Magic22 as srutis

Magic[22] as srutis

Original article by Gene Ward Smith, on the Yahoo tuning forum, is quoted here.

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.

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Shrutar[22] as srutis

Original article by Gene Ward Smith, on the Yahoo tuning forum, is quoted here.

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].