Magic22 as srutis
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- This revision was by author hstraub and made on 2007-08-11 06:34:38 UTC.
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[[http://launch.groups.yahoo.com/group/tuning/message/63593|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 [[Regular Temperaments#magic|magic temperament]]. Using the generator of 13 steps of [[41edo|41-et]], if we take the strutis 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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<html><head><title>Magic22 as srutis</title></head><body><a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/63593" rel="nofollow">Original article</a> by Gene Ward Smith, on the Yahoo tuning forum, is quoted here.<br /> <br /> What srutis are seems to be fairly flexible. However, reasonably authentic conditions to impose are the following:<br /> <br /> (1) It should contain the Sa-grama, 9/8-5/4-4/3-3/2-27/16-15/8-2<br /> <br /> (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.<br /> <br /> (3) 9/8, 10/9 and 16/15 are each always of the same size, and distinguished, with 9/8>10/9>16/15.<br /> <br /> Many scales fulfill these conditions, and one of the most interesting, I think, is Magic[22], the 22-note MOS of the <a class="wiki_link" href="/Regular%20Temperaments#magic">magic temperament</a>. Using the generator of 13 steps of <a class="wiki_link" href="/41edo">41-et</a>, if we take the strutis 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]:<br /> <br /> 1-(2212)-9/8-(222)-5/4-(22)-4/3-(1222)-3/2-(2221)-27/16-(222)-15/8-(22)-2<br /> <br /> Here the numbers in parethesis are the scale step patters between one note of Sa-grama and the next.</body></html>