Meantone family: Difference between revisions
m →Mohajira: missing info; noticed due to discussion with fumica |
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[[Badness]] (Sintel): 0.347 | [[Badness]] (Sintel): 0.347 | ||
=== 2.3.5.7.23 subgroup === | |||
There is a reasonable extension to the 2.3.5.7.23 subgroup, which tempers out [[161/160]] and [[162/161]], and maps the [[23/16]] to the diminished fifth (C–G♭). | |||
Subgroup: 2.3.5.7.23 | |||
Comma list: 81/80, 126/125, 161/160 | |||
Mapping: {{mapping| 1 0 -4 -13 14 | 0 1 4 10 -6 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1201.3627{{c}}, ~3/2 = 697.2263{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.5082{{c}} | |||
{{Optimal ET sequence|legend=0| 12, 19, 31, 81, 112bi }} | |||
Badness (Sintel): 0.451 | |||
=== Undecimal meantone (huygens) === | === Undecimal meantone (huygens) === | ||
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* [http://soonlabel.com/xenharmonic/archives/607 Scott Joplin's "The Entertainer" tuned into meanpop]{{dead link}} | * [http://soonlabel.com/xenharmonic/archives/607 Scott Joplin's "The Entertainer" tuned into meanpop]{{dead link}} | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3 ''Twinkle canon – 50 edo''] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3 ''Twinkle canon – 50 edo''] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] | ||
==== 2.3.5.7.11.23 subgroup ==== | |||
It is very reasonable to extend meanpop to the 2.3.5.7.11.23 subgroup. In this temperament, [[21/20]], [[23/22]], [[24/23]], [[25/24]] and [[28/27]] are mapped to the augmented unison. | |||
Subgroup: 2.3.5.7.11.23 | |||
Comma list: 81/80, 126/125, 161/160, 231/230 | |||
Mapping: {{mapping| 1 0 -4 -13 24 14 | 0 1 4 10 -13 -6 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1201.3759{{c}}, ~3/2 = 697.2251{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.4318{{c}} | |||
{{Optimal ET sequence|legend=0| 12e, 19, 31, 81, 112bi }} | |||
Badness (Sintel): 0.615 | |||
==== Tridecimal meanpop ==== | ==== Tridecimal meanpop ==== | ||