Toward an analysis of polyphonic music in the textual symbolic segmentation MICHELE DELLA VENTURA Department of Technology Music Academy “Studio Musica” Via Terraglio, 81 TREVISO (TV) 31100 Italy dellaventura.michele@tin.it Abstract: The listener is able to identify a melody (motif) within a "sonorous image" created during the per- formance of music, be it generated by a single voice (monody) or by several simultaneous voices (polyphony). The "sonorous continuum" of a musical piece, in fact, does not exhaust itself in the mere acoustic - perceptive fact, yet it has a meaning that emerges from the structural properties of the musical piece, cognitively processed by the listener and linked back to conceptual structures. This article presents a model of analysis developed so as to identify a melodic line inside a polyphonic musical structure. Study highlights the manner in which the horizontal (monody) and vertical (polyphony) dimensions of a given musical piece must be pondered, on the basis of recent considerations on a harmonic and cognitive level developed respectively by D. de la Motte and D. Huron. The algorithm conceived to this effect was tested on a set of data (scores) of small dimensions serv- ing as a sample. Key-Words: analysis, monody, musical object, musical surface, polyphony, segmentation 1 Introduction The concept of melody or motif is well known to musicians, yet there is no theory to describe how a certain motif may be identified. In Fremdwörter- Duden 1 the item Motif reads: "1) foundation, im- pulse, cause... 3) the smallest musical unit". Hugo Riemann defines motif as a "melodic fragment" ... which forms by itself a minimal unit possessing au- tonomous expressive meaning". Whereas Herman Grabner believes that: "Motif (ultimately from Latin movere) means the smallest autonomous and characteristic unit of melodic movement ... It gives a decisive motor impulse to the consecutive evolu- tion". Generally speaking, motif may be defined as a me- lodic fragment possessing individuality and recog- nizability [1]. D. de la Motte [2] valorizes this aspect by high- lighting the absence of rules concerning the struc- tural characteristics that the motif must have, even with respect to the simplest element that is its length intended as its number of bars (see fig. 1). 1 A dictionary of foreign words that is part of a German dic- tionary family which is well-known in Germany. Fig. 1: Examples of melodies. The first one is an ex- cerpt from Die Schöne Müllerin by Schubert: here the singer is involved in three bars in which melody flows without returning elements. The second mel- ody, made up of only three bars, is an excerpt from a Piano Sonata by Haydn. The third melody, made up of 10 bars, is an excerpt from Sonata No. 1 op. 2 by Beethoven. A second equally important aspect that D. de la Motte highlights in his analyses is the one concern- ing the theory of harmony that draws its foundation from the polyphonic aspect of the musical text. In this field, certain rules (in western music) remain valid throughout time: many aspects of these rules change, upgrade, get old, get modified, but their a) b) c) Mathematical Models in Engineering and Computer Science ISBN: 978-1-61804-194-4 19