Interpretation of tone: Take 2

We now take a closer look at the issue of tone boundary and the system-atic exploitation of ‘inter-tone’ boundaries in Carnsystem-atic music. It is generally claimed that the notes were supposedly derived mathematically as cycles of

fths and cycles of fourths from a fundamental note (see Sambamurthy 1999, V for a fuller discussion).

In other words, tuning for the fth note proceeded from a fundamental, then taking the fth as the fundamental the subsequent fth was arrived at and so on. The derived notes were then transposed to the lower octave (if necessary) and the other notes in the octave were determined. Similarly, from a fundamental the fourth was derived, keeping the fourth as the fundamental the next fourth was arrived at and if the notes went beyond the octave they were transposed to the lower octave. By these two operations, the twelve notes in an octave were mathematically arrived at (supposedly).

80 Conversion of pitch values to notes

Table 1. Hypothesized pitch values in cents of the Indian scale and the even tempered scale⁶⁰

Tone label Western Indian

1. Df ra – suddha riҌabham 100 112

2. D ri – caturҌruti riҌabham 200 204

3. Ef gi – saadhaaraͣa gaandhaaram 300 316

4. E gu – antara gaandhaaram 400 386

5. F ma – suddha madhyamam 500 498

6. Fs mi – prati madhyamam 600 588 (590)

7. G pa – pancamam 700 700 (702)

8. Af da – suddha dhaivatam 800 814

9. A di – caturҌruti dhaivatam 900 906

10. Bf ni – kaisiki niҌaadam 1000 1018

11. B nu – kaakali niҌaadam 1100 1088

The values for the 12 Indian ‘notes’ and their related note in the even tem-pered scale are given above, along with the labels for the notes in both the systems.⁶¹ But notice, that because of the different modes of derivation in the Indian and the Western scales, we see that the cent values of the Indian scale and Western scale do not match. However, notice that the ‘notes’ of the major scale, i.e. ‘ri’, ‘ma’ and ‘di’ differ minimally from the notes of the Western major scale in their cent values but ‘gu’ and ‘ni’ deviate quite a bit from the even tempered Western scale.

Now consider the real pitch values of the twelve tones in my veena tuned to ‘E’ on the pitch pipe, given in Figure 2. These frequencies translated to cent values presented below for comparison with the Western system and Indian theory are given below. The differences in cent values are quite be-wilderingly different from any of the other values. Consider the differences in Table 2 on the following page.

The major point worth noting is that the Western even tempered cent values, the supposedly mathematically derived cent values in Indian mu-sic theory and the real values from my veena do not match (with the real frequencies in my veena converted to cent values). Not only do the values on my veena not match either value, they are far off the mark for even the

Interpretation of tone: Take 2 81 major landmark like ‘pa’. Thus we see that we have practical proof of Indian music theory being just that – ‘theory’. It must be mentioned that the entire demonstration was done with this tuning on my veena which is attested in the demonstration MP3 collection. I have listened to my recording and so has the recordist and we found the note values ‘tolerable’. Since these are the stable values of the twelve notes on my veena, we do not even have the excuse of saying that they are idiosyncratic points on the Indian scale.

Figure 2. Frequency values on my veena set at E

I have no option but to say that the musical reality of the Carnatic scale has nothing to do with the Indian ‘mathematical’ values. The analogy is once again language. In language, when languages make use of pitch variation either for intonational or lexical purposes, they typically do not aim at ‘ab-solute’ values. Firstly, the pitch range of the speaker is age-sex dependent:

younger people and women have higher pitch ranges and secondly, for the same speaker, depending on the emotion/expressive nature of the output the pitch range can vary rather widely. Thus what constitutes a ‘high’ pitch for one speaker may constitute a ‘mid’ pitch for another and what constitutes a ‘high’ pitch in one style for one speaker may constitute a ‘low’ pitch for the same speaker in another style. Thus in language, pitch labels like ‘high’,

82 Conversion of pitch values to notes

‘mid’ and ‘low’ make no sense in isolation or in absolute terms as they vary with the speaker and with the register. To labour the same point, the same speaker when excited or when speaking to a child is likely to use an extended pitch range where the ‘high’, ‘mid’ and ‘low’ would be exaggeratedly far apart.

Table 2. The values of notes in cents in the Western, even-tempered scale, the Indian theoretical system and my veena⁶²

Note Western Indian Theory my veena

D at; ra 100 112 +12 98 –2

D; ri 200 204 +4 163 –37

E at; gi 300 316 +16 241 –59

E; gu 400 386 –14 327 –73

F; ma 500 498 –2 419 –81

F sharp; mi 600 588 –12 511 –89

G; pa 700 700 ±0 618 –82

A at; da 800 814 +14 710 –90

A; di 900 906 +6 824 –76

B at; ni 1000 1018 +18 944 –56

B; nu 1100 1088 –12 1065 –35

C upper; Sa 1200 1200 1200

Unlike language, the only mathematical reality given to a Carnatic musi-cian is the value of the octave (approximately). Everything else is culture-bound. The conclusion that I wish to draw is not that a cent value difference of, say, 37 between my veena and the Western absolute scale or a cent value of 41 between my veena and that of the Indian mathematical tradition is re-ally imperceptible to the Indian ear. I would like to maintain that ‘absolute’

values are really irrelevant to the Carnatic music system. What the Carnatic music system deals with is pitch relations – as long as, perceptible boundar-ies are dened with respect to the twelve ‘static’ tones. And we will see in the next chapter that the Carnatic music fraternity can perceive differences as low as 20 cent values and make ne distinctions between different types of pitch movements. But more of this later.⁶³

Interpretation of tone: Take 3 83 While the cycle of the fths gives us a fairly close approximation to cent values in the Western major scale, i.e. the notes ‘sa’ C, ‘ri’ D, ‘gu’ E, ‘ma’

F, ‘pa’ G, ‘di’ A and ‘nu’ B in the Indian theoretical scale, it is quite likely that the hypothesized cycle of the fourths which is supposed to give us the

‘minor’ tones, i.e. ‘ra’ D at, ‘gi’ E at, ‘mi’ F sharp, ‘da’ A at and ‘ni’ B at are just that – a theoretical hypothesis worked out mathematically. But the cent value of my veena and the twelve tones is a real eye-opener. The entire exercise is only a theoretical justication of sorts, the actual reality cannot be determined mathematically or by any cycle of the fths or the fourths. Like the setting of the pitch values of tones in language, the distinct twelve tones are perceptual landmarks in the octave which guide further minute pitch variations in a number of grammatically determined ways.

As is obvious by now, no instrument maker in India ever tunes all the twelve notes using the cycles of the fths and fourths as theorized. The large part of the setting is done just by ear (and sometimes re-adjusted when there is disagreement between the tuner and the musician). Therefore, it is clear that the theory of the cycle of the fths and the fourths is just that – theory.

But an elegant one nevertheless. Notice that some of the differences in tones between the Western and the Carnatic systems are fairly large and, I think, perceptible to the musically trained ear. This difference is easily demonstrat-ed comparing the scales renderdemonstrat-ed on a veena and any keyboard instrument.

Therefore, since this is a major instance of re-interpreting pitch values which is culture bound, we denitely need the tone interpreting mechanism.