________________
256
THE INDIAN ANTIQUARY
[NOVEMBER, 1912.
semitones to the octave, with the intervals of 2, 2, 1, 2, 2, 2, 1 semitones between its successive notes. A scale constructed according to these data would be
c d e f g a b o'
Cents 0 200 400 500 700 900 1100 1200 Here the fourths and fifths are more accurate than those in the 22-srutis scale, but all other intervals show the same or greater deviations than are found in that soalo.ca But on that account we do pot say that in the European scale tho major thirds are wrong by - cunima, etc. The only legitimate remark that can be made would be that the expression of the Earopean scale in terms of twelve semitudes as given above, is not an accurate one. Similarly, it is quite as probable that the expression of the Hindu scale in terms of 22-śrulis is oniy an approximation. The question then arises-"Do we possess any indications which will enable us to make an accurate determination of the Hindu scale, of which the cycle of 22 árutis might simply be an approximate expression ?" To which the reply is, “Yes, for some notes at least."
In the Bh. we are told what notes are consonant or sashvádlins. Two notes with an interval of nine or thirteen brutis between them are consonant with each other. Thus, in the shaljagrdna. (1) shadja and panchama, (2) pishabha and dh ciputa, (8) gdadhara and nishada, (4) shadja and madhyama. So also in the madhyamagráma with the exception of shadja and panchana. Here [in the madhyamagrama] there is consonance of panchama and rishabha. 164 This at once enables us to write the exact values of all the notes except two, since it is evident that the interval of nine frutis represents the just Fourth, and that of thirteen tbe just Fifth Thas we have
46 36 26 46 36 24 46 Notes ma pa dha ni sa riga ma
9 4 3
16 A Ratios
3 2 Cents 0 204
498 702
996 1200 Only two notes romain, vis., dha and ri. They are mutually consonant, bat neither of them being consonant with ate of known value their owa ralaus mit not be determ ned by this method. Bat before considering any suggestions as to their probable values, it is necessary to note the difference between the exact values thas obtained of the various intervals, and those calculated from the cycle of 82, which was brought into existence in order to express them. Intervalo. Exact value in cents.
Defectivo expression of the valgo
by the cyou of 22. Major toue of 4 árutis ...
204
218 Minor Third of 5 árutis...
294
273 Just Fourth of 9 srutis ...
498
491 Just Fifth of 13 krutis ...
702
709
* This is the well-known equal temperament soale of Europe, and though in extensive use, is not the ideal jast scale.
Indeed, this ought to be evident a priori. Tuns for instance, a noto and its fifth or a note and its ootave are the actualities presented to us first, and afterwards ou mes the idea of measuring and comparing them. Now, it is easy to see that we may be in possessiou of two definite magnitudes, but for various reasona may not be able to expross one exactly in terms of the other. The intervals of an octave and a ffth are examples in point. Hence the various ayoles proposed, such as those of 12 ani 22. It would be putting the cart before the horse to treat tho semitone or the fruti as the primary notion and to seek to establish the fifth of a noto by going up 7 nemitones or 13 brutis.
" Bh. p. 303. The 8. R. means the same thing when it says that those notes, in the interval between which there are twelve or eight srutis, are consonant with each other' But this modo of expression is objectionable for the same reason that it is objectionable to say that between the 1st and 14th of January intervene twelve days, and between the 1st and the 10th eight.
