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262
THE INDIAN ANTIQUARY
(NOVEMBER, 1912
of the preceding one so that the fourth gave the shadja note and the last the nishada.ce From all this it is clear that the áruti interval could not have had its origin in the measurement of a stretched string. But even supposing that the value of the interval was thus fixed by subdividing a string into 32 parts, for obtaining the value of 2 árutis we must take 31 of these parts and divide this again into 32, and so on for larger intervals, with the result that every such successive operation must increase the error, which unavoidably attends the experiment as noticed above. This makes it more probable that the relative values of the different notes in the scale were actually determined by trial by means of the ear with the help of strings rising in piteb step by step, as conceived, for example, by Sarngadeva. This I think may also account for the name sruti (something heard) given to the unit of measurement which resulted from such a process. Now, since equal rises in pitch have to be determined only by the ear, it is easy to see that the greater the number of degrees in a cycle the smaller is the value of each degree, and consequently the more difficult it is for the ear to appreciate the equality of each step in the pitch. We need not wonder then that the Hindus could not resort to a cycle like that of 53 and had to stop at one of 22, which, by the way, as pointed out above, cannot be excelled by another of less than 34 degrees.
To sum up, the values of notes in the Classical Hindu Scale (the shadjagrama) are as follows:
16
Notes
pa dha ni 84 riga ma
4 85 B Ratios
Cents 0 204 886 498 702 884 996 1200 Ag previously remarked, the values, given in this table, of all notes except dha and ri are absolutely certain, and I believe the evidence I have given is sufficiently convincing as regards the correctness of the values of the latter two also.
Now, we arranged the shadjagrama thus, with its keynote at the commencement, to enable a comparison to be made with the modern European major scale, from which it differs only in the seventh note being fatter by a chromatic semitone + & comma. The correct way, however, of representing it, is this, viz., with sa as the lowest note :
The shadjagrama.,
sa
riga
ma
pa
dha
ni
[sa]
• S. R. I. iii. 12 et seq. The experiment is not as accurately described as one would wish. Wo aro asked to tone the 82 strings each a little higher-pitched than the preceding so that between two successite notes produced by them there should not e.cist an intermediate note. These direotions are evidently defootive, for we can bare notes of intermediato pitch. Then again, it would have been better to havo 28 stringe with
intervals, so that at the fourth lowering of the strings it would have been possible to show that the sa string of the changeable vind was in unison with the ni string of the fixed vina. A similar inaccuracy of expression of the author I have noticed above. But the experiment was probably not quite imaginary like that in the Bh., referred to above. At any rato we are not asked to have the strings and danda of the same dimensions but are only required to construot two similar viņas, the similarity oonsisting in their producing identical Bounda- ft ayat are : A . I think Simha bhupala's explanation of this verse is correct, and Kalinatbat is not. The latter aays सदृशो सदृशाकारे; the former सदृशी समान |भाकारसाम्यं नात्रीपयुज्यत Feate 'AUT TT
UT T HAT T Tata Indeed one might almost think that the author had before him the expression T
h at of the Bh. and wrote 9 T: HT ** & correction. In passing, it may be noted that this experiment does not go against the values we have come to assign to the Classical Hindu Soale, remembering that the intervals are to be judged by the ear.
