysis of one particulartonal composition, Schubert's Opus 94, No.1. Krumhansl (1982) noted that the relativedurations of the tones in this composition cor-related almost perfectly with the probe toneratings (as measured by Krumhansl & Kessler,1982) for the predominant key of the com-position. This was true even though the mu-sical contexts used to collect the probe tonedata did not themselves contain the same dis-tribution of durations. Other evidence for theinternalization of the distribution of musicalelements comes from a more recent study(Krumhansl, 1983), which investigated theperceived relative significance of chords inmajor and minor key contexts. These ratingscorrelate highly with their frequency of use inrepresentative eighteenth and nineteenth cen-tury Western compositions as measured byBudge (1943).

These'studies together support the notionthat the distribution of durations or frequen-cies of musical elements is a salient deter-minant of perceived tonal organization. Thepresent study shows that in the case of Indianmusic, the duration distribution of the tonesis an important factor for listeners both fa-miliar and unfamiliar with the musical tra-dition when the experimental context is itselfmusically rich. In the case of Western tonalmusic, this factor appears to be effective forboth tones and chords even when the exper-imental context does not itself reflect the dis-tribution generally found in the musical tra-dition.

In addition to the relative durations of tones,other features would be expected to contributeto the assimilation of the tonal organization.For example, tones to be heard as stable mayappear in positions of rhythmic stress and nearthe beginning and end of phrases. In addition,the sequential ordering of pitches and the useof tones sounded simultaneously as chords orsounded sequentially to suggest harmonies areimportant in Western tonal music. A recent


study by Bharucha (in press) used sequencesof tones that were all equal in duration andfound evidence of a subordination of non-harmonic tones to chord tones in both ratingand memory judgments. The results of thatstudy conform to the theoretical analyses pro-posed by Schenker (1935/1979) artd are foundeven under conditions in which the durationdistributions of the tones do not provide suf-ficient information to drive this subordination.Thus, factors other than the relative durationof tones contribute to the listener's derivationof a sense of the underlying tonal hierarchy.

Similarity to Western tonal hierarchies.Dowling (1978) and Meyer (1956, p. 63) sug-gested that Western listeners would assimilatenon-Western music to the scale and harmonicstructures with which they were familiar. Ifthis were the case, the rating profiles for majorand minor keys (Krumhansl & Kessler, 1982;Krumhansl & Shepard, 1979) would be ex-pected to correlate more highly with the ratingprofiles of the Western listeners than with thoseof the Indian listeners. Although there was aslight tendency for this to be the case, the effectaccounted for only a small percentage of thedifferences between the ratings of Western andIndian listeners. Moreover, the responses ofthe Western listeners depended very stronglyon the particular rag of the context. For somerags, the correlation with major or minor keyswas quite high, but in other cases, it was quitelow. This was also the case for the ratings ofthe Indian listeners. Thus, there is little evi-dence that the Western tonal hierarchies weredominant for either group of listeners. Instead,listeners appeared to base their responseslargely on the particular musical materialsemployed within the context of the experi-ment, regardless of their relative experiencewith Indian and Western music. Thus, the re-sults showed considerable sensitivity to thestructure made explicit by the contexts usedin the experiment.

Indian scale structure and the circle ofthdts.The factor that did distinguish between Indianand Western listeners was the North Indianscale structure. As noted earlier, the responsesof both groups of listeners reflected the relativeemphasis explicitly given to the tones in theexperimental contexts; beyond this, only theIndian listeners showed sensitivity to the func-tions of tones in the underlying parent scale

(that). Although scale membership and thedistribution of tone durations within a musicalpassage are necessarily correlated, they are notidentical; in the present experiment, scalemembership as distinguished from tone du-ration appeared as a factor only for the Indianlisteners. In addition, the Indian listenersshowed greater sensitivity to the cases in whichthe tuning of a rag differed from its underlyingthat. Western listeners, although sensitive tomany of the structural features described byIndian music theorists and made explicit inthe musical contexts, do not appear able toextract from the experimental contexts thedesignation of certain tones as scale members.

This differential sensitivity of the listenersto scale membership is perhaps brought outmost clearly in the multidimensional scalinganalysis of the correlations between the ratingprofiles for the 10 rags. For the Indian listeners,the multidimensional scaling solution recov-ered quite precisely the theoretical relationsexisting among the thats underlying the rags(Jairazbhoy, 1971), which are based on theoverlap of that tones. Rags based on the samethat or closely related thats were representedby closely positioned points; rags based on dis-tantly related thats were represented by pointsthat were far apart. As would be expected,given the reduced effect of that membershipfor Western listeners, the scaling of their datacontained deviations from the expected pat-tern.

Thus, the tonal hierarchies measured in thisand in previous experiments (Krumhansl &Kessler, 1982; Krumhansl & Shepard, 1979)have been shown to give rise to relations atmore abstract levels of musical structure. InWestern music, these relations are at the levelof tonal centers or keys. Interkey distance, al-though shown by Krumhansl and Kessler(1982) to be derivable from probe tone ratings,might also depend on the harmonic functionsof chords in keys or the frequency of modu-lations between different keys. These factorsare inextricably interconnected in Westernmusic, so that their relative contribution tointerkey distance cannot be determined un-equivocally. Indian music, in contrast, employsneither chords nor modulations, and yet mu-sic-theoretic treatments refer to both the or-dered structural significance of tones and tothe varying degrees of relatedness between


tonal organizations. The present study indi-cates that the relations between thats may bepsychologically mediated through tonal hier-archies. In the absence of other factors, theinternalization of tonal hierarchies is sufficientto induce the internalization of a more abstractlevel of musical structure: the relations be-tween different tonal organizations.

General Discussion and Conclusions

The experiment reported here extended theprobe tone method developed by Krumhansland Shepard (1979) to the music of NorthIndia, a musical system with features quitedistinct from traditional Western music. Theprobe tone ratings were strikingly similar forthe listeners trained in Indian music and forthose trained only in Western music. The re-sults of both groups confirmed several pre-dictions from music theory concerning tonalhierarchies in North Indian music. These re-sults were attributed to the use of relativelycomplex musical contexts. The tones thatdominate in the hierarchy are given emphasisin the contexts in one way or another, beingsounded in the drone or for longer durationsin the melodies.

Thus, in the present case, there is a con-vergence between the relative emphasis givento the various elements in the music itself andto their theoretical stability or structural sig-nificance. This convergence may be due to thefact that the musical selections used in theexperiment establish the melodic materials ofthe rag. We would expect to see in these sec-tions the exposition of features useful to thelistener for achieving an initial sense of theunderlying organization. The results suggestthat even listeners unfamiliar with Indian mu-sic are sensitive to these features.

Once the tonal hierarchy has been estab-lished perceptually, the music can elaborateon or deviate from this basic organization.During the improvisatory sections of the rag,for example, a poorer match would be ex-pected between the explicit emphasis given thevarious musical elements and the abstract hi-erarchy of stability that applies to the broadertonal context. A similar divergence would bepredicted for the development sections and forsections with modulations or tonal ambiguityin Western music.

Despite the strong commonalities found be-tween the two groups of listeners, Indian lis-teners showed greater sensitivity to scale (that)membership than did Western listeners. Ap-parently, Western listeners were unable to ex-tract from the musical contexts the Indian scalestructure beyond internalizing informationabout the relative durations of the varioustones in the perceptually immediate context.A number of considerations suggest, however,that with somewhat more experience, Westernlisteners may be able to gain an appreciationof the complex system of scales.

In the present experiment, there was littleevidence that the Western listeners assimilatedthe musical contexts to the Western system ofmajor and minor scales. Thus, the activationof these scale schemata in Western listeners isnot obligatory, leaving open the possibility ofinternalizing quite different scale systems. Forthese listeners, the probe tone ratings wereconsistently related to the distribution of tonesin the contexts, which in general reflects scalemembership. Greater experience with a some-what wider variety of musical contexts wouldlead, in principle, to the differentiation be-tween scale and nonscale tones.

Additional evidence that scale structure maybe fairly readily abstracted comes from anumber of other studies. Krumhansl and Keil(1982) showed that scale structure in Westernmusic is internalized relatively early in the de-velopmental sequence. By the early grades ofelementary school, listeners preferred diatonicto nondiatonic tones as completions of shortmelodies. Hansen, Kessler, and Shepard (1983)found both Western and Balinese listeners tobe sensitive to the tonal hierarchies that applyto both Western diatonic and Balinese pelogscales, despite the marked deviations betweenthe tunings of the two systems. For Balineseslendro scales, however, the pattern of resultswas less clear for all listeners, suggesting, pos-sible limitations in the tuning systems that cangive rise to perceived tonal hierarchies. Finally,PoUard-Gott (1983) recently showed that, withrepeated exposures, eVen listeners with littlemusical training are able to gain an appreci-ation of the similarities between variations ofthemes despite considerable surface differencesamong the instances heard.

By using naturalistic musical contexts, thepresent experiment and that of Pollard-Gott


(1983) have shown that listeners are remark-ably sensitive to organizational features un-derlying richly structured musical contexts.This suggests that considerable cognitive re-sources are applied to the problem of ab-stracting conceptual features from complexmusical materials. In the present cross-culturalinvestigation, we demonstrated that listenershave considerable flexibility in the tonal or-ganizations that can be internalized. Moreover,we identified features of the music itself thatappear to promote the internalization of hier-archies of tonal stability, a music-theoreticconcept that applies to virtually all musicalsystems.

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Received August 2, 1983Revision received December 20, 1983

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