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260
THE INDIAN ANTIQUARY
[NOVEMBER, 1912.
by # sruti so as to make it consonant with the rishabha. But acoording to the values which we have come to assign to the different notes (see Table B), the necessary lowering amounts to only a comma or 22 cents, which is less than even half of the average value of a sruti, which is 540 cents. It is not this discrepancy, however, which is the difficulty in our way, as it is really of Do importance. For, it is easy to see and the reader may convince himself of it by actual trial) that it must necessarily occur in all cycles, whenever it is sought in this manner to find the value of one particular degree, unless indeed the cycle chosen is such that the difference between the major and the minor tone is represented by one degree, and that the value of each degree is as nearly as possible 22 cents, consistently with its giving good values for other intervals. Such a cycle is that of 53 in the Table 0 above. Why this cycle was not adopted by the Hindus to express their scale, if the latter was really the same as that I have arrived at from other considerations, will be discussed further on. It is sufficient for my present purpose to make the reader understand that the fact of the difference between the major and minor tones being only 22 cents (i..., very much less than the average value of Sruti) in no way goes against the value we have come to assign to the Hindu scale. Indeed, we can even go further and say that wboever might have originated the cycle of 22 to represent the Hindu scale, Bharata and Matanga were misled into straining it in an unjustifiable way, when they said that the amount of flattening necessary to make the pañchama of the shadjagrama consonant with the rishabha was the measure of a sruti. It will be seen that this error is quite natural, since with the adoption of the cycle of 22 we are forced to represent the major tone by 4 and the minor tone with 3, and the jast Fourth and Fifth with 9 and 18 respectively. Now in the shadjagrama the panchama is not consonant with the rishabha and the interval between the two is expressed by 10 or 12 according to the direction in which you measure. In order to make it consonant (as in the madhyamagrdma), it must be flattened by a certain amount ; but no sooner this is done the interval must be expressed by 9 or 13 (according to the direction in which you measure), since those are the numbers by which we must denote the intervals of consonance in the cycle of 22. In other words, you are obliged to say that the panchama has been flattened by one unit, however much the necessary amount of flattening may actually differ from the average value of tbat anit.
This apparently correct but really erroneous statement then can in no way go against the value we have come to assign to the Classical Rinda Scale. But the same cannot be said of the experiment described in the Bh, in connection with the exposition of the Srutis (808 the section on the svaras and arutis" above). In this experiment, it will be remembered, we have, at starting, two vinds in unison tuned to the shadjagrama. The taning of one of them is subsequently changed to the madhyamagrama by lowering the panchama by the requisite amount, which with our present values for the notes of the scale will only be a comma or 22 cents. The remaining strings are now lowered so as to have the shadjagrama tuning once more. Sapposing this can be accurately done, every string of this sind ought to give a note lower by a comma than the note of the corresponding string of the other. Performing this double operation once more, the difference in notes of corresponding strings will be two commas or 44 cents only, and the gândhara and nishada strings of the changing viņá cannot possibly give notes in unison with the rishabha and dhaivala of the other. But Bharata says that they do ; and there will be the same discrepancy in the rest of the experiment. Now if we believe that this experiment was actually performed by some musician with the stated result, we are forced to give up the values we have assigned to the notes in the Hinda scale and to admit those found by actual calculation on the supposition that the 22-srutis cycle represented the scale exactly (see Table 1). But this necessarily leads to the consequence that we must admit that the Hindu year was so peculiar that when it declared two notes to be consonant they were not so according to our present notions, but that the just Fourth was
