Magic22 as srutis
Magic[22] as srutis
Original article by Gene Ward Smith, on the Yahoo tuning forum, is quoted here.
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What srutis are seems to be fairly flexible. However, reasonably authentic conditions to impose are the following:
(1) It should contain the Sa-grama, 9/8-5/4-4/3-3/2-27/16-15/8-2
(2) It should give the major whole tone, 9/8, four srutis, 10/9 three srutis, and 16/15 two srutis, hence giving the octave 22 srutis.
(3) 9/8, 10/9 and 16/15 are each always of the same size, and distinguished, with 9/8>10/9>16/15.
Many scales fulfill these conditions, and one of the most interesting, I think, is Magic[22], the 22-note MOS of the magic temperament. Using the generator of 13 steps of 41-et, if we take the shrutis for 10/9 to always be 222, and the srutis for 16/15 to always be 22, we are left to give three steps of size 2, and one of size 1, for the srutis given to 9/8. If we vary the pattern of doing this we can get Magic[22]:
1-(2212)-9/8-(222)-5/4-(22)-4/3-(1222)-3/2-(2221)-27/16-(222)-15/8-(22)-2
Here the numbers in parethesis are the scale step patters between one note of Sa-grama and the next.
Shrutar[22] as srutis
Original article by Gene Ward Smith, on the Yahoo tuning forum, is quoted here.
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Magic is the 22&41 temperament; we can also concoct srutis out of shrutar, the 22&46 temperament. We now make each 9/8 a 2222 in 46et, and each 16/15 a 22. This leaves two 2 steps and a 3 step for 10/9, where we can vary the pattern. This time we make it
1-(2222)-9/8-(322)-5/4-(22)-4/3-(2222)-3/2-(2222)-27/16-(223)-15/8-(22)-2
This gives Shrutar[22].