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Proposal for a Grammar of Melody: The Bach Chorales PDF

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PROPOSALF OR A - GRAMMARO F MELODY UNIVERSITA DI BOLOGNA ML Lf-l+O .1333 TRANSLATED FROM ITALIAN BY THE AUTHORS 1978 LES PRESSES DE L'UNIVERSITE DE MONTREAL C.P. 6128, SUCC. •A», MONTREAL, QUE., CANADA H3C 3J7 - 7 - TABLEO F CONTENTS Pages INTRODUCTION 9 CHAP. I - THEO BJECTA NDM ETHOODFS THEA NALYSIS 15 I .1 The object 15 1.2 The method 24 CHAP. II - THEA NALYS-ISG ENERACLH ARACTERISTICS 33 11.1 The notes : features and values 33 11.2 Movementsa nd transitions - Decorations 43 II.3 Decoration and tie transformations 46 11.4 Classification of decorations 50 11.5 Fields 54 CHAP. I I I - THER ULES 61 lII.l The configuration of the phrases 63 III.2 The transitions 66 a. The first note 66 b. The first transition 67 c. The transitions of the central body 69 Observation 70 Observation 2 73 Obser va ti on 3 74 d. The anticadential transitions 78 III.3 The cadence 80 a. The basic notes of the cadence 81 b. The cadential decorations 84 III.4 Contextual constraints 88 a. Ties 89 b. Skips 91 Observation 4 91 - 8 - ' c. Mobile degrees 99 d. Decorati ans 101 e. Recurrences 103 Observation 5 107 f. Body-cadence relationships 109 g. General rules of movement 112 h. Relationships between the phrases 119 CHAP. IV - THEG ENERATIPORNO GRAM 123 IV. l General scheme of the program 123 IV.2 The duration of the phrases 126 IV.3 The use of random numbers 127 IV.4 The first note of the first phrase 129 IV.5 The principle of a priori equiprobability 129 IV.6 The construction of the phrases 132 IV.7 Global controls 133 IV.8 The printing of the phrases 135 TABLES 137 APPENDICES 143 REFERENCES 153 - 9 - INTRODUCTION* This work is an attempt to resolve some of the problems of musical language scientifically. Obviously, speaking about a scientific approach to music is as vague and imprecise as speaking about a scientific approach to man this we know composers appreciate, having also discussed with some of them the import and results of our work. Their objections arise mainly from the natural conception that music is a universal and synthetic fact of such intricate com plexity that it is impossible to confront with the pretension of scientific definitions. The opinions of those who live and experience every day this complex phenomenonc annot be ignored. No one more than the musician himself knows how, in music, emotive facts and personal memories continually mingle, how social and cultural environment, not to mention perceptional data and problems about the structure of sound, are inseparably tied together in such a way as to prove most discouraging to anyone with ambitions to investigate this * Note on graphic conventions In this note we list some graphic conventions adopted in the present work; we also indicate the page of the text in which these conventions are explained. G - F transition page 64 ~ G - F(S-) transition JJ J page 64 G !tC descending interval ~ page 67 G! C A/A transition J I J page 70 /A-A/ transition j j page 70 Chorale 11+ Chorale 11 of Appendix land its variants page 64 - - - l O - this field. If Galileo, however, instead of observing objects rolling down inclined surfaces had taken up the search of the secret of the philosophers' stone, he would have remained one amongm any other alchemists and not the founder of modern experimental science. Thus, our proposed enquiry is well limited and anything but compre hensive. Wea re making an attempt to examine some musical structures in order to see to what extent it is possible to identify certain scientific principles based on an account of their structural processes. Wet urn our attention only to the sign on its own, not to the man, and neither, we must stress, to the sign intended in its full context, but only to the sign as significant, to use a semiological terminology to which, from time to time, we have had recourse. Wea lso appreciate the fact that musical semiology is an extremely young branch of science, still a long way from having its own, well defined investigative methods and, in this respect, our work is an attempt to contribute something to the discussions and building up of these methods. Such efforts owe their value to another factor also. A great part of the experience out of which musical semiology has developed has been the analysis of the relationships between verbal and musical structures, which has involved attempts to transfer, often too directly, linguistic methodology and principles elaborated in the linguistic ~ context, into music analysis. Efforts have also been made to clarify a number of epistemological problems connected with attempts to include music in the wider field of general semiotics(l). Both directions have led us to a point where, (1) For a general picture of the situation in semiotics today, cf. U. Eco (1975), also U. Valli, 0. Calabrese, and P. Magli (1974), and, specifi cally in regard to musical semiology, J.J. Nattiez (1975). - 11 - with a framework of concepts and with some related experience, we can begin some serious investigative work in this field. However, the framework on which musical semiology is based is still very fragile and this is because a large amount of methodological and epistemo logical research has not been accompanied by equally productive work on specific and concrete problems of analysis. Only by concentrating on problems that have directly arisen from research on musical language, will we able to question or confirm the theoretical apparatus we have had at our disposal at this stage. This is another of the motives that moved us to make our analysis. In our work, we make use also of the computer, and so perhaps it is ~ appropriate at this point to make some observations. The computer's ability to calculate and to perform formalized elaborations are much superior to man's and for this reason the computer will be a very useful aid. Nevertheless, we feel that in studying something as complex and elusive as music (this is also true of the apparently very elementary texts we have studied), it is notsufficient simply to find numerable and comparable structures, but one has also to select from all the structures one can identify in an objective manner, those YJhicha re useful for an analysis of the larger aspects of musical communication. For this reason, in our opinion, some of the mathematical and in particular statistical investigations which have taken place in recent years, especially in American musicology, possess a sort of inertia which may render them, to some extent, fruitless. For the same reason, we find the epistemological work mentioned above useful. Also the use of the computer in our analysis is to be seen from this particular point of view. Our task is that of generating a sort of grammarw ith which we can describe the musical texts we have chosen for study. Such a grammar, if it were complete, would be able to generate examples of the studied language different from the original ones we began with, as happens with the grammars of natural languages. One can thus speak of a sort of generative grammar of the studied texts, giving the term a more general meaning without precise parallels with the formal Chomskyana pproach. The relative simplicity of the sample we have chosen has helped us in our attempt at an effective production of musical structures using our grammar (or, rather, our collection of rules). It is at this point that the computer comes into play, precisely as a generator of musical phrases. It is, in fact, an automatic generator unintelligent enough to guarantee that the results are not the products of a subjective or creative interpretation of the rules, but rather are derived directly from the rules themselves. At this point usually composers prick up their ears and start making objections about generated phrases. To such objections we usually answer that these pieces do not have to be "beautiful" but just "correct". With this answer, however, we are entering extremely dangerous territory. Wew onder, in fact, if there exists in musical language, as in verbal language, a distinction that can be drawn between the grammarw e use for day to day communication and that of ~ poetical language which has different structures and functions. Our answer tends to the negative : it is difficult for us to find a qualitative difference between two corresponding kinds of rules, and therefore we have not adopted such a dis tinction in our work. It is also worth noting that for musical analysis, as a science at the embryonic stage, it is not fitting to take a stance on this parti cular problem. Only a lot of experimental work delving into the problem of 2 musical semantics will provide further elements for the solution of this problem( ). (2) N. Ruwet (1975 : 26) tends, on the contrary, to make a distinction between grammatical and aesthetical levels in musical language when he proposes a project of analysis of counterpoint exercises. "Un exercice de contrepoint doit se conformer a un ensemble de regles tres strictes, qui sont formulees explicitement dans les traites, mais aussi a certains principes implicites, auxquels recourt constamment tout ban professeur. L'explicitation de ces principes ... ne devrait pas etre une entreprise impossible, etant donne precisement le caractere simplifie du materiel ... L'interet de ce travail - 13 - Nowi t only remains to say that this research is an enlargement of the communication (Baroni-Jacoboni 1975) given on the same subject at the First International Congress on Semiotics of Music (Belgrade, oct. 1973). The organi zation of the paper is however different: we have divided the work into four chapters. In the first we talk about the~criteria we have used in selecting the corpus of music we have investigated and also about the general methodological factors that determined this choice. The second chapter is devoted to the study of the material out of which our selected phrases have been made. In the third, we deal with the results of our analysis, which are given by a set of 56 rules. The last chapter is reserved for a brief outline of the computer program used for the automatic generation of phrases. serait de fournir une voie d'approche, encore modeste, a une etude objec tive des jugements de valeur esthetique en musique." From the results arrived at in our work, which set out on lines not dissimilar to Ruwet's, we conclude that the distinction he makes between judgements of correct ness and judgements of value is inappropriate. Wec an say, from what the generating process revealed, that the evidence has not been sufficient for us to confirm the existence of such a clear distinction. The elimi nation of phrases that we regard as being incorrect and of those which we regard as inelegant, which brings us progressively nearer to the ori ginal model, has been only possible through the gradual identification of rules which are ever more minute and refined, but not qualitatively diffe rent from each other. - 15 - CHAPTEIR - THEO BJECTA NDM ETHODOSF THEA NALYSIS I.1. The object The present work forms the first part of a larger project of an analysis of the chorales for four voices by J.S. Bach. Here we will take into consideration only certain fragments from the corpus of chorales, namely the first two soprano phrases that are in major mode, without modulations, and that are in 4/4 time(l). Weh ave chosen to limit ourselves to such small components of the whole for two reasons : to make a more exhaustive study of the chosen texts and to explain as clearly as possible our methodology, that is, to render the approa ches used in the analysis explicit. To the limits concerning the object of the study, there is another limit to add regarding the content of the analysis. A musical text, even when it is reduced and fragmented, as it is in our case, is a complex entity whose struc- ture is tied to the functions of communication. The process of communication which the text is destined to establish could be analyzed on different levels, and for this reason we must first clarify to which of these levels our analysis is aimed if it is directed at a study of the production of the text (i.e., the relations (1) Weh ave taken all the chorales in the Bach Ausgabe, including those which are not present in the collection by J.Ph. Kirnberger and K.Ph.E. Bach, and which therefore do not appear in the alphabetically ordered list of chorales made by Schmieder (1950 : 380-387). In order to help the reader to identify the single melodies, in Appendix l we have given three distinct numerations, from the BWVf, rom the first Bach Ausgabe, and, where it exists, also from the Neue Bach Ausgabe. In this section, however, we will only use the BWV numeration although for the rest of the text, once the sample has been defined., th.e p.rog.ressi ve numeration of Appendix l will be used. --- - - -- - - 16 - between the composer and the work) or at a study of the fruition of the work (i.e~ the relations between the finished work and those for which it is intended), or at a study of the structure of the text as a neutral object taken out of these 2 contexts of production and fruition( ). Our analysis concentrates on the latter approach. For an exhaustive analysis as explicit as we should like it to be, the problem about the choice of material to undergo analysis is a particularly delicate one. Such material has to have two fundamental characteristics : maximumex tension and homogeneity. The former condition must guarantee a suffi cient number of examples for the study from which we can derive precise struc tural hypotheses and the latter condition is essential in order to avoid contra dictions in this set of hypotheses. Hoping to find in these pieces some features that indicate the presence of a grammatical structure, as with the linguistic approach that examines natural languages, we encounter one particular problem: western musical tradition, the area in which our study will remain, is characterized by the great variety and instability of musical codes. Between the code, (here one means a set of con ventions that insures communication to a certain social group) and the composer (upon whomt his group lays the task of music production), there exists an uneasy relationship, this rapport not being based on mere acceptance, but proving to ~ (2) The distinction between these three levels defined as "poietique, esthesique et neutre", respectively, which has been used by J. Molino (1975 : 46-49) on the guidelines laid downb y Paul Valery and Etienne Gilson, has been also used by J.J. Nattiez (1975), and systematically studied by G. Naud (1975). Wea lso find the tripartition useful in our present work.

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