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4.3 Postulate of Local Consonance
The sense in which consonance will be used subsequently needs some clarification. Generally it is used when two notes are sounded together. Consonance is then said to be the absence of dissonance, which is caused by rapid beats [4]. These rapid beats cause subjective feeling of roughness, which is found to be strongly correlated to dissonance. With simultaneous sounding of two complex tones, roughness may be produced by the production of beats for a large number of adjacent overtones. It has been suggested that for a complex-tone-pair with a given structure of partial amplitudes, the number of beating partials is smallest when the fundamental frequencies are related by a ratio of small integers [5]. On this basis Terhardt defines psycho-acoustic consonance, as the undisturbed simultaneous sounding of pure tones, the disturbing elements destroying consonance is roughness. However he also asserts that 'roughness principle' is not a sufficient basis of consonance and harmony [6]. For the purpose of studying vaditya in the context of Indian classical music it is necessary to consider consonance even when there is no simultaneous sounding. It seems that the remnant of the previous note, through some short-term memory, can neuro-physiologically interact with the current note and the musical sense of consonance remains still active. For this it is necessary to consider consonance in a positive sense i.e., to define consonance as the matching of a large number of higher partials rather than the negation of a non-match causing roughness. It has been shown that this also requires the fundamental frequencies to be related by a ratio of small integers [7]. In fact this definition appears to be relevant more in the cognitive domain rather than the physio-acoustical domain of inner ear. It seems that if before the activated pattern for the earlier partial structure of the previous note in the cortex dies out, the new activation is such that some of the earlier regions are rejuvenated, then a pleasing sensation is generated. This is the manner in which consonance in Indian music i.e. vaditya is viewed here.
It is postulated here that musicality, in Hindustani music, requires two consecutive notes to be consonating in the aforesaid sense and that in turn requires the two pitch values to bear a simple ratio of small numbers. This is referred to as local consonance hereinafter [8].
In a singing a single steady pitch for a note may not always bear small ratios to those on either side. In that case the central note cannot be locally consonant with notes on both sides. In such cases the pitch contour of the central note could possibly be usefully split up into different pitch states such that both the pitch values still remain in the same interval but each can bear small ratios with the pitch value in the notes in the corresponding consecutive side. Categoricity of pitch perception would keep intact the grammatical and other musical requirements, which are dependent on the perception of notes.
The relevance of the above postulate may be examined in two ways. One is to design a set of controlled perceptual experiments and the other is through an analysis of data on live performances. The first experiment, though very attractive, is also very difficult to do with the natural voice. The main problem here is that it is difficult to get an established performer to agree to cooperate simply because they can perform at their best only when the mood and musical ambiance are appropriate, as in a performance of raga. However such an experiment may be quite possible using singing synthesis. The other one is to study the problem through an analysis of recorded performances. The present study uses the second approach.
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References
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4. Plomp R and Levit W J M, "Tonal consonance and critical bandwidth", JASA, 38, 548-560, 1965.
5. Terhardt E, "Pitch consonance and harmony, JASA, 55,5, 1061-1069, 1974.
6. Terhardt E, "On the perception of periodic sound fluctuations (Roughness)", Acustica, 30, 3, 1974.
7. Datta A K and Kundu R, "A psycho-perceptual hypothesis for Indian musical scale", pre-proc. Second Int.Workshop on Recent Trends in Speech, Music and Allied Signal Processing, New Delhi, December 9-11, 1991
8. Datta A K, Dey N, Sengupta R, Banerjee B M, Nag D and Kichlu V K, "Relevance of consonance in Indian musical scale: theory and practice", J. Acoust. Soc. India, XXIII(1), pp. 110-115, 1995
