Measuring Similarity between Flamenco Rhythmic Patterns

Catherine Guastavino1,2, Francisco Gomez2,3, Godfried Toussaint1,2, Fabrice Marandola1,2, and Emilia Gomez4

1McGill University, Canada; 2Centre for Interdisciplinary Research on Music Media and Technology (CIRMMT),Canada; 3Polytechnic University of Madrid, Spain; 4Universitat Pompeu Fabra (UPF), Spain

Abstract

Music similarity underlies a large part of a listener’sexperience, as it relates to familiarity and associationsbetween di!erent pieces or parts. Rhythmic similarity hasreceived scant research attention in comparison with otheraspects of music similarity such as melody or harmony.Mathematical measures of rhythmic similarity have beenproposed, but none of them has been compared to humanjudgments. We present a first study consisting of twolistening tests conducted to compare two mathematicalsimilarity measures, the chronotonic distance and thedirected swap distance, to perceptual measures of similar-ity. In order to investigate the e!ect of expertise on theperception of rhythmic similarity, we contrasted threegroups of participants, namely non-musicians, classicallytrained percussionists and flamencomusicians. Results arepresented in terms of statistical analysis of the raw ratings,phylogenetic analysis of the dissimilarity matrices, corre-lation with mathematical measures and qualitative analy-sis of spontaneous verbal descriptions reported byparticipants. A main e!ect of expertise was observed onthe raw ratings, but not on the dissimilarity matrices. Noe!ect of tempowasobserved.Results of both listening testsconverge to show that the directed-swap distance bestmatches human judgments of similarity regardless ofexpertise. The analysis of verbal descriptions indicates thatnovice listeners focused on ‘surface’ features, whilemusicians focused on the underlying rhythmic structureand used more specialized vocabulary.

1. Introduction

Musical discourse progresses through transformationsof musical material. For such transformations to be

meaningful to a listener, there must be an underlyingnotion of musical similarity so that the musical progres-sion may be perceived and assessed. Such a notion isacquired through exposure to music within a specificcultural context. Among the musical parameters thatundergo transformations rhythm is one of the mostprominent. Therefore, the study of musical similarity,and in particular of rhythmic similarity, bears somerelevance. There is a large body of literature onthe perception of rhythm structure in music (e.g.Gabrielsson, 1973; Honing, 2002; Lerdahl & Jackendo!,1985). However, as paradoxical as it may seem, rhythmicsimilarity has received scant research attention incomparison with other aspects of music such as melodicor harmonic similarity (see Hewlett & Selfridge-Field(1998) and the references therein for a review on melodicsimilarity). Studies on rhythmic similarity can be foundin Toussaint (2004) from a symbolic point of view, andFoote et al. (2002), from an audio point of view.

Many measures of rhythm complexity have beenproposed (Gomez et al., 2007), but very few have beencompared to perceptual human judgments, a situationthat may raise objections to their validity. Much thesame can be said about rhythmic similarity measures. Infact, to our knowledge, none of the measures proposedso far have been tested on subjects. In this paper wepresent two experiments conducted to compare twomathematical similarity measures, the chronotonic dis-tance and the directed swap distance, to actual percep-tual measures of similarity. Of interest, too, is the set ofrhythms chosen to carry out our study. Because of itsrhythmic vitality and use of rhythm as unifying principle,and also because of the lack of systematic researchconcerning the genre, we have chosen our set of rhythmsfrom flamenco music. In our experiments we investigated

Correspondence: Catherine Guastavino, McGill University, School of Information Studies, 3459 McTavish, Montreal, QC, H3A 1Y1,Canada. E-mail: catherine.guastavino@mcgill.ca

Journal of New Music Research2009, Vol. 38, No. 2, pp. 129–138

DOI: 10.1080/09298210903229968 ! 2009 Taylor & Francis

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which mathematical measure best matches humanjudgments. We presented the listeners a set of flamencorhythmic patterns, which will be described below indetail, and asked them to rate their similarity. In order toinvestigate the e!ect of expertise on the perception ofrhythmic similarity, we contrasted three groups ofparticipants: non-musicians, classically trained percus-sionists (both recruited in Canada) and flamencomusicians (recruited in Spain). Indeed, previous researchon rhythmic perception has highlighted di!erencesbetween novice listeners and musicians in their abilityto label perceived di!erences as well as strategies forrepresenting musical structures (see Duke, 1994, for areview). As we shall see, novice listeners tend to focus on‘surface’ features, while musicians tend to focus on theunderlying rhythmic structure and develop a specificvocabulary. Moreover, statistical tests to determine thecorrelation between similarity measures have beencarried out. Finally, we used phylogenetic trees tovisualize our results.

1.1 Flamenco music

Flamenco music is the result of a complex amalgam ofseveral musical traditions coming from diverse geogra-phical origins and forged over centuries of musicalpractice. Several authors have highlighted a wide varietyof influences for flamenco, namely the influence ofliturgical music, the marks of the Moorish music, thefootprint of Jewish music, the more modern influence ofSouth American music, and above all, the strongpersonality of Gypsy music (see Hernandez-Jaramillo(2002) and Cruces (2002) for more details on the musicaland historical origins of flamenco music). As forgeographical origins, although flamenco music origi-nated in Andalusia, it soon received influences frommusical traditions from other areas such as Castilia,Murcia, Extremadura or South America. By the lateeighteenth century, flamenco music was characterized byunique features that constituted its identity and distin-guished it from local folk music. Its evolution hascontinued through to the present day.

According to Fernandez (2004, p. 32), one of the mostdistinctive characteristics of flamenco music is therichness of its rhythmic structures. Flamenco rhythmpermeates its harmonic and structural elements, and isone of the main features used to distinguish flamencostyles. Most flamenco styles are accompanied by handclapping, where rhythmic patterns are performed bychanging the clapping intensity and timbre (or playingmode). The main function of those clapped rhythms is toprovide a metrical reference, that is to structure the timeby establishing how it is divided and set the distributionof accents. In flamenco music, all pulses are played with aclap, but non-accented pulses are played with a soft clapand accented pulses are played with a strong clap. There

are five ternary metrical patterns and only one binarypattern (namely, [. x x x], described in box notation). Inour experiments we only utilized the ternary metricalpatterns, shown below in box notation. Here an ‘x’means a loud clap and ‘.’ a soft clap.

(1) Fandango [x . . x . . x . . x . .](2) Solea [. . x . . x . x . x . x](3) Bulerıa [. . x . . . x x . x . x](4) Seguiriya [x . x . x . . x . . x .](5) Guajira [x . . x . . x . x . x .]

Each pattern has been labelled with a style that uses itas a metrical reference, but, as a matter of fact, manystyles can use the same pattern. For example, thefandango pattern is used by the sevillana.

The origin and evolution of the di!erent flamencostyles (palos) and variations have been studied indi!erent disciplines, including ethnomusicology, litera-ture and anthropology (see Diaz-Banez et al., 2005, for areview). We refer the reader to Fernandez (2004) for anaccount of flamenco genres, including musical featuresand criteria for style classification. Rhythmic similarityand its possible use as a tool for classifying styles andvariants among performers have always spurred greatinterest among flamenco scholars.

1.2 Mathematical measures of rhythmic similarity

In computational music theory, measuring the similaritybetween rhythms is a fundamental problem with manyapplications such as music information retrieval andcopyright infringement resolution. Toussaint (2006)reviewed computational methods for evolutionary musi-cology using approaches derived from bioinformatics(phylogenetic analysis), where musical sequences aremodelled as sequences of symbols.

In this paper the validity of two mathematicalmeasures proposed in Diaz-Banez et al. (2005) weretested from a perceptual point of view. The measures arethe chronotonic distance and the directed swap distance.The chronotonic distance is based on histogram repre-sentation, specifically on the so-called TEDAS represen-tation (Gustafson, 1998). The vertical axis displays theinter-onset intervals, while the horizontal axis showswhere the onsets occur. The result is a histogramrepresenting the pattern that contains both pieces ofinformation; see Figure 1 below. The distance betweentwo rhythmic patterns is obtained by computing the areabetween the two given histograms. Figure 1 shows thehistograms corresponding to fandango and bulerıa;the area of the ruled regions in the third graph is thechronotonic distance between the two rhythmic patterns.Considering the example given in Figure 1, if the area ofthe ruled regions is added up, the result is 14, which is thechronotonic distance between fandango and bulerıa.

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The directed swap distance is computed by countingthe number of swaps (exchanges between adjacentaccented positions) needed to transform one pattern intothe other and then summing them all up. More formally,if P and Q are two patterns with the same number ofpulses, where P, say, has more onsets than Q, then thedirected swap distance between P and Q is the minimumnumber of swaps to convert P to Q under the followingconstraints: (1) each onset of P must move to an onset ofQ; (2) each onset of Q must receive at least an onset fromP; (3) no onset may travel across the boundary betweenthe last and the first onset. See Toussaint (2004) for adetailed explanation of this measure. To illustrate, let uslook at the directed-swap distance between seguiriya andfandango illustrated in Figure 2. Here the number ofswaps needed to transform seguiriya to fandango is 4;notice that two onsets in the seguiriya have beentransformed into one onset in the fandango.

In a previous study, Diaz-Banez et al. (2005) identifieda rhythm from a phylogenetic tree as a hypotheticalancestral rhythm (it appeared on one of the central nodesof the phylogenetic tree). The pattern was [x . . x . . x . . xx .] and, in fact, such a pattern exists: it is the main

pattern for the fandango de Huelva (Solo Compas,1998). Notice that the pattern was obtained under atemporal interpretation of the tree. So far this hypothesishas not been examined in depth by flamenco musicolo-gists so as to confirm it or reject it. In our study weincorporated the ‘ancestral’ rhythm because we deemed itinteresting to collect perceptual ratings for this patternand compare it to the rest of the patterns. We also denoteit as the ‘ancestral’ pattern, but further research isrequired to investigate the role it actually played in theevolution of flamenco patterns. In general, computingancestral nodes on a phylogenetic graph is a di"cultproblem in computation and is still under investigation.Diaz-Banez et al. were able to compute the ancestralpattern for the directed swap distance because of thesmall number of patterns involved.

Distance matrices obtained for both measures areshown in Tables 1 and 2.

Based on these two measures, dissimilarity matriceswere derived and a phylogenetic analysis of the fiveflamenco patterns was reported by Diaz-Banez et al.(2005). The program used to construct the phylogeneticgraphs for the distance matrices was SplitsTree (Huson &Bryant, 2006) and the algorithm NeighborNet (Bryant &Moulton, 2004). The phylogenetic algorithm outputs aplane graph embedding the set of rhythmic patternswhere the distance on the graph reflects as closely aspossible the true distance between the correspondingrhythmic patterns in the matrix. Distances in the matrixare represented by the distance between nodes in the

Fig. 1. Chronotonic distance.

Fig. 2. Directed swap distance.

Table 1. Dissimilarity matrix for the chronotonic distance.

Solea Bulerıa Guajira SeguiriyaFan-dango

Ances-tral

Solea 0Bulerıa 6 0Guajira 4 8 0Seguiriya 8 12 8 0Fandango 10 14 6 6 0Ancestral 8 12 4 6 4 0

Table 2. Dissimilarity matrix for the directed swap distance.

Solea Bulerıa Guajira SeguiriyaFan-dango

Ances-tral

Solea 0Bulerıa 1 0Guajira 7 8 0Seguiriya 11 12 4 0Fandango 7 8 2 4 0Ancestral 6 7 1 7 1 0

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graph along the edges of the graphs (neither theorientation of the edges nor the Euclidean distancesbetween nodes in the plane is relevant). The LSfit index isa measure of the goodnes-of-fit of the graph. If the indexis very close to 100%, then the graph represents thedistance matrix faithfully; otherwise, the graph is of littlevalue. The trees corresponding to the directed-swapdistance and the chronotonic distance are presented inFigures 3 and 4, respectively, along with the LSfit values.

2. Experiment 1

Experiment 1 was conducted as a first attempt tocompare the two mathematical measures described aboveto perceptual judgments of rhythmic similarity on the fivemost common flamenco rhythmic patterns. The mathe-matical measures considered here have been designed toonly keep track of note-value changes in rhythmicpatterns. Thus, in this first investigation, we comparedthem to perceptual judgments of synthetic MIDI-generated patterns. By doing so, the emphasis was put

on note-value di!erences rather than expressiveness ortimbral features that could be used to rate highlyexpressive, rich-timbre renditions of these rhythmicpatterns. That being said, we have tried to preserve themost essential rhythmic characteristics of flamenco musicin the MIDI-generated patterns, namely: (1) the hand-clapping sound (although MIDI-generated); (2) theclapping on all the pulses; (3) the combination of softand loud (accented) claps in the hand clapping.

2.1 Participants

Twelve participants (mean age: 25, S.D. 4) with anaverage of 3 years of musical training were recruitedfrom the student population at McGill University. Theyreceived 10$ for their participation.

2.2 Stimuli

The sound files were generated using the music notationsoftware Finale. The output was MIDI-generated soundsof hand clapping (channel 10, key 39) produced throughthe native instruments audio unit of Finale. The rhythmswere generated at three di!erent tempi: 50, 70 and 90dotted quarter notes per minute (or 400, 285 and 222 msbetween consecutive claps, respectively). There was aclap every eighth note, some soft, some loud. The MIDIvelocity of all soft (non-accentuated) claps was set to 80.The loud (accented) claps were generated by setting theMIDI velocity to 125% of the original value.

2.3 Procedure

The graphical interface was programmed in Java on aMacPro computer. The experiment took place in anacoustically treated room. Sounds were presented overheadphones (AKG 240) after digital-to-analogue con-version and amplification (Motu 828 MKII). Theexperiment consisted of three blocks corresponding tothe aforementioned tempi. In each block, participantswere first asked to listen to the five rhythmic patternspresented in the experiment to become familiar with therange of variation. After three randomly chosen practicetrials, they were asked to rate the similarity for allpossible non-identical pairs of the five patterns (tenpairs). Each combination occurred twice within a block,resulting in 20 trials in total per block. The order ofpresentation was randomized across trials within eachblock. The order of presentation of the three blocks wascounterbalanced across participants using a Latin squaredesign. Dissimilarity ratings were made by using a slideron a scale presented on the computer screen with endpoints labelled ‘very di!erent’ and ‘very similar’. Scalevalues were digitized on a 0 to 100 scale. Listeners wereallowed to listen to the patterns as many times as desiredbefore entering their ratings, but each pattern was

Fig. 3. Directed-swap tree.

Fig. 4. Chronotonic tree.

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presented only once (i.e. the patterns were not looped).They were requested to keep their rating strategy asconstant as possible. After the experiment, they were askedto freely describe the di!erences between the presentedpatterns and explain how they made their ratings.

2.4 Statistical analysis

A three-way (Tempo6ComparisonPair6Repetition)repeated measure ANOVA, conducted with SPSS,revealed no significant e!ect (F5 1 for Tempo andComparisonPair, F(1,11)! 4.4 for Repetition), that is,no significant di!erences were observed across tempi,stimuli combination, or order of presentation of thestimuli combination (since each combination was pre-sented twice).

2.5 Phylogenetic analysis

A dissimilarity matrix was created for each participantbased on the ratings. Values corresponding to the samepair of patterns (each pair was presented twice in counter-balanced order) were averaged for each participant toobtain symmetric matrices. A global dissimilarity matrixwas obtained by summing individual matrices across the12 participants. In this first experiment we did not includethe ancestral pattern. In order to better quantify thecorrelation between the matrices we performed Mantel(1967) tests. A straightforward correlation analysis of twodistance matrices cannot be carried out because thedistances in the matrices are not independent. The Manteltest provides a way to overcome this di"culty. Therationale behind the Mantel test is that, if there is nocorrelation between the matrices, then random permuta-tion of their rows and columns will produce equally likelylow correlation coe"cients. Thus, the test performsrandom permutations of the rows and columns of thematrices and computes the normal correlation coe"cient;after that, it counts the proportion of those permutationsthat led to high correlation coe"cients. A hypothesistesting is then computed to determine the final correlationof the distance matrices.We began by carrying outManteltests to assess the relationship between the matricescorresponding to the three di!erent tempi using the ztsoftware tool (Bonnet & Van de Peer, 2002). Thecorrelations between the matrices were all very high(r4 0.8) and significant (p5 0.02). Specifically, the resultsare the following: for slow andmedium tempi: r! 0.82 andp! 0.016; for medium and fast tempi: r! 0.92 andp! 0.008; for slow and fast tempi: r! 0.92 and p! 0.008.

Subsequently, and given the lack of significant e!ectof tempo in the ANOVA, we collapsed the results acrosstempi by summing the matrices corresponding to thedi!erent tempi. The SplitsTree program (Huson &Bryant, 2006) was used to construct the phylogenetictree for the overall matrix, presented in Figure 5.

2.6 Comparison with mathematical measures

Guajira and fandango always form one cluster, solea andbulerıa form another cluster, and seguiriya is isolatedfrom the others. Bulerıa comes out as the most di!erentfrom all the rhythms, according to the chronotonicdistance, and guajira and fandango come out as the twomost similar according to the directed swap distance.

We also carried out Mantel tests to determine thecorrelation between the overall matrix for the perceptualjudgments and the matrices obtained with the mathema-tical measures, namely, for the directed swap distanceand the chronotonic distance.

. Perceptual judgments and directed swap distance:r! 0.76 and p! 0.03.

. Perceptual judgments and chronotonic distance:r! 0.66 and p! 0.017.

It can be seen that correlation is higher for thedirected swap distance than for the chronotonic distance,both being significant. As it can be seen, humanjudgment matches the similarity measures using thedirected swap distance more than that using thechronotonic distance, both in terms of clusters and mostdistinct rhythmic pattern (seguiriya).

3. Experiment 2

Experiment 2 was designed to extend Experiment 1 inthree ways. First, the di!erences between novice listeners,classically trained musicians and flamenco musicians areinvestigated. Second, we analyse the verbal data used byparticipants to describe the di!erences between thedi!erent patterns and the strategy used to comparethem. Third, we added the possible ancestral rhythmidentified by Diaz-Banez et al. (2005), which is positionedin the central position of the phylogenetic graphsderived from the mathematical measures of rhythmicsimilarity.

Fig. 5. Phylogenetic tree for 12 non-musicians in Experiment 1(LSfit! 99.56).

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3.1 Participants

Sixteen non-musicians (mean age 27.2, SD 7.4) with anaverage of 3.9 years of musical training were recruitedfrom the student population at McGill University inMontreal, Canada. Twelve classically trained percussio-nists (mean age 24.6, SD 7) with an average of 14 years ofmusical training were recruited from the Schulich Schoolof music at McGill University. Seven flamenco musicians(mean age 31.8, SD 8.6, four guitar players, two singersand a percussionist) with an average of 13 years ofmusical training were recruited from the teacher andstudent population at the Escola Superior de Musica deCatalunya (ESMUC) in Barcelona, Spain. All partici-pants received a nominal fee for their participation.

3.2 Stimuli

As in Experiment 1, participants listened to the MIDI-generated patterns using Finale (using the same handclapping sounds from the standard percussion kit withthe same parameters). In addition to the five patternsused in Experiment 1, we added the ancestral rhythm [x .. x . . x . . x x .], resulting in six patterns. The rhythmswere generated at two di!erent tempi, namely 70 and 90dotted quarter notes per minute, respectively denotedMedium and Fast in the figures. The procedure was thesame as in Experiment 1: after three randomly chosenpractice trials, participants were asked to rate thesimilarity for all possible non-identical pairs of the sixpatterns (15 pairs), presented in random order. Everypair occurred twice within a block in counterbalancedorder, resulting in 30 trials in total per block. Thestimuli were blocked by tempo condition following aLatin-square design. The within block order wasrandomized. In addition to similarity ratings, partici-pants were asked to freely describe the di!erencesbetween patterns presented in each trial, as well as theirstrategy for evaluation similarity.

3.3 Statistical analysis

A four-way (Expertise6Tempo6ComparisonPair6 -Repetition) repeated measure ANOVA, conducted withSPSS, revealed significant main e!ects of Expertise(F(2,29)! 3.6, p! 0.04) and ComparisonPair (F(9,21)!36.2, p5 0.001). No other significant e!ects wereobserved. For the main e!ect of expertise, classicallytrained percussionists gave the lowest ratings (average of42 out of 100), i.e. judged patterns as more di!erent,followed by flamenco musicians (average of 46 out of100) and non-musicians (average rating of 54 out of 100).Post hoc tests revealed a significant di!erence betweennon-musicians and classically trained percussionists(p! 0.017), but no significant di!erences were foundbetween the two groups of musicians (percussionists and

flamenco musicians) or between non-musicians andflamenco musicians.

3.4 Phylogenetic analysis

As in Experiment 1, no significant di!erence wasobserved between the two tempi in the ANOVA. Manteltests were performed to assess the relationship betweenthe matrices corresponding to the two di!erent tempi.The correlation between the matrices was very high(r4 0.85) and significant (p5 0.03). Specifically, theresults are listed below:

. non-musicians: medium and fast tempi: r! 0.92 andp! 0.005;

. percussionists: medium and fast tempi: r! 0.95 andp! 0.001;

. flamenco musicians: medium and fast tempi: r! 0.85and p! 0.028.

Subsequently, we collapsed the results across tempi.The SplitsTree program (Huson & Bryant, 2006) wasused to construct the phylogenetic tree for the overallmatrices. The results are presented in Figures 6, 7 and 8

Fig. 6. Phylogenetic tree for 15 non-musicians in Experiment 2(LSfit! 95.72).

Fig. 7. Phylogenetic tree for 12 percussionists in Experiment 2(LSfit! 97.38).

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below for non-musicians, classically trained percussio-nists and flamenco musicians (respectively). Threeclusters emerge from the analysis, the first one containsfandango and ancestral, the second one contains guajiraand seguiriya and the third one solea and bulerıa, whichboth begin with soft claps resulting in anacrusis if thepatterns were repeated. It is interesting to note that theancestral was positioned in the middle of the phyloge-netic graphs given by the mathematical measures, but itdid not keep the same position in the phylogenetic graphsgiven by the perceptual measures, where it was groupedwith fandango.

3.5 Comparison with mathematical measures

Mantel tests were performed to determine the correlationbetween the overall matrix for the perceptual judgmentsand the matrices obtained with the mathematicalmeasures, namely for the directed swap distance andthe chronotonic distance. The results are reported inTable 3.

In this case, it can be seen that the correlations arehigher for the directed swap distance than for thechronotonic distance in the case of non-musicians andmusicians as in Experiment 1 (they are both significant,with p5 0.02). As for the flamenco musicians, that wasnot the case as the correlation coe"cient was higher forthe chronotonic distance than for the directed-swapdistance. There was a small di!erence between ther-value for musicians (r! 0.61) and flamenco musicians(r! 0.69), although the p-values of both are significant.The directed-swap distance only takes into account thedistance between adjacent onsets. The chronotonicdistance, however, not only considers the attacks, butalso the inter-onset interval information. Indeed, thehistogram associated with the chronotonic distance is

composed of squares (but not rectangles) put together,whose height is exactly the inter-onset interval. A changeof position of an onset also implies a change of the inter-onset interval. From this point of view, the chronotonicdistance embeds more information than the directed-swap distance. It seems that the two first groups ofsubjects mainly rely on the adjacency, whereas theflamenco musicians seem to use more informationbesides note proximity. Interestingly enough, we observethat in their verbal comments musicians and flamencomusicians often talk about groups of 2 and 3 (see theanalysis of verbal comments below). As a matter of fact,it is possible that flamenco musicians use extra informa-tion associated with the rhythms themselves irrespectiveof the chronotonic distance. Therefore, further experi-ments should be carried out in order to elucidate thispoint.

3.6 E!ect of expertise

In addition, to investigate the e!ect of expertise, Manteltests were performed to compare the overall matrices foreach group of participants. Very high correlations wereobserved (r4 0.85, p5 0.002). The results are reportedbelow.

. Non-musicians and percussionists: r! 0.96 andp! 0.001.

. Flamenco musicians and percussionists: r! 0.94 andp! 0.001.

. Flamenco musicians and non-musicians: r! 0.87 andp! 0.001.

These results suggest that expertise did not have ane!ect on the perceptual organization of the rhythmicpatterns. The analysis of the verbal comments was usedto complement this observation by looking at thestrategies used by the di!erent groups of participants.

3.7 Analysis of verbal comments

Participants were asked which criteria they used to maketheir judgment and how they would describe the

Fig. 8. Phylogenetic tree for 7 flamenco musicians in Experi-ment 2 (LSfit! 97.56).

Table 3. Mantel tests for correlation between dissimilaritymatrices in Exp. 2.

Mantel tests

Directed-swapdistance

Chronotonicdistance

r p-value r p-value

Non-musicians 0.8 0.004 0.59 0.001Percussionists 0.78 0.008 0.71 0.0014Flamenco musicians 0.61 0.017 0.69 0.0014

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di!erence between each pair of patterns, besides generalcomments. We used the constant comparison techniquefrom Grounded Theory (Glaser, 1967) to extract theemergent concepts from the free-format data. Occur-rences within each concept are presented for each groupof participants, concepts with only 1 occurrence wereexcluded from the analysis. Non-musicians based theirjudgments on whether the pattern started with anaccentuated or non-accentuated beat (3 occurrences),‘fast and slow parts’ (3 occ.), and by re-creating mentallya polyphonic pattern, by mentally superimposing the firstpattern as they listened to the second pattern (2 occ.).Classically trained musicians, on the other hand, reliedon groupings of 2’s and 3’s (6 occ.), the presence/absenceof two consecutive accentuated beats (2 occ.), andwhether the pattern started with an accentuated ornon-accentuated beat (2 occ.). Musicians also used thesuperimposing strategy (2 occ.), but gave explicitcomparison criteria somewhat similar to the directedswap distance, defined as the minimum number ofposition interchanges of adjacent ‘x’s and ‘.’s. Indeed,they seem to be matching each onset of one pattern to thenearest onset of the other pattern (3 occ.), as illustratedin the following quotation:

I studied the first example’s accents, and played them over

again in my head while listening to the second example to see

where it lined up and where it did not. If it rarely lined up

and was completely o!, the 2 rhythms appeared very

di!erent. If it lined up sometimes, they appeared slightly

similar, and if they lined up at least 90% of the time I noted

them as being very similar.

More detailed interviews will be conducted to furtherinvestigate this comparison strategy.

Flamenco musicians also determined a clear list ofcriteria, somewhat similar to those used by percussionists:namely whether the pattern started with an accentuated ornon-accentuated beat (5 occ.), whether the pattern wasshifted (4 occ.) and groupings of 2’s and 3’s (2 occ). Themain di!erence is their knowledge of the patterns involved,identifying and referring to the di!erent styles (palos)

involved in the experiment (4 occ.). However, without aclear reference to the underlying meter (also expressed asthe di"culty to establish the first beat without a referenceto the harmony), they tended to identify three patterns as‘the same pattern shifted’, rating them at 50%, betweensimilar and dissimilar. Those patterns are the solea, theseguiriya and the guajira, which share the same alternationof groups of 2 and 3, but starting at a di!erent point withinthe metric frame of 12 claps. It should be noted that thepercussionists who identified this particular feature usedthe same rating strategy. Another di!erence in the verbaldata of flamenco and classically trained musicians andnon-musicians is the vocabulary used to describe thecriteria of segmentation; musicians had developed voca-bularies and used formal terms to describe their strategies,whereas non-musicians used broader terms such as ‘beats’(all 16 non-musicians) and ‘rhythm’ (5 occ.). The results ofthe qualitative analysis of verbal descriptors are summar-ized in Table 4.

4. Discussion

Our results indicate the directed swap distance proposedby Diaz-Banez et al. (2005) closely matches humanjudgments of perceived similarity made by classicallytrained musicians. Results from Experiments 1 and 2provide converging support for the directed swapdistance for all groups of participants and all tempi.Few di!erences are noticeable between non-musicians,percussionists and flamenco musicians, and they are notbig enough to lead to the definition of di!erentcategories. Significant di!erences were observed for theactual ratings but no significant di!erences were foundacross participants with di!erent levels of expertise interms of the resulting clusters. This finding could beinterpreted as suggesting that when the input isabstracted away from the context, the underlyingpsychological perceptual mechanisms take over anddominate higher-level cultural e!ects.

Regarding the e!ect of expertise in Experiment 2,our results show that trained musicians and novices

Table 4. Summary of the qualitative analysis of verbal descriptors. An x indicates that the criterion was used by at least twoparticipants in the corresponding group, an X indicated that it was used by more than half of the participants in this group.

Strategy and criteria used to compare rhythmic patterns

Start withaccent or not

Groupingsof 2’s and 3’s

Superimposingpatterns

Reference topalos (styles)

Patternsshifted

Fast andslow parts

2 consecutiveaccents

Directedswap

strategy

Non-musicians x x xPercussionists x X X x xFlamenco X x X Xmusicians

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organized the di!erent rhythmic patterns in a verysimilar way, but using di!erent cognitive processingstrategies, as indicated by the qualitative data analysis.We observed a significant e!ect of expertise on the rawsimilarity ratings. The fact that non-musicians ratepatterns as more similar to one another than musicianscould suggest that musical training results in finer-graindiscrimination abilities. In addition, the qualitativeanalysis of verbal descriptors revealed that percussionistscould describe very explicitly the di!erences acrosspatterns and the strategies they used to compare themand rate the similarity. However, we failed to observe ane!ect of expertise at the level of the phylogeneticanalysis. We speculate that the lack of di!erences acrossour three groups of participants could be due to therestricted set of patterns, the fairly large di!erencesacross patterns, and the simplified nature of the MIDI-generated patterns used. However, further researchwould be needed to test this hypothesis on a wider rangeof rhythmic patterns, specifically by including variationson the main patterns used in the present studies, forwhich di!erences would be subtler. In addition, weintend to replicate these experiments by varying theinstructions to ask participants to focus on specificcomparison criteria. This would allow us to quantify therelative contribution of each criterion to the overallsimilarity and to compare the e!ect of expertise on eachcriterion.

Regarding the e!ect of tempo, we did not observe anysignificant e!ects of tempo, or interaction e!ect betweentempo and expertise. This lack of e!ect may be seen ascontradicting previous results (Duke, 1994), but it shouldbe noted that in our experiments participants werealways asked to compare patterns presented at the sametempo within an experimental block. That is, we did notintroduce tempo variations within a given comparison.

Further research is needed to investigate the e!ect ofrepeating the patterns on perceptual measures ofrhythmic similarity, specifically on the perception of thethree ‘shifted’ patterns in relationship to the underlyingmetric structure. Repetition might indeed attenuate theimpact of a beginning on soft claps, which could result inlisteners grouping solea closer to buleria than to theseguiriya/guajira. In addition, we will compare ourfindings with new listening tests using actual recordingsof hand clapping in order to capture subtle variations inperformance.

Furthermore, flamenco genres are mainly character-ized by a particular rhythmic pattern, but other musicalfacets contribute to their identity (e.g. instrumentation,key and harmony). Hence further research is required toinvestigate rhythmic similarity of the analysed genres andits relationship to other musical facets (e.g. chordprogression, dynamic variation, melodic contour), whichmay complement the perception of music similarity andthe definition of di!erent styles.

Acknowledgements

This research project is supported by Centre for Inter-disciplinary Research on Music Media and Technology(CIRMMT) through the Strategic Innovation Fundingawarded to the authors in 2007–2008. The authors wouldlike to thank Rafa Absar for designing the graphicalinterface and running participants (for Exp. 1 and 2),Graham Lavender for running participants (Exp. 2), EricThul for help with obtaining the figures, Ilja Frissen forassisting in the statistical analysis, Aaron Rosenblum forproofreading, Perfecto Herrera for his help recruitingflamenco musicians and all the participants for their time.

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