________________
AUGUST, 1912.]
wrong, as anybody with some acquaintance of the elements of acoustics can easily see.33 The same sort of gross mistake had been committed previously by J. D. Paterson,34 with this difference that this writer saw that even with his naive rejection of fractions, which he resorted to with apparent success in the first tetrachord sa-ma, he could not get anywhere near the numbers he desired in the case of the distances between successive frets of the second tetrachord pa-sa, and had recourse to the very ingenious suggestion that as they considered the 2nd Tetrachord as perfectly similar to the first, they probably made use of the same numbers to express that similitude.' Verily scholarship must have been comfortably unexacting in those happy old days!
There is thus absolutely no basis for Râjâ S. M. Tagore's fancied modern arrangement of the rutis, there being no authority for it. Nor does the observed difference in the position of the semitones in the classical and the modern scales stand in need of such an hypothesis, as it is capable of more than one other explanation as will be seen hereafter. But in putting forward a probable explanation of the supposed displacement of the śrutis, the writer says: "According to a fule laid down in the classical treatises, the disposition of the notes is reversed in the case of Dáravi (literally, wooden, i. 6., stringed) instruments, and out of this reversed arrangement, perhaps, the modern theory about the arrangement of the position of the śrutis has been evolved.' As usual the Raja does not quote his authority; but it seems certain that he is referring to the lines
4 brutis
33 If we suppose with the Raja the length of the string producing sa to be 90 inches, then theoretically the lengths giving the succeeding seven notes of the octave [on the Raja's assumptions about (1) the disposition of the śrutis in the modern Hindu scale and (2) the values of the three sorts of intervals being a major tone, a minor tone and a diatonis semitone] will be 80, 72, 67, 60, 534, 49 and 45 inches respectively, and the difference in lengths of strings will be as shown in the following table:
90
80 above.
sa and ri 10 inches ma and pa 71, pa and dha 6"
67
60
9
80 -; &-brutis - 72
ANCIENT HINDU MUSIC
A mere glance at the table shows the error of the Raja's statement. The fact is that there is a radical error in representing musical intervals by differences in the lengths of strings producing the notes. The correct way to represent them is by means of quotients of the respective lengths. Thus the 4-srutis intervals above are
531
72
49
16
60 531
48
67
45
1
44
Difference in length of strings of sucoessive notes.
3 śrutis
2
8
{ //
4
8 44 x -
9
On the Gramas or Musical Scales of the Hindus (Asiatic Researches, Vol. IX), reprinted in Tagore's Hindu Music from Various Authors, and quoted in Capt. Day's The Music and Musical Instruments of 8. India and the Deccan. What J. D. Paterson says amounts to this:-The madhyama-grama is formed from the shadja-grâma (see Sir W. Jones' scheme above) by flattening dha by one śruti, which thus becomes identical with the major mode of European diatonic scale (of course, according to the wrong notions of that author and Sir W Jones). Now take a sounding string 44 units in length between the nut and the bridge; then half the length or 22 units will give the ootave of the open string, representing the 22 śrutis. The lengths for the different notes will theoretically be as follows:
Note
ww
Length of string
[ri and ga 8 inches dha and ni 53,
44 x
8
10
41
; 2-árutia
9
41 x
3
2 srulis
2 44 × - 8
189
2
3
Sga and ma 4 inches. ni and sa 3"
See the Preliminary Remarks
15
6
3 41 X
2
14 215
14 215
7 115
Reject the fractions of the first three differences, says Mr. Paterson, and you have the figures 4, 3, and 2 respectively, the number of árutis supposed to be there by the Hindu musicians. But the remaining figures do not fit in, even with the extreme liberality with which the reader has been asked to reject fractions, and the author has, therefore, recourse to the ingenious suggestion given above. Not to mention the hugeness of frac tions omitted, it will be at once seen that the writer's way of representing musical intervals is radically wrong (see the last footnote).
7 8 or ootave.
1 2
8
44 X15
41 x
