| Carnatic |
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SWARAS
AND SWARASTHANAS
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we come to an important limitation of the keyboard - the way the
octave is divided into the twelve swara sthanas. Since it
is based on current western music norms, the division is done on a
logarithmic basis (which is just a more technical way of saying that
the pitch values of the successive swara sthanas form a geometric
progression). An octave is a factor of two and there are twelve
intervals in it. If we make all the intervals equal to a
multiplicative factor x, then the pitch corresponding to any key
will be x times the pitch of the key (white or black) immediately to
the left of it. Extending the procedure we arrive at what the value
of x should be. The thirteenth swara sthana results in an octave,
or, stated mathematically, x12=2. Then, we have x to be the twelfth
root of two or a factor of approximately 1.06. Using this logarithmic
division procedure, Pa (the 8th swara sthana) corresponds not to a
ratio of 1.5 but 1.498. Though the discrepancy is very small, a well
trained ear (eg. professional musician) can pick out this difference. |
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Swaras And Swarasthanas |
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