Diaschismic family: Difference between revisions

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__FORCETOC__

The 5-limit parent comma for the '''diaschismic family''' is 2048/2025, the [[diaschisma|diaschisma]]. Its monzo is |11 -4 -2>, and flipping that yields <<2 -4 -11|| for the wedgie for 5-limit diaschismic, or '''srutal''', temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. [[34edo|34edo]] is a good tuning choice, with [[46edo|46edo]], [[56edo|56edo]], [[58edo|58edo]] or [[80edo|80edo]] being other possibilities. Both [[12edo|12edo]] and [[22edo|22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities.

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[|1 0 0 0 0>, |7/4 0 0 1/4 -1/4>, |2 0 0 -1/2 1/2>,

|37/12 0 0 5/12 -5/12>, |37/12 0 0 -7/12 7/12>]

|37/12 0 0 5/12 -5/12>, |37/12 0 0 -7/12 7/12><nowiki>]</nowiki>

Eigenmonzos: 2, 11/7

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Compositions:

[http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3 ~~http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3]~~

http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3

(the description says "lemba" which has a similar ~~sale~~ structure but different mapping for 5)

(the description says "lemba" which has a similar scale structure but different mapping for 5)

=Shrutar=

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 __FORCETOC__
 The 5-limit parent comma for the '''diaschismic family''' is 2048/2025, the [[diaschisma|diaschisma]]. Its monzo is |11 -4 -2&gt;, and flipping that yields &lt;&lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or '''srutal''', temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. [[34edo|34edo]] is a good tuning choice, with [[46edo|46edo]], [[56edo|56edo]], [[58edo|58edo]] or [[80edo|80edo]] being other possibilities. Both [[12edo|12edo]] and [[22edo|22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities.
@@ Line 323: / Line 324: @@
 [|1 0 0 0 0&gt;, |7/4 0 0 1/4 -1/4&gt;, |2 0 0 -1/2 1/2&gt;,
-|37/12 0 0 5/12 -5/12&gt;, |37/12 0 0 -7/12 7/12&gt;]
+|37/12 0 0 5/12 -5/12&gt;, |37/12 0 0 -7/12 7/12&gt;<nowiki>]</nowiki>
 Eigenmonzos: 2, 11/7
@@ Line 394: / Line 395: @@
 Compositions:
-[http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3 http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3]
+http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3
-(the description says "lemba" which has a similar sale structure but different mapping for 5)
+(the description says "lemba" which has a similar scale structure but different mapping for 5)
 =Shrutar=