Magic22 as srutis
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[[toc|flat]] ---- =Magic[22] as srutis[[#magic22assrutis]]= [[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 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[[#shrutar22assrutis]]= [[http://launch.groups.yahoo.com/group/tuning/message/63594|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 [[46edo|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].
Original HTML content:
<html><head><title>Magic22 as srutis</title></head><body><!-- ws:start:WikiTextTocRule:4:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:4 --><!-- ws:start:WikiTextTocRule:5: --><a href="#Magic[22] as srutis">Magic[22] as srutis</a><!-- ws:end:WikiTextTocRule:5 --><!-- ws:start:WikiTextTocRule:6: --> | <a href="#Shrutar[22] as srutis">Shrutar[22] as srutis</a><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --> <!-- ws:end:WikiTextTocRule:7 --><hr /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Magic[22] as srutis"></a><!-- ws:end:WikiTextHeadingRule:0 -->Magic[22] as srutis<!-- ws:start:WikiTextAnchorRule:8:<img src="/i/anchor.gif" class="WikiAnchor" alt="Anchor" id="wikitext@@anchor@@magic22assrutis" title="Anchor: magic22assrutis"/> --><a name="magic22assrutis"></a><!-- ws:end:WikiTextAnchorRule:8 --></h1> <br /> <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/63593" rel="nofollow">Original article</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a>, 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 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]:<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.<br /> <br /> <hr /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Shrutar[22] as srutis"></a><!-- ws:end:WikiTextHeadingRule:2 -->Shrutar[22] as srutis<!-- ws:start:WikiTextAnchorRule:9:<img src="/i/anchor.gif" class="WikiAnchor" alt="Anchor" id="wikitext@@anchor@@shrutar22assrutis" title="Anchor: shrutar22assrutis"/> --><a name="shrutar22assrutis"></a><!-- ws:end:WikiTextAnchorRule:9 --></h1> <br /> <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/63594" rel="nofollow">Original article</a> by Gene Ward Smith, on the Yahoo tuning forum, is quoted here.<br /> <br /> 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 <a class="wiki_link" href="/46edo">46et</a>, 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<br /> <br /> 1-(2222)-9/8-(322)-5/4-(22)-4/3-(2222)-3/2-(2222)-27/16-(223)-15/8-(22)-2<br /> <br /> This gives Shrutar[22].</body></html>