For those who are interested:
Here are the tuning ratios of the Indian 22 shrutis in use (the lower
octave is below).
As there are mostly only 7 notes of these in simulataneous use, our flat
and natural notes are both called "ri", "ga" etc., and apart from the
Fifth and Octave which are always perfect, there are four of each to
choose from. The highest Fourth is used as a low Fifth.
In ancient Indian theory, all possible modes are divided by those that
are based on the Perfect Fifth, and those that are based on the
imperfect Fifth (40/27)
A different concept, yet it seems to work.
(Note X 1-4 | Shruti No. | Tuning Ratio)
Sa Sa 22 2/1
Ni 4 21 243/128
Ni 3 20 15/8
Ni 2 19 9/5
Ni 1 18 16/9
Dha 4 17 27/16
Dha 3 16 5/3
Dha 2 15 8/5
Dha 1 14 128/81
Pa 13 3/2
Ma 4(Pa)12 40/27
Ma 3 11 45/32
Ma 2 10 27/20
Ma 1 9 4/3
Ga 4 8 81/64
Ga 3 7 5/4
Ga 2 6 6/5
Ga 1 5 32/27
Ri 4 4 9/8
Ri 3 3 10/9
Ri 2 2 16/15
Ri 1 1 256/243
Sa 0 1/1
It would be interesting if these are useful in lute/keyboard tuning -
maybe our tuning nerds can make something of it.
At least on a keyboard, it would be possible to make up a 12 tone
solution from these - it would be interesting how they sound in true
polyphony.
I am not very familiar with Vicentino, but as I recall he proposes a
similar solution.
Also most archicembali around 1600 seem to use a similar number of
octave divisions.
Does anyone have any experiece with these?
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