Perception of the "Macroform" in the Quartetto per Archi in due Tempi (1955) by Bruno Maderna Anna Rita Addessi 1, Roberto Caterina 2 1 Università di Bologna Dipartimento di Musica e Spettacolo Via Barberia 4, 40133 Bologna addessi@muspe.unibo.it 2 Università di Bologna Dipartimento di Psicologia V.le B. Pichat, Bologna caterina@psibo.unibo.it Abstract. The study is part of a wider project carried out at the University of Bologna, which deals with the macroform in post-tonal music, that is, the problem of the overall form of a piece. We believe that the cognitive sciences may help us to understand some aspects of this problem. The present experimental study on Maderna s quartet aims at investigating both the relationships between: 1. macroform perceived by subjects while listening to the piece in real time and macroform carried out by the analysts, and 2. macroform and perception of tension/relaxation: does the perception of tension and relaxation affect the memorisation of the macroform? Two groups of subjects took part in the experiment: 25 non-musicians and 32 musicians. The experiment was made both in Bologna and Edinburgh. We made use of a special computer program, which allows each subject to listen to a piece through head-phones and indicate the segmentations and the tension/relaxation perceived while listening in real time. The experiment lasts approximately 60 minutes and involves various steps and tasks. After an initial listening to become familiar with the piece and with the computer program, the subjects have to listen to the piece again and identify its main sections; then they have to indicate the criteria they used in formulating their solutions; in the next listening they have to indicate the largest zones of tension and relaxation they perceived. The macroforms perceived by the subjects are compared with 4 macroforms carried out by the analysts. The experimental hypotheses are the following: 1. the macroforms perceived by the subjects are correlated to the macroforms carried out by the analysts; 2. there is a correlation between macroforms and tension/relaxation perceived by the subjects; 3. finally, the difference between musicians and non musicians is not significant. The data analysed until now show a correlation between the macroforms perceived by the subjects and only 2 macroforms carried out by the analysts, and a correlation between the macroforms and the tension perceived by subjects. The differences between musicians and non musicians is not significant. The results are discussed in terms of Deliège s and Imberty s theories. M. Olivetti Belardinelli et al. (eds.): Proceedings of the 2 nd International Conference Understanding and Creating Music, 21 st 25 th November 2002, Caserta. Seconda Università di Napoli, Facoltà di Scienze Matematiche Fisiche Naturali, 2002.
1 Introduction This study is part of a wider project carried out at the University of Bologna, which deals with the macroform in post-tonal music, that is, the problem of the overall form of a piece (Baroni 2002). The research has concentrated mainly on string quartets. In this article we present an experimental study on Maderna s quartet that aims at investigating both the relationships between: 1. macroform perceived by subjects while listening to the piece in real time and macroform carried out by the analysts, and 2. macroform and perception of tension/relaxation: does the perception of tension and relaxation affect the memorisation of the macroform? 2 Macroform, Segmentation and Tension By the term macroform we refer to the global form of a piece, that is, the division of the piece into its largest parts with reference to its overall structure. In musicological literature various terms are used a similar sense but with meanings that are sometimes quite different: e.g. large dimensions (La Rue 1970), or large scale form (Levinson 1997). In the field of psychology Imberty (1981, 1993) uses the term "macrostructure", which originates from the field of linguistics, but is here considered from a perceptual point of view: a "scheme for structuring time, where sound events are arranged a priori according to rules drawn from the perceptual mechanisms involved in the detection of changes within the continuum of sound" (Imberty, 1981, p. 90). Our use of the word basically derives from Imberty s concept of macrostructure, but we have felt the need to distinguish between the concept of division into parts, which only identifies the macroform, and that of the perception of change, which we have defined with the term segmentation. The reasons behind the choices used for segmentation vary considerably, but generally speaking they include: repetition (Ruwet, 1966), change or discontinuity (Imberty, 1981), rhythmic grouping (in metrically organized music, Lerdahl and Jackendoff, 1983) and the principles of difference and similarity (Deliège and Mélen, 1997; Deliège 2001a, 2001b). Although the term segmentation is invariably used as a synonym for the division into parts, the analysis carried out during the research of the GATM group, however, has shown that segmentation is not a sufficient criterion to identify the main parts of a piece (i.e. its macroform) since the perception of a strong local discontinuity does not necessarily produce a division in terms of the piece as a whole. A very long pause, for example, may give rise to the perception of a segmentation but this does not necessarily constitute a separate self-contained section. The analysis of macroform poses different problems to that of segmentation, especially where memory is concerned. For the purposes of this article, then, the term segmentation will be used only to indicate the exact point where two sections are separated, a local phenomenon brought about by the presence of a contrast or discontinuity that involves one or more parameters of the musical material (duration, dynamics, timbre, density, register, etc.). The term macro-
form, on the other hand, is used to indicate the result of a process of memorisation involving the division of a piece of music into its largest parts, where each part has structural coherence and homogeneity. In the Imberty hypothesis the macrostructure is assimilated by the listener through the tension and relaxation schemes (Imberty 1993): in the tonal music these schemes would be activated above all by the tonal syntax. In the atonal music, as the quartet by Maderna, the schemes of tension and relaxation plays a determinant role because they would allow the listener to assimilate the total form of the musical piece even if there is a lack of the tonal reference points. But what it is determining the tension in the atonal music? How is the music structured when we feel the tension while the listening to it? The tension concept in music is a concept difficult to define, both due to the problem of describing the experience itself, and the musical structures genereting tension (Meyer 1956; Nielsen 1987; Lerdahl 1987, 1996; Krumhansl 1996, 1997; Bigand, Parncutt, Lerdahl 1996). In this sense, our study has very limited aims: it is an explorative observative study about the relationship between the memorisation of macroform and the perception of tension while listening in real time. Also in this case we have tried to formulate an operating definition of the tension arising from the necessity to explain to the listeners what they had to indicate. The solution was to ask them to indicate some tension and relaxation zones: the tension zones will be characterised by instability, as in an inspiration gesture; the relaxation zones will be characterised by stability, as in an expiration gesture. We asked them to identify only wide tension/relaxation zones and not the smaller tension/relaxation changes. 3 The Experimental Study In our previous experimental studies (Addessi, Caterina 2000a, 2000b), we investigated the perception of macroform in a several quartets from XXth century. The experimental study on Maderna s quartet aims at investigating both the relationships between: 1. macroform perceived by subjects while listening to the piece in real time and macroform carried out by the analysts, and 2. macroform and perception of tension/relaxation. 4 Method Subjects. Two groups of subjects took part in the experiment: 25 non-musicians and 32 musicians. The experiment was made both in Bologna (10 non-musicians, 12 musicians) and Edinburgh (15 non-musicians, 20 musicians).
Materials. Bruno Maderna, Quartetto per archi in due tempi, II movement (1955), duration 6 57, performed by Ex Novo Ensemble (CD Stradivarius STR 33330). Apparatus. We made use of a special computer program called EPM (Experiments on the Perception of Music), devised at the University of Padua. This program allows each subject to listen to the piece through head-phones and indicate the point of division perceived while listening in real time, by clicking on the mouse, and the tension/relaxation by shifting the mouse up (tension) and down (relaxation). Procedure. Each subject was allocated a computer and given a questionnaire which, in addition to the written answers, involved the tasks to be carried out using the EPM program. The questionnaire also contained details of how to use the program. The experiment took place in a room containing more computers. The subjects were called in several sessions of mixed groups (musicians and non-musicians) of 5, 10, 15. An operator read out the general instructions for the use of the questionnaire. If necessary two assistants were available to resolve individual problems. The experiment lasts approximately 60 minutes and involves various steps and tasks. After an initial listening to become familiar with the piece and with the computer program (task 1), the subjects had to listen to the piece twice and identify its main sections, the task was: "According to you, into how many principal sections, can it be divided? We remind you to identify only the large-scale sections and not the smaller sections. In total, the sections you identify should be non less than 2 and no more than 8". After this listening they were instructed to mark the perceived sections along a line on a sheet of paper (task 2); in the next two listening they had to indicate the section on the computer using the EPM program: after the second listening they saved the results (task 3). In the next task the subjects have to indicate the adjectives and type of sounds that characterised each section: they are asked to choose among a list of adjectives and a list of types of sounds given to them (task 4). In the next two listening they have to indicate the largest zones of tension and relaxation they perceived, by shifting the mouse. The task was: "We now ask you to try to identify some tension and relaxation zones. The tension zones will be characterised by instability, as in an inspiration gesture; the relaxation zones will be characterised by stability, as in an expiration gesture. We ask you to identify only wide tension/relaxation zones and not the smaller tension/relaxation changes". After the second listening they saved the results (task 5). The macroforms perceived by the subjects are compared with 4 macroforms carried out by the analysts. The 4 macroforms are obtained by the following procedure:1. each analyst can listen to the piece as many time as he likes, memorise the macroform, analyse the macroform on the score and explain his hypotheses, criteria and method; 2. the analyses are collected and checked by all analysts; 3. only the analyses showing coherence between hypotheses, criteria and method, were accepted for the experiment. Experimental hypotheses: 1. the macroforms perceived by the subjects are correlated to the macroforms carried out by the analysts; 2. there is a correlation between macro-
forms and tension/relaxation perceived by the subjects; 3. finally, the difference between musicians and non musicians is not significant. 5 The Analysts' Macroforms Macroform no.1. The first macroform is based on the hypothesis that the memorisation of the macroform depends on the perception of the alternation of tensions and relaxation (Imberty, 1993) and on the model of "cues abstraction" by I. Deliège (2001a, 2001b). In the Maderna quartet the tension/distension alternation would be principally due to the alternation of "violent" cues (short lengths, stressed notes, tallone, tremolo, sfz, pizz., detaché, dense texture, intensity from mf until fff, noise sounds, not vibrato), prevailing in the zones of tension, and "light" cues (long lengths, ponticello, col legno, intensity mp, ppppp, con sordina), prevailing in the relaxation zones. Sometime the tension/relaxation also depend on the length of the parts (i.e. when violent and light cues follow each other in close way we have an only moment of tension) and on the rhetorical functions which some parts seem suggest (introduction, climax, coda).the macroform no. 1 divides the piece into 7 parts: I part, mes. 1-10 (tension 1); II part, mes. 10-55 (tension 2); II part, mes. 55-96 (relaxation 1); IV part, mes. 97-117 (tension 2); V part, mes. 118-132 (tension 3); VI part, mes. 132-173 (relaxation 2); VII part, mes. 174-199 (relaxation 3) (see Ex. 1). Macroform no. 2. This macroform derived from macroform 1. The parts I and II, IV and V, VI and VII, was grouped: I part, mes. 1-55 (increasing tension); II part, mes. 55-96 (relaxation); III part, mes. 97-132 (top of the tension); IV part, mes. 132-199 (increasing relaxation) (see Ex. 1). Macroform no. 3. This macroform is based on the hypothesis of cues abstraction by I. Deliège (2001a, 2001b). This macroform divides the piece into 4 parts, each part is characterised by a very perceptual element: the I and III parts are characterised by inside variability, the II part is characterised by the regular beat played by the cello from mes. 73 until 87, the IV part by light sounds and it is also a final part (rhetoric function). The variability of the I and III parts depends on the alternation of "violent" moments (characterised by strong, stressed and long notes), and "light" moments (characterised by pedale, high and weak notes, melodic fragments, whisper). The 4 parts are the following: I part, mes. 1-72 (variability), II part, mes. 73-87 (regular beat), III part, mes. 88 131 (variability), IV part, mes. 132 199 (light end) (see Ex. 1). Macroform no. 4. This macroform is based on the strong segmentations, on the groupment of sections, and on repetition of that sections. The sections are characterised by inside coherence, but every part of the macroform can be composed by more different sections. In this case the definition of macroform is a bit different from the one used in the other analists macroform. Every part is characterised by the tempo. The macroform is the followiong: I par, mes. 1-62 (Allegro); II par, mes. 63-96 (Adagio); III part, mes. 97-141 (Presto); IV part, mes. 142-199 (Adagio II).
6 Results In our data we firstly considered how similar or dissimilar were the macroforms proposed by the listeners to those suggested by musical analysts. Our data indicate that macroform 1 was the most similar and macroform 3 the most dissimilar. The difference between the means of correspondence concerning macroform 1 and macroform 3 are statistically significant according to the Wilcoxon test (p<.001); the difference between the means of macroform 1 and 4, 2 and 3, 2 and 4, 3 and 4 are also statistically significant (respectively p<.01, p<.001, p<.01 and p<.05 according to the Wicoxon test). No significant differences are between the means of correspondence concerning macroform 1 and macroform 2. No significant differences in the means of correspondence concern the independent variables nationality and education according to the Mann-Whitney test. All these results are summarised in table n.1. Table 1. Index of Correspondence* of Macroforms proposed by Musical Analysts and Macroforms perceived by the Subjects According to Their Nationality and Musical Education Macroforms Scottish Italians All subjects Means of Musicians Non Musicians Non Musicians Corrispondence Musicians Musicians and Non Standard Deviation Musicians Macroform 1 37.4 35.9 33.9 33.1 35.6 18.8 Macroform 2 30.7 39.1 40.1 51.7 37.8 23.4 Macroform 3 16.3 7.2 14.6 9.3 13.0 18.3 Macroform 4 22.1 21.7 18.1 13.6 19.8 14.9 * Index of Correspondence is an empirical measure that we have adopted given by the number of the points coincident with macroforms (1, 2, 3 and 4) multiplied by 100 and divided by the number of all the points given by the subjects to define their macroforms. Then we examined the relation among tension, relaxation and macroforms. Considering all the points of division given by our subjects, the points when tensions were perceived and the points when relaxations were indicated, we can see that there is a positive and highly significant correlation between the points of division and tension. These results are summirised in table n. 2.
Table 2. Correlation Analysis Coefficient among Segmentation, Tension and Relaxation Tasks Points of division Tension Relaxation Points of division 1.00.7639**.0562 Tension.7639** 1.00 -.1483 Relaxation.0562 -.1483 1.00 * p<.05 ** p<.01 (two tailed) Finally we checked if tension and relaxation could be predictive of the points of division. The results of multiple linear regression indicate that both tension and relaxation are predictive of points of division also if the beta values are much higher when we assume tension as the independent variable as you can see in table n. 3 Table 3. Multiple Linear regression Dependent Variable Independent Variable Beta P Points of division Tension.783102.0000 Tension Relaxation.170434.0156 In conclusion we can see that the indications concerning macroform were mainly suggested by tension. 7 Discussion The results allow us to suppose that the perceptual and analytical hypotheses used in the macroforms no. 1 and no. 2, based on the tension/relaxation and on the cues abstraction, could be effectives while listening to Maderna's quartet. The listening of this piece, in fact, is particular but also typical of the post-tonal music. The perceptual cues divide the piece into a lot of very small sections: sometime these sections last a few seconds and the perceptual result is not a macroform but a fragmentary feeling. The local discontinuities would seem to dominate: every time you begin to hear the repetition of a cue, this disappears, and a new cue begin, or it appears a cue heard a few seconds before. It seems to lack the condition of repetition and variation (principles of similarity and difference, Deliège 2001a), that allows the listener to categorise and divides the piece in the mainly sections. It seems the piece doesn't have a macroform (Baroni 2002). Instead, the Imberty hypothesis about the macrostructure as
succession of tension and relaxation, together with Deliège's theory, would allow us to explain why it is possible to receive large and coherent sections, in spite of strong discontinuity. We don't observe significant differences between the different groups of subjects (Italian and Scottish, musicians and non-musicians): that is this phenomenon doesn't depend on the musical training. Nevertheless, the problem of the method is very important in this study. First, for the delivery about the tension given to the listeners: what do they mean by the word tension? We give the listeners an operating definition of tension, based on the concept of inspiration/respiration, but maybe, this is not enough. Second, the correlation between tension and macroform could derive from the high number of answers made by the listeners. Therefore, our study will continue with two new analyses of data that could verify whether the previous results are valid: that is, the analysis of the correlation between the perceived tensions and the macroforms no. 1 and no. 2, and the analysis of the closed answers (task 4). Finally, is it possible to describe the musical structures that affect the perception of tension and relaxation while listening? The analyses used in our study proposed some structural characteristics in an intuitive way. This problem, in fact, isn t infocus in the present experimental study, even if it represents one of the main motivation for doing it. Example n 1 (p.1, 2, 3). Bruno Maderna, Quartetto per Archi in due tempi (1955), II moviment, fragments
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