Indian Antiquary Vol 41

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

Page 262

238
THE INDIAN ANTIQUARY
(NOVEMBEE, 1912.
small difference being due to the unavoidable defect of the system of 22-srutis, selected for expressing the relations of the notes in the scale. This defect is shared by all systems, and it can be diminished only by admitting a greater number of degrees.
Finally at express statement in the S, P.65 gives a death-blow to the 4-tone notion, and in. directly supports the value which we must assign to the 3-srutis interval as a consequence of the value we have found for the 7-śrutis interval. With 386 cents for the latter, we bave 182 cents (a minor tone) for the former, whereas the 4-tone is only about 150 centa. From the data given in the S. P. for the division of a string the ratio of the 3-árutis interval between sa and ri isor 204 cents (a major tone), and of that between pa and dha is or 231 cents. Even allowing for the errors inevitable in determinations of the values of notes by the division of string in a fretted instrament like the Hindu bin, it is evident that a minor tone may be confounded with a major tone, but it is not easy to believe that a 4-tone can thus be confounded. On the other hand it would be quite legitimate to bring forward the objection that originally tho 3-srutis interval might have had a different value from that which it came to have in the days of the S. P.; bnt there is no evidence to support this hypothesis.
Inserting the value w have found for the 7-ýrutis interval in the Table A, we have the complete scale as follows:
46 3 2 4 86 2 4s ma pa dha ni sa riga ma
B Ratios
1
j
.
Cents 0 204 386 498 702 884 996 1200 from what has been said above it will be evident that the values of all notes given in this tablo are perfectly certain, except those of dha and ri which may be looked upon as almost certain
It is now necessary to notice the following remarks of Mr. A. J. Hipkins : “ The Indian scale intervals ought to be understood as they are explained by native writers-namely, A9 a tone, * -tone, and 3-tone, composed of 4, 3, and 2 árutis respectively. With this conception of intervals, and it must be borne in mind the 4-tone is still approved of in the East, a division of the octave into 24 equal quarter-tones becomes impossible. For as it was essential to secare an approximately perfect fourth with 9 árutis, and a fifth with 13, the division of the octave by 22 was the only one available. The error in the fourth of 9 equal frulis of a 22 division is no more than t-comma, in melody scarcely noticeable, but the error in a 21 or in a 23 division could not have been easily tolerated."66 At the outset, in this connection let me ask the reader to recall what I have said above, about the system of 22 śrutis being called into requisition to express the relations of the notes in an already existing scale and the inherent inability of all systems to express accurately the so-called n tural scale unless the octave is subdivided into a very large number of degrees. But this is not all. Mr. Hipkins is actually in error when he supposes that Hindu writers explain the intervals of their scale as being a tone, & t-tone, and a -tone.' Hindu writers have never said this ; they only say that there are three sorts of intervals, consisting of 4, 8 and 2 árutis respectively-in other words in the ratio 4:8:2. This is very different from what is understood by Earopean writers by a tone, a 4-tone, and a 3-tone. Consider the intervals 200, 150, and 100 cents. European writers will call them a tone, a 4-tone, and a t-tone respec. tively, which is correct. But now take the well-known intervals 204, 182, and 112 cents, or a major tone, a minor tone, and a diatonic semitone. These they will forth with describe as a tone, . tone, * Seo below.
# Capt. Day's The Music of Southern India, pp. 20-21.