Diaschismic family: Difference between revisions

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~~__FORCETOC__~~

The 5-limit parent comma for the '''diaschismic family''' is 2048/2025, the [[diaschisma]]. Its monzo is {{monzo| 11 -4 -2 }}, and flipping that yields {{multival| 2 -4 -11 }} for the wedgie for 5-limit '''diaschismic''', or '''srutal''', temperament. This tells us the period is half an octave, the [[Wikipedia: Greatest common divisor|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]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]] or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities.

~~The 5-limit parent comma for the '''~~diaschismic family''' is 2048/2025, the [[diaschisma]]. Its monzo is {{monzo| 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 [[Wikipedia:Greatest common divisor|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]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]] or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities.

= Srutal aka diaschismic =

[[~~Tuning_Ranges_of_Regular_Temperaments|valid range~~]]: ~~[600.000 to 720.000] (2 to 5)~~

[[Comma list]]: 2048/2025

~~nice range~~: [~~701.955~~, ~~706.843~~]

[[Mapping]]: [{{val| 2 0 11 }}, {{val| 0 1 -2 }}]

~~strict range~~: ~~[701~~.~~955, 706.843]~~

[[POTE generator]]: ~3/2 = 704.898

[[~~POTE_tuning|POTE generator~~]]: ~~~3/~~2 ~~= 704~~.~~898~~

[[Tuning ranges]]:

* valid range: [600.000 to 720.000] (2 to 5)

* nice range: [701.955, 706.843]

* strict range: [701.955, 706.843]

~~Map: [<2 0 11~~|~~, <0~~ 1 -2|]

~~EDOs:~~ 34, 46, 80, 206c, 286bc

== Seven limit children ==

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-__FORCETOC__
+The 5-limit parent comma for the '''diaschismic family''' is 2048/2025, the [[diaschisma]]. Its monzo is {{monzo| 11 -4 -2 }}, and flipping that yields {{multival| 2 -4 -11 }} for the wedgie for 5-limit '''diaschismic''', or '''srutal''', temperament. This tells us the period is half an octave, the [[Wikipedia: Greatest common divisor|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]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]] or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities.
-The 5-limit parent comma for the '''diaschismic family''' is 2048/2025, the [[diaschisma]]. Its monzo is {{monzo| 11 -4 -2 }}, 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 [[Wikipedia:Greatest common divisor|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]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]] or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities.
+= Srutal aka diaschismic =
-[[Tuning_Ranges_of_Regular_Temperaments|valid range]]: [600.000 to 720.000] (2 to 5)
+[[Comma list]]: 2048/2025
-nice range: [701.955, 706.843]
+[[Mapping]]: [{{val| 2 0 11 }}, {{val| 0 1 -2 }}]
-strict range: [701.955, 706.843]
+[[POTE generator]]: ~3/2 = 704.898
-[[POTE_tuning|POTE generator]]: ~3/2 = 704.898
+[[Tuning ranges]]:
+* valid range: [600.000 to 720.000] (2 to 5)
+* nice range: [701.955, 706.843]
+* strict range: [701.955, 706.843]
-Map: [&lt;2 0 11|, &lt;0 1 -2|]
+{{Val list|legend=1| 34, 46, 80, 206c, 286bc }}
-EDOs: 34, 46, 80, 206c, 286bc
 == Seven limit children ==