Indian Antiquary Vol 41

Author(s): Richard Carnac Temple, Devadatta Ramkrishna Bhandarkar
Publisher: Swati Publications

Page 261

NOVEMBER, 1912.)
ANCIENT HINDU MUSIC
257
The interval of 8 krutis is of no value for our present purpose, being simply composeil of two intervals of 4 srutis. Similarly other available intervals being only defects of these intervals from the octave of 22 árutis, need no separate consideration. From the above table it will be seen that the system of 22 irutis is capable of introducing an error of as many as 21 cents or nearly a comma in an attempt to express by means of it an interval, the value of which is known beyond all doubt by the method of consonances. We can now proceed to discuss some values for the uniletermined notes, which offer themselves for consideration, remembering that a deviation to the extent of about a comma need not by itself stamp them as improbable:
(1) The first value we shall consider will be that suggested ty Mr. Hipkins, who holds that the 3 frutis interval must be taken as a 4-tone. We have seen that on the 22-śrutos scale the enlculated value of the 4-srutis interval is 218 cents but that the real value was 204 cents. A 4 tone, therefore, must be equal to 153 cents, an interval known to be used in the East. But the substitution of this value leaves 141 cents as the value of the 2-srutis interval between dha And ni, or between ri and ga, and it is impossible to believe that the two intervals of 153 and 141 cents, differing from each other only by 12 cents, should have been expressed by 3 and 2 krutis respectively. We cannot, therefore, look upon the 3-srutis interval as a 4-tone. The same fact may be put in another light. The two intervals of 153 and 141 cents are so nearly equal that each of them may be looked upon an equal to 8-brutis, and it will be found that the whole scale can then be more accurately expressed by means of the cycle of 24 than by means of one of 22, thus : Notes
... ... ma pa dha ni sa riga ma The scale to be expressed ... 0 204 857 498 702 855 996 1200 cents Values expressed by means 4's
26 46 36 21 46 of cycle of 22 árutis ...SO 218 382 491 709 878 982 7200 cents Valnes expressed by means 46 86 36 46 34 34 45
of cycle of 24 árutis o 200 350 500 700 850 1000 1200 cents A glanre at this table shows the greater accuracy of expression obtainable by means of 24-srutis scale, if the 3-srutis interval were intended to be a 4-tone as Mr. Hipkins supposes. But since the Hindus fixed upon 22-śrutis only, it is evident that they did not intend the 3-srutis interval to be a 4-one.
(2) Secondly, we shall consider the value of the 3-srutis interval calcnlated on the basis of 22-srutis to the octave, which is 164 cents. In the first place let it be noted that if this value has & claim on our consideration, that claim is shared to an equal extent by the value assignable to dha by a calculation on the same basis, vie., that of 7-srutis= 382 cents, and this we shall proceed to do in the next paragraph. In the meanwhile if we take 164 cents as the value of the 3-srutis interval, the value of the neighbouring 2-srutis interval becomes 180 cents, and the same objection presents itself as before, viz., the improbability of taking the two intervals of 164 cents and 130 cents for a 3-árutis and a 2-srutis interval respectively.
(3) Lastly, let us consider the value of dha obtained by calculating on the same basis as in the last paragraph, which is 382 cents. This gives very remarkable results. The 3-erutis and 2árutis intervals have now the values of 178 cents and 116 cents respec:ively, which are almost exactly in the ratio of 3: 2. An additional argument for accepting this value is the consideration that the Hindas in choosing the cycle of 22 were more likely to bave aimed at securing a greater accuracy in the expression of the relations of the fourth, the fifth and the thirds than that of smaller intervals like the seconds. It will be noticed that this value of the niajor Third, riz., 882 cents, differs only by 4 cents from the value of the just major Third which is 386 cents, and there is nothinz against the supposition that probably this was the actual value of that interval; the