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The influence of implicit harmony, rhythm and musicaltraining on the abstraction of tension-relaxationschemas in tonal musical phrasesEmmanuel Bigand aa Laboratoire de Psychologie de la Culture Universit Paris X Nanterre, Paris, FrancePublished online: 21 Aug 2009.

To cite this article: Emmanuel Bigand (1993): The influence of implicit harmony, rhythm and musical training on theabstraction of tension-relaxation schemas in tonal musical phrases, Contemporary Music Review, 9:1-2, 123-137

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Contemporary Music Review 9 1993 Harwood Academic Publishers GmbH 1993, Vol. 9, Parts 1 & 2, pp. 123-137 Printed in Malaysia Photocopying permitted-by license only

The influence of implicit harmony, rhythm and musical training on the abstraction of "tension- relaxation schemas" in tonal musical phrases

Emmanuel Bigand

Laboratoire de Psychologie de la Culture Universitd Paris X Nanterre, Paris, France.

Tension-relaxation schemas are an important meaningful structure in music. The two present experiments investigate the main factors involved in their abstraction. The experimental method, similar to the procedure used by Palmer and Krumhansl (1987) consists in segmenting into several fragments 6 melodies varying in their implicit harmony or their rhythmic structure. Asking the subjects to evaluate the degree of completeness of each fragment may be thought of as an indirect way of measuring the degree of musical stability. The collected responses define an average profile which may be considered as an approximation of the musical tension/relation network abstracted by the listener. Results indicate that a level of coding exists where the musical phrase could be represented by its network of musical tensions and relaxations, which is in accordance with the Lerdahl & Jackendoff's prolongational hypothesis. Abstraction of this network is influenced by the implicit harmony, the rhythmic structure, and, for musician-subjects by the interaction of these two factors. Results of the second experiment seem to suggest that the psychological processes involved in such an abstraction are not strongly influenced by the musical training. In conclusion, some suggestions about a systematic formalisation of the rules involved in the determination of tension-relaxation schemas are put forward.

KEY WORDS: Prolongational reduction, interaction pitch hierarchy x rhythm musical training, tension- relaxation network, psychological representation of musical structures, musical phrase.

Music is one of the most complex acoustical structures of our environment. The study of the way a listener perceives, organises and memorises musical pieces fundamentally improves our knowledge about the complex perceptual and cogni- tive processes human beings are able to perform. But considering music only as a complex acoustical structure would be restrictive; from a psychological point of view, music is primarily an informative structure which enables us to exchange different emotions, and so to communicate in a non-verbal fashion. Understanding how a listener uses all his perceptual and cognitive competence to extract musical informative structure is the main goal of the research.

From this perspective, there are two questions to be distinguished: the first concerns the nature of meaningful musical structures, the second the psychological processes involved in their abstraction. Research on musical expressivity and on musical semantics, carried out by Francbs (1958) and Imberty (1979,1981) showed the essential part played by musical tension and relaxation schemas; these schemas are extracted from the musical piece and then assimilated to kinetic and emotional schemas of tension and relaxation, which accumulate all of the affective experience of the listener. Therefore, it seems reasonable to consider that the most important part of musical expressivity might be determined firstly by the specific way each

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124 Emnmnuel Bigand

composer organises the musical tension and relaxation in time, and secondly by the kinds of musical tension and relaxation the listener manages to abstract.

I shall now expand upon this second point. What are the psychological processes involved in such an abstraction; how does a listener interpret all the musical parameters to determine the musical tensions and relaxations of the piece?

Lerdahl and Jackendoff's theory is a very important contribution to this question. The authors claim that intuitions about tension and relaxation are determined by the combination of the grouping structure, the metrical structure, and the tonal hierarchies. This combination leads to the abstraction of an event hierarchy from which a hierarchy of tensions and relaxations ("Prolongational reduction") may be derived.

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Schematic representation of the theory by Lerdah11989.

Many of these components are psychologically plausible. First, we know that grouping is a major characteristic of perception (Fraisse 1974) and the experiments carried out by Deli6ge (1987) confirm the psychological validity of different grouping rules involved in the model. Second, several experiments have shown the listener's ability to abstract metrical structure (Povel 1981, Essens & Povel 1985, Sloboda & Parker 1985), and many others have pointed out a very sophisticated implicit knowledge of tonalhierarchies by the listener (Krumhans11979, Krumhansl & Kessler 1982, Bharucha & Krumhans11983). Other data indicates that the listener manages to organise musical events in a hierarchical way (Deutsch 1980, Stoffer 1985, Serafine 1989). At the very least, the possibility of extracting a link between different variations and a theme, suggests that a level of coding exists where the musical phrase is represented by its underlying network of tension and relaxation (Bigand 1990a, 1990b, 1990c).

The main problem however, is to understand how these different components really interact. Lerdahl and Jackendoff's theory suggests that: the metrical and grouping structures have a double function. First they divide the piece into groups, and then they add rhythmic values to the tonal hierarchy to determine the relative stability of each event.

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Influence of the rhythmic structure on the tension-relaxation schemas by Lerdahl & Jackendoff

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Tension-relaxation schemes 125

Let us look at figure 2. Because of the tonal hierachy the D (quaver) creates a strong musical tension that is resolved on E. At a more abstract level, the D (minim) institutes a relative tension which will be resolved on C. Finally, at the most abstract level, the E (minim) produces a fundamental tension which will be resolved on C. Because of his implicit knowledge of the tonal hierarchy, we may reasonably suppose that a listener would abstract these three levels of tension and relaxation. But what will happen if the rhythmic structure is changed? As Lerdahl and Jackendoff remarked, the musical tensions will be differently organised.

Experiment I

Thus, it is probable that rhythmic values are added to the tonal weight to determine the musical tension. The few experiments on this issue suggest that the structural importance of the notes comprising a melody is not only determined by the tonal hierarchy but also by their rhythmic position (Palmer and Krumhansl 1987a, 1989b). More recently Serafine (1989) has observed that this structural importance is also strongly influenced by the metrical position: events on the strong beat tend to be perceived as more important. Though these experiments are of great interest, the way these different factors really interact in music perception is still little known and many problems remain.

The first concerns the psychological importance of the tonal hierarchy in the perception of musical phrase. Can two melodies having the same rhythmic structure, the same melodic contour, the same tempo, the same dynamic, but differing in their implicit harmonies, really generate different networks of musical tensions and relaxations?

The second concerns the role of the rhythmic structure in the determination of musical stability: can two melodies differing only in their rhythmical structure generate different tension/relaxation schemas? It may be interesting to distinguish which part of this effect relates to the metrical structure and which to the different durations.

The third problem concerns the eventual interaction of the pitch hierarchy and the rhythmic structure. Palmer and Krumhansl's results (1987a, 1987b) tend to confirm an independent relationship suggesting that each structure is treated by two separate cognitive processes. As Peretz and Morais (1989) emphasised, this question is important for the cognitive sciences, since it improves our knowledge of the possible modularity of the musical mind.

The last question concerns the role of musical training. Are processes involved in the abstraction of a network of musical tension determined by musical training, or do they reveal a competence to structure musical pieces, which does not require any particular learning, as in the case of the understanding of language? The purpose of these two experiments is to address to these questions.

Experimental method

To measure the tension/relaxation schemas generated by a musical phrase it is necessary to register the degree of musical stability of each note. The procedure used by Palmer and Krumhansl (1987a, 1987b) appears very efficient: it consists in

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126 Emmanuel Bigand

segmenting the melody into several fragments; each stops on a different note defining differently-ending units. In HIR1 (fig. 3), the first fragment stops on the G#, the second on the A, and so on. A melodic fragment stopping on a very stable note (a tonic in a strong rhythmical position for example) does not contain any musical tension: in this case a musical continuation seems unnecessary and the fragment can be considered concluded. But when the melodic fragment stops on an unstable note (leading note) it contains a strong musical tension that requires musical continuation: in this case the melodic fragment would appear weakly concluded.

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Tension-relaxationschemes 127

Therefore, asking the subjects to evaluate the degree of completeness of each fragment may be thought of as an indirect way of measuring the degree of musical stability. As musical tension may be varied in a subtle way, it is necessary to provide the subjects with a scale of responses. Here this scale contains 7 steps and the subjects' task is to choose those which best correspond to the degree of complete- ness of each fragment. The collected responses define an average profile which may be considered as an approximation of the musical tension/relaxation network abstracted by the listener. If a tonal melody does not generate musical tensions, these profiles would look like a straight line. If a musical phrase generates a hierarchy of musical tension/relaxation effectively, the profiles would present a great contrast.

Material

In order to study the effects of the tonal hierarchy on this profile we must define another melody with the same rhythm and same melodic contour, but differing in its n~usical progression. As indicated in figure 3, the melodies H1 and H2 differ in their implicit harmonies and thus in their prolongational structures; the main tension appears on bar 3 in H2, whereas a the main relaxation appears in H1, and the main tension appears on bar 4 in H1, whereas there is a large relaxation in H2. Because of this different implicit harmony the tonal weight of an identical ending unit would not be the same considered with respect to H1 or to H2. For example, the E on ending unit 12 is more stable in H2 where it is a prolongation of the local tonic, than in H1 where it is a third subordinate to the local tonic C.

In order to study the effect of the rhythmic organisation we now define two other melodies. R2 is obtained by shifting the rhythmic structure of R1 by one quaver; let us note that many ending units which were on a strong beat in R1 are on a weak beat in R2. A more important rhythmic change is performed in R3 so that the effect of duration may be measured. Let us note, for example, that the quaver A in HIR1 becomes a dotted crotchet in HIR3 (ending unit 2).

Finally, in order to study the interaction, these rhythmic changes are applied to the melody H2. Each of the six melodies is segmented into 19 fragments, 114 fragments in all, played by a computer, strictly at the same tempo and without accentuation.

Procedure and subjects

The procedure is similar to that of Palmer and Krumhansl (ibid): each subject listens to all the fragments and the presentation order is varied randomly. 18 subjects are employed: 9 musicians from the Marseilles' Philharmonic Orchestra, 9 non-musi- cians who have never played or learned music.

Experimental hypotheses

1. If the tonal hierarchy influences the tension/relaxation schemas, the profiles should differ in the melodies H1 (R1, R2, R3) and the melodies H2 (R1, R2, R3).

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128 EmmanueI Bigand

2. If the rhythmic structure influences the tension/relaxation schemas, the profile of R1, R2, R3 would differ. In this case two other hypotheses might be tested: one concerning the effect of the duration, the other that of the metrical structure. 3. If tonal hierarchy and rhythm are two independent musical dimensions, chang- ing the rhythmic structure from R1 to R3 should alter these profiles in the same way in H1 and in H2. 4. Finally, if musical training influences the abstraction of tension/relaxation schemas, the effect of the preceding factors should differ in musicians and non- musicians.

Resu l ts o f the f i rst exper iment

First let us consider the musicians' results. Profiles obtained in each experimental situation are shown in Figure 4. We can see immediately that each melody generates varied tension/relaxation schemas, and that these schemas differ strongly in each experimental situation. These differences are examined using the Multivariate statistical analysis method. First the effects of the factors are analysed on each ending unit (univariate analysis of variance). The profile differences are then tested by a multivariate analysis of variance.

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Figure 4 Average profiles of musical tension obtained in the first experiment9

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Tension-relaxation schemes 129

These are the main results of this analysis.

1. The difference in the profiles observed in H1 and H2 is significant at p

130 EmnLanueI Bigand

While a musical stability period appears at H1 in bar 3, a strong tension period is observed in H2 in bar 4. The phenomenon is reversed at bar 5 which accords with the prolongational tree. Let us consider some of these differences in more detail. At ending unit 5 we have the tonic A at H1 and a D# at H2, which does not belong to the tonality and introduces a strong musical tension. Because of this different tonal weight the degree of musical stability observed here is higher in H1. An opposite result is observed on the ending unit 8. A more interesting fact is shown for ending unit 12. Here the two melodies have the same note E, but as the implicit harmonies are different, those Es do not have the same musical function and therefore the same tonal weight: at H1 the E is a third subordinate to the local tonic C, and at H2 the E is a prolongation of the local tonic. Experimental data confirms that the musicians perceived these different functions; indeed the degree of stability is higher in H2 and this difference is significant at p

Tension-relaxation schemes 131

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profiles shows that the implicit harmony/rhythm interaction is not signifi- cant.

Therefore, these results suggest that musical training has a strong effect on the abstraction of the tension/relaxation schemas: they seem to suggest that the non- musicians' aptitude in abstracting these schemas is less developed. Indeed their profiles appear almost monotonically related to overall melody duration, suggest- ing that for them, irrespective of the musical function, the longer the fragment, the higher its degree of achievement.

Comments

Before interpreting these different results, let us note that two are surprising. First, the lack of effect of the metrical structure might suggest that this structure has no influence on the musical tension and relaxation. Second the strong difference between the two populations is inconsistent with other recent experimental results indicating that the non-musician has a very sophisticated musical competence (Bigand 1990b, Deli6ge 1990). For these two reasons the experimental procedure was considered critically. Two main weaknesses should be mentioned. First, each subject listens to all the musical fragments. As these fragments are very similar, this design produces interferences which could obscure many subtle effects of the different factors. Second, as the presentation order is determined at random, it often appears that a short fragment follows a longer one. In this case the degree of

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132 EmmanueI Bigand

completeness is not only defined by musical stability but also by the listener's knowledge of the continuation of the melody. These two defects might seriously confuse the subjects: the main purpose of the second experiment is to remedy to them.

Exper iment 2

Only four melodies are used (HIR1, HIR2, H2R1, H2R2). 8 independent groups of 9 subjects are formed: 4 groups of musicians (graduate conservatory students studying musicology), 4 groups of non-musicians (students of the same age, but without formal musical training or practice). 2 x 4 x 9 (72) subjects were required for this experiment. Each group listened to fragments of only one of the 4 melodies. This time, a fragment (x) immediately follows the fragment (x-l) and precedes the fragment (x+l). This new presentation respects the chronology of the melody and permits observation of how the listener abstracts the different stages of the musical progression. As he does not know when the melody will stop his responses can only be based on the musical tension or relaxation he perceived. Because many interfer- ences are now ruled out, it may be conjectured that the effect of the factors will appear in a more relevant way.

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Tension-relaxation schemes 133

Resu l ts

As we can see in figure 7, the musicians' profiles are roughly the same as those of the first experiment, although much more constrasted. Again we find a main effect of the implicit harmony significant at p

134 Emmanuel Bigand

To summarise, the musicians' results are consistent with those of the first experiment and they give more information about the interaction between implicit harmony x rhythm.

It is not the same when we look at the non-musicians' results. These new profiles differ radically from those of the first experiment: they are

more contrasted, and more opposite in each experimental situation generated. The multivariate analysis of variance points to an effect of the implicit harmony significant at p

Tension-relaxation schemes 135

experiments suggests that it is also strongly influenced by rhythmic value. The experiment showed that two kind of rhythmic values are relevant. The first concerned the metrical position of the event, the second its duration. As we have ascertained, even a small difference in duration can slightly alter the local tension/ relaxation schemas. This result explains how subtle variations in duration effectu- ated by the performer may be appreciated by the listener.

These results demonstrate, in accordance with Lerdahl and Jackendoff's theory, that tonal weight and rhythmical value interfere in the determination of tension/ relaxation schemas. They show that an interactive relation between these two musical dimensions cannot be ruled out; it means that musical dimensions are not processed independently; as we have seen the effect of a change on one dimension depends on the musical context where it appears. This result contradicts others obtained by P.almer and Krumhansl (1987a, 1987b). This divergence may be explained by the different methodologies employed. In order to study the interac- tion between two factors, it could be better to use a classical factorial design where the two factors are systematically varied. The experiment of Palmer and Krumhansl varied only one; the rhythmical factor. The presence of interaction suggests that the cogriitive processes implicit in the determination of tension/relaxation schemas are unlikely to be modular.

The last factor which influenced this outcome is musical training. Results of the two experiments seem to suggest that the tension and relaxation schemas ab- stra.cted by the musicians tend to be more varied. However the results of the second experiment point to the fact that this difference should not be exaggerated; a detailed analysis will convince us that these listeners managed to abstract very subtle differences in musical structure. Obviously, a musical competence to struc- ture musical pieces exists, which does not require any specific training: for this reason, the main hypothesis of Lerdahl and Jackendoff's model may be extended to inexperienced listeners as well.

Conclusion

In conclusion, I would like to offer some suggestions about the formalisation of the rules involved in the establishment of tension/relaxation schemas. Given the effect of the tonal hierarchy we could assign to each note of a melody a specific tonal weight. The tonic of the main key would receive a weight of 7, the dominant a weight of 6, the third, a we ig~ of 5, the other notes of the key a weight of 4, and a note which does not belong to the key a weight of 3 or 2, depending whether they belong to a near or far key. When a modulation appears the notes in the new key may be assigned values using the same system with a decrease of a value of I or 2 depending whether the new key is near or far from the main key. Applied to the melody H1, this system produces the line I (fig. 9). Of course this line differs from H1 to H2. Given the effect of duration we can allocate to each note a duration value varying here from I to 2 (line 2). We can apply a similar system in determin- ing metrical value, varying here from 1 to 3 (line 3). Of course these lines vary from R1 to R2. If we consider the musician-subjects, because of the interaction, we can assume that the multiplication of these three lines can produce a theoretical profile of musical tension/relaxation, which should not be too different to that observed.

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136 Emmanuel Bigand

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Certainly the similarity observed in figure 9 is a good starting point, but obviously the lack of total adequacy implies that other factors should be included. This system could be useful in formalising the missing factors, and it will be the object of future experiments.

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