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Version: 1.3
31. August 2001

Dynamic Potential of Harmonic Structures - The Way of Evaluation

Abstract

Dynamic Potential of Harmonic Structures
The Way of Evaluation

The situation in Slovakia is permanent changing and it is not easy to do scientific research, and it is almost impossible  to find programmer for cooperation (there is a contradiction between best paid programmers and worst paid research workers).  According to this reality, we provide only meditation or a proposal how to find one of the possible ways to analyze harmony in music by computer and to find one alternative for enumeration of  tensional  changes and appropriate visualisation of development of this  kind of tensional motion. 

Harmony is the structural quality of music,  in which dynamics and tension or stress of music  is inherent, especially in tonal music, which was dominant in Europa through three centuries (17th - 19th) and recently we could observe a new comeback to it. We suppose  that the tension and stress of harmonic structures in tonal music is  inherent and connected  with listeners feeling  in perception. This opinion confirms Nicolas Cook, too."At the beginning of the century, as indeed nowadays, it was harmony that was regarded as the most crucial aspect of musical content", ((6), p.16). We assume, that content and tension of music are inseparable. 

The measurment and evaluation of tension in music therefore is not possible only by acoustical measurement of loudness or tempo (and eventually with ascending and descending of melody (8)), it is necessary to make harmonic analysis, too, and to evaluate the motion in harmony according to the structural direction and development of chords and according to their  place in so called cadence (musical instance ñ A. Dvo?ák, Symphony n.8 op.22, 1st Movement, 2´40´´)

It seems, that the Schenkerian way of harmonic analysis (5), (6) doesn´t focus an interest on a fluctuation of stress, it´s oriented preliminary to find  "foreground", "middleground" and "background" of  the harmony by reduction of many chords, which are not so important for basic tonal key, which are only embalishing, or which are secondary (lend from other tonal keys) respectively which are connected more with melody.

Listener  is hearing music from the beginning, and he doesn´t reduce no one chord in his hearing. Temporal stress is therefore not so important from the point of view of Schenkerian analysis, but in progress of the full composition. In the moment of sounding, the tension, higher or lower, is brought by every chord sounding inherently with its environment (previous and next chord), by its development and in connection with melodical motion of individual voices. We assume, that the way of traditional harmonic analysis (9), (10), where every chord has its tonal function, is for our purpose in this project better root.

Tonal functions as tonic ñ T, subdominant ñ S and dominant ñ D are representatives of various sizes of harmonic tension and in this sense they control psychological quality of hearing, too. Tonic (the triad on the I-st degree of tonal key) as a chord of harmonic peace, subdominant (the triad on the IV-th degree) as a chord of middle tension or harmonic digression and dominant (the triad on the V-th degree) as a chord of highest tension or maximal harmonic stress are the basic functions. Chords on other degrees of tonal key were used in tonal music as modifications or combinations of basic functions. In our opinion it could be useful to consider every other degree as a double function, ie. the II-nd degree SD function (two pitches from S and one from D), the III-rd degree TD or DT (two pitches from T and two from D), the VI-th degree TS or ST (2 pitches from S, 2 from T) and the VII-th degree DS (2 pitches from D and 1 from S). The size of tonal tension of these chords probably depends on how much is the chord similar to the basic function or how is it used as (the very usual way of using similarity is the way of placing the chord instead of basic function in cadence). It is well known use of II in cadence T-II-D7-T, or use of VII as T-S-VII-T.

We could  try to propose the evaluation (and enumeration necessary for computer processing) of this ability of harmonic structures for control tension in  listeners feeling.  The evaluation/enumeration should be made in three basic levels:

1. consonant/disonant sounding of chords  - vertical or structural tension
2. tonal function of chords  and their place in cadence ñ tension of tonal relation
3. development and connection of chords with previous and following chords ñ tension of chordal relation

Traditional music theory considered as a consonant only two chords ñ major and minor triad. (The fact, that these triads could take place like disonances, if they are not used as basic functions, will be satisfied in level of tonal functions.) The dynamics of these triad  we will consider to cause the lowest tension. "...the major triad is in itself static..." ((6) p. 40). Other chords are more or less disonant and bring higher tension. The most disonant interval (of highest tension) is a major seventh and a minor second, then minor seventh and major second and then diminished fifth or augmented fourth. Two major thirds in superposition are disonant despite of that major third alone is a consonant interval

Perception of tonality in European music is based on perception of chordal relation of fifth (interval of 7 semitones) and on perception of tension of so called "leading" (8) tones. The chord having one or more leading tones to the next one, is strongly directed to it. Therefore D7 (in c major this chord consists of g-b-d-f) which has two leading tones to the tonic (b gravitates up to c ñ this is ascending leading tone, and f gravitates to e ñ this is descending leading tone) is dominant, strongly gravitated to the tonic.

Development of every secondary dominant seventh chord to its tonic is everytime full of tension caused by leading tones.
In most cases the chord directed to its tonic is built up by thirds, but also there is a most important intervalic distance full of tension ñ diminished fifth (or augmented fourth) ñ named also tritonus. It is well known characteristic of this interval ñ diabolo in musica ñ bringing feeling of tension and stress. Therefore many authors consider this interval as a dynamic substance of  chords. This interval should be the decisive one in evaluation of dynamical size of chords.

We regard as reasonable to divide evaluation and enumeration of above mentioned levels of tension, and after that to make some correlation between them. It will bring new, graphically visualizable motion of tension or dynamics of harmony.
 

References:

(2) Ferková, E. (1992).  Computer analysis of classic harmonic structures,  Selfridge- Field,  E.  -  Hewlett, W.  (Eds.), Computing in Musicology, CCARH, Menlo Park, 85 ñ 89.

(3) Ferková, E., Dudek, M. (1992). CACH: Computer analysis of classical harmony, Secondo Convegno Europeo di Analisi Musicale, Trento, 619 ñ 621.

(4) Ferková, E. (1999). Harmonic-tonal motion as a reflection of the development of musical form, Diderot Forum on Mathematics and Music,  Vienna, 169-177.

(5) Salzer, F. (1952).  Structural hearing: tonal coherence in music., Dover Publications, New York. 

(6)Cook, N. (1987). A guide to musical analysis, J. M. Sons & Ltd., London.

(7)Randal,. M. (1978). Harvard Concise Dictionary of Music, Cambridge, London. 

(8)Selfridge-Field, E., Hewlett, W. B. Eds.(1998). Melodic similarity: concepts, procedures, and applications, Computing in Musicology, 11, Stanford.

(9) Kresánek, J. (1982). Tonalita, Bratislava.

(10)Filip, M. (1998). Súborné dielo I: vývinové zákonitosti klasickej harmónie, Bratislava.