Interpretation of tone: Take 1

The question before us now is whether the grammar of music, Carnatic mu-sic in particular, requires a mechanism equivalent to the PF component in the grammar of language. Contrary to Lerdahl and Jackendoff (1983) (see Foot-note 53 of Mukherjee (2000: 120)), music and Carnatic music in particular, denitely requires a module analogous to the PF component for language.

Speaking up for music, Mukherjee correctly says

“Conception of pitch-boundaries and their relations with each other subtly changes across periods and traditions and there is nothing like ‘xed’ pitches (McLain 1976). Traditions differ extensively regarding which set of pitches to choose, and the rules of putting them together. Musical systems in that sense are ‘parametric’ more or less in the sense in which languages are...”

(2000: 111)

It could not have been put more succinctly. As Sambamurthy says, “(i)n the scale of equal temperament, the octave is divided into 12 equal parts of cy-clic cents and each semi-tone comprises 100 cents.”(1999V: 42). And in the West, prior to the adoption of the even tempered scale, tones were dened

differently.

I present two arguments in this preliminary section arguing for the need for a PF-like mechanism. Firstly, in the Indian context, since there is no

‘ab-Interpretation of tone: Take 1 77 solute’ value attached to any tone, the task of discovering the fundamental pitch – the rst tone of the octave – requires an interpretive mechanism⁵⁸. Secondly, the ingenuity of the Carnatic music system has re-interpreted the 12 tone system as a 16 tone system with D, E at, A and B at per-forming overlapping functions (owing to the ingenuity of the musicologist VeenkaҲamakhi) given below in Figure 1. In the re-interpreted scheme, the tonal equivalents of ‘D’, ‘E at’, ‘A’ and ‘B at’ perform dual roles as ‘re-duced E’, ‘augmented D’, ‘re‘re-duced B’ and ‘augmented A’ respectively. Since a scale is allowed to choose only one tone to represent ‘D’, ‘E’ , ‘A’ and ‘B’

and since Carnatic music allows a scale to choose combinations of tones such as 2 and 3, 3 and 4, 9 and 10 and 10 and 11 of the Western numbering system, such a re-interpretation is necessitated.

ru du

ra gi mi da ni

Df Ef Fs Af Bf

C D E F G A B C

sa ri gu ma pa di nu sa

ga na

Figure 1. The Carnatic 16 tone system

This is the phenomenon I have termed as dual representation of tones as notes since ‘D’ can be interpreted as either ‘ri’ or ‘ga’ , ‘E at’can be inter-preted as either ‘ru’ or ‘gi’, ‘A’ can be interinter-preted as either ‘na’ or ‘di’ and ‘B

at’ can be interpreted as either ‘du’ or ‘ni’. Only the context can disambigu-ate the tones as notes of Carnatic music.

These overlapping functions are interpretable only in context. Thus if ‘ri’

is selected after ‘ra’, it performs the function of a Gaandhaaram, now newly termed ‘ga’. Similarly, after ‘sa’, if ‘gi’ is selected before a ‘gu’, then the former is re-interpreted as ‘ru’; after ‘pa’ and ‘da’, if ‘di’ is selected it is interpreted as ‘na’ and if after ‘pa’ and ‘ni’, ‘nu’ is selected, ‘ni’ is re-interpreted as ‘du’. Thus there are in addition to a unique ‘sa’ and ‘pa’ and

78 Conversion of pitch values to notes

two Madhyamams, three RiҌabhams, three Gaandhaarams, three Daivatams and three NiҌaadams with the octave containing sixteen ‘notes’ and not twelve as in the Western system. Thus, for VeenkaҲamakhi, if every full scale has to have seven notes with the ‘sa’ and ‘pa’ xed and the choice is between

‘ma’ and ‘mi’, by permutation and combination, we arrive at 72 full scales, called Mee̓akartaa. (i.e. in the rst half and second half of the octave twice two sets of three notes; 6 × 6 = 36 × 2 (ma or mi) = 72).

To quote Ayyangar’s (1972) quotation from VeenkaҲamakhi:

“The 72 Mee̓akartaas I have suggested are doubtless the product of my cre-ative urge. That is not their sole criterion. If it were so it is a waste of ingenu-ity. Nor do I claim that the scheme as a whole is practicable here and now.

True, it covers only a few raagas in circulation at present. I have designed it as a honeycomb cabinet to provide a niche for all raagas past, present and future.” (p. 159–160)

The comparison that readily comes to mind is with the periodic table constructed on the basis of the atomic weight of elements developed by Mendeleev which could predict elements not yet discovered. Similarly, VeenkaҲamakhi’s Mee̓akartaa schema could predict raagas like Kalyaaͣi

and Karaharapriyaa though he himself was very skeptical of the former (his schema was greater than him). In the centuries following VeenkaҲamakhi, his schema found general acceptability (in spite of a lot of skeptics) with many composers and performers taking up the rarer scales for creating composi-tions and for elaboration.

Further possibilities of ‘full’ scales are explored in Sambamurthy (1999) with scales selecting one or more different notes in the ascending and de-scending scale. Therefore, the actual list of possible ‘full’ scales is a very large number (of course not fully exploited till now).

Now, with the schema in place, if we allow scales that are not full (with a minimum of ve (four?) per ascending or descending scale and scales that may be called ‘non-linear’ (known as vakra raagaa, literally ‘crooked’) scales which prohibit certain tone sequences⁵⁹, then we have the best example of creativity in Carnatic music as we can create new scales and, in principle, the set of possible scales is innite. Therefore, in principle, new raagas can be invented/created by the Carnatic music fraternity (it is another matter for the new raagas to nd acceptance among the fraternity).

Keeping all these possibilities in mind, if we consider the function of interpreting tones in a musical phrase/line, the inescapable conclusion is that

Interpretation of tone: Take 2 79 interpretation is not always a simple ‘local’ phenomenon but may involve non-adjacent tones in long sequences of tones.

(5) Musical demonstration [ 4.33] & [ 4.34]

Local interpretation

Sa ra ‘gi’ ma interpreted as ‘gaandhaaram’ as E at Sa ‘gi’ gu ma interpreted as ‘riҌabham’ – augmented D Non-local interpretation

Sa gu ma .. ..

And much later

ma gi sa where ‘gi’ interpreted as ‘riҌabham’, as an augmented D if and only if ‘ra’ and ‘ri’ are never attested anywhere in the entire musical discourse.

Therefore, the role of the PF-like component is unquestionably necessary in the context of the grammar of Carnatic music.