Influence of the harmonic/functional analysis on the musical execution: representation and algorithm
Michele Della Ventura · 2012
The importance of the analysis in the execution of a musical piece is a concept that is shared by most of the interpreters and scholars: highlight hierarchical relations, deep structures, motivic thematic aspects and the like, it is necessary for a better comprehension of the ”musical logic” of the piece. The composer gives a definite shape to his ideas, configuring and organizing the musical material. The executant reproduces that particular shape in order to convey the ideas of the composer, yet he fails in doing his task if he does not manage to understand how the shape is organized: it is the very structure of the music, resulting from its melodic, rhythmic, harmonic and dynamic component that determines at the same time shape and character. The identification of the melodic, rhythmic or harmonic cells is a first and fundamental step for the interpretation of a musical piece, yet not enough in order to confer it the right character intended by the composer: it is the latter that gives us a significant indication in this respect, by means of the harmonic structure, particularly by means of the “function” that every single harmony (or chord) performs in the context in which it is inserted. In this article I will present a model of harmonic analysis able to explore progressively the symbolic level of the musical text, identifying its harmonic structures and by means of the “function” carried by every single one of these, provide useful information for the dynamics. The efficiency of the model was verified through the analysis of various musical pieces, by different authors and from different times trying to range over various styles. Key-Words: harmony, harmonic function, segmentation, analysis, Musical Object, Musical surface 1 Analysis and execution One of the recurrent themes within the framework of the musical execution is the necessity ratio existing between analysis and execution [1]: the analysis has the task of making tangible (i.e. listenable) all the ratios, all the aspects of the musical nexus, of the contrast and of the construction lying at the heart of the sonorous image (deriving from the execution) [2]. Fig. 1: Prelude in E-flat Minor BWV 853 by J.S. Bach (the first four beats). Fundamental rhythmic and melodic cells generating thematic and timbral structures within the entire piece. The identification of rhythmic or melodic elements (see fig. 1), also called pre-thematic because they form together the various musical phrases, allows the executant to give a shape to the musical piece [3]. Melody and rhythm are, therefore, tightly knit with each other: the former represents meaning developed from a succession of sounds, while the latter is the shape and the proportions of that specific succession [4]. Hence, the rhythm confers individuality and recognizability to the melody (see fig. 1) [5], but at the same time it characterizes the entire musical piece by means of rhythmic cells, that is groups of signs (or signs and rests) which create within the musical discourse recurrent rhythmic, even different at a melodic level, schemes (see fig. 2 and 3) [6]. Fig. 2: Prelude in E-flat Minor BWV 853 by J.S. Bach. Rhythmic cell C of the 4th beat repeated several times on different degrees A B C Latest Trends in Applied Informatics and Computing ISBN: 978-1-61804-130-2 85 Fig. 3: Prelude in E-flat Minor BWV 853 by J.S. Bach. Rhythmic cell (3) of the 4th beat repeated several times, contrariwise, on different degrees. How to interpret these rhythmic/melodic elements belonging to the musical piece? Do they all have the same importance? How can they give shape to the musical piece? One of the fundamental criteria, at the level of execution, is that of using different levels of intensity between elements or different voices [1]. With intensity we have already entered the field of values that are not defined in absolute terms in the score: the sign “f”(forte) means, for example, that a certain sound must be executed with a superior dynamics than the one marked with “p”(piano), but it does not give us precise information with respect to the actual decibels that need to be produced. Being precise in this field, relating to the dynamics is one of the main tasks of the interpreter who must scale its values by carefully studying the score and the semiographic habits of the composer [7]. The musical analysis provides, by means of the study of the harmony, a corpus of rules studied and extrapolated a posteriori by the operas of the authors [5]: it is a cognitive tool to be used in order to analyze a particular musical piece. Although extremely useful, such knowledge basis is to be used with both thoughtfulness and caution, because of its intrinsic non-univocalness. 2 Functional harmony In the functional theory, the goal is to identify in a sound, a chord or a chord succession, the “intrinsic sonorous value” assumed, compared to a specific reference system polarized in a center, or the capacity to establish organic relations with other sounds, chords or chord successions of the same system [8]. The functional theory tends to go beyond the sonorous event as it manifests itself, to interpret what lies behind that which appears in a particular instant, to seize the meaning, the “role” that it covers in comparison to other events that come before and after it, therefore the “function” that it performs in the context within which it is immersed. In particular, as far as the chord is concerned, the functional theory tends to research, beyond what it represents by itself in comparison to a certain reference system (for instance, the chord G-B-D, compared to the tonal system and the tonality of C Major, is the dominant chord), the harmonic function performed, the organic relation established with the one that comes before and the one that comes after it. The pillars of the functional theory are the harmonic functions of tonic (T), subdominant (S) and dominant (D), that Riemann was the first to identify as the foundation and pivot of any type of chord succession, hypothesizing in the connection I-IV-V-I (fig. 4) the archetype of the tonal harmony and the model which any type of chord concatenation should be traced back to (fig. 5). Fig. 4: Archetype of the tonal harmony according to Riemann. Fig. 5: Riemann’s analysis of Beethoven’s Piano Sonata n° 1 op. 2 It follows that all the chords will have a harmonic function of relaxation or of tonal center T, or of tension towards such center D, or of breakaway from it S. The three harmonic functions of I, IV and V degree are called main because they are linked by a relation based on the interval of the perfect 5 that separates the keynotes of the three corresponding chords; the chords relating to the rest of degrees on the scale are considered “representatives” of the I, IV and V degree (with which there is an affinity of the third two sounds in common because the 3 is actually the interval that regulates the distance between the respective keynotes) and secondary harmonic functions rest with it. Latest Trends in Applied Informatics and Computing ISBN: 978-1-61804-130-2 86 The identification of these harmonic functions within the various rhythmic/melodic cells and the relationship that every single one of them has within the context in which it is inserted (with what comes before and after it), allow the executant to have an image of the character of the piece so as to better define the field of dynamics.