Miscellaneous 7-limit temperaments: Difference between revisions
Move 7-limit varuna and trimyna here |
+ intro to varuna and trimyna. - typo |
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== Varuna == | == Varuna == | ||
: ''For extensions, see [[Werckismic temperaments #Varuna]].'' | : ''For extensions, see [[Werckismic temperaments #Varuna]].'' | ||
Varuna tempers out the [[varunisma]] in the 7-limit, and splits the octave in two. It then finds [[7/4]] by a stack of two [[10/9]]'s and a semi-octave period. The obvious 11-limit extension tempers out the kalisma, [[9801/9800]]. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~567/400 = 600.1005{{c}}, ~3/2 = 701.3045{c}}, ~5/4 = 386.3934{{c}} | * [[WE]]: ~567/400 = 600.1005{{c}}, ~3/2 = 701.3045{{c}}, ~5/4 = 386.3934{{c}} | ||
: [[error map]]: {{val| +0.201 -0.449 +0.482 -0.353 }} | : [[error map]]: {{val| +0.201 -0.449 +0.482 -0.353 }} | ||
* [[CWE]]: ~567/400 = 600.0000{{c}}, ~3/2 = 701.2691{{c}}, ~5/4 = 386.5935{{c}} | * [[CWE]]: ~567/400 = 600.0000{{c}}, ~3/2 = 701.2691{{c}}, ~5/4 = 386.5935{{c}} | ||
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== Trimyna == | == Trimyna == | ||
: ''For extensions, see [[Werckismic temperaments #Trimyna]].'' | : ''For extensions, see [[Werckismic temperaments #Trimyna]].'' | ||
Trimyna tempers out the [[trimyna comma]] in the 7-limit, and finds the [[6/1|6th]] [[harmonic]] by a stack of five [[10/7]]'s. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.1652{{c}}, ~10/7 = 620.4031{c}}, ~5/4 = 387.0990{{c}} | * [[WE]]: ~2 = 1200.1652{{c}}, ~10/7 = 620.4031{{c}}, ~5/4 = 387.0990{{c}} | ||
: [[error map]]: {{val| +0.165 -0.105 +1.116 -1.634 }} | : [[error map]]: {{val| +0.165 -0.105 +1.116 -1.634 }} | ||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 620.3427{{c}}, ~5/4 = 387.2591{{c}} | * [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 620.3427{{c}}, ~5/4 = 387.2591{{c}} | ||