Greenwoodmic temperaments: Difference between revisions
ArrowHead294 (talk | contribs) No edit summary |
m Spell 1\1 etc. in decimal; note the badness metric being used; misc. cleanup |
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This is a collection of [[ | This is a collection of [[rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the [[greenwoodma]], 405/392 ({{monzo| -3 4 1 -2 }}). | ||
Temperaments discussed elsewhere are | Temperaments discussed elsewhere are | ||
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{{Multival|legend=1| 5 -6 7 -21 -3 33 }} | {{Multival|legend=1| 5 -6 7 -21 -3 33 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[POTE]]: ~2 = 1200.000, ~16/15 = 137.958 | |||
{{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }} | {{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }} | ||
[[Badness]]: 0.089840 | [[Badness]] (Smith): 0.089840 | ||
=== 11-limit === | === 11-limit === | ||
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Mapping: {{mapping| 1 1 3 2 3 | 0 5 -6 7 4 }} | Mapping: {{mapping| 1 1 3 2 3 | 0 5 -6 7 4 }} | ||
Optimal | Optimal tunings: | ||
* POTE: ~2 = 1200.000, ~12/11 = 137.900 | |||
{{Optimal ET sequence|legend=0| 9, 17, 26, 61bc, 87bcc }} | |||
Badness: 0.042562 | Badness (Smith): 0.042562 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
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Mapping: {{mapping| 1 1 3 2 3 2 | 0 5 -6 7 4 15 }} | Mapping: {{mapping| 1 1 3 2 3 2 | 0 5 -6 7 4 15 }} | ||
Optimal | Optimal tunings: | ||
* POTE: ~2 = 1200.000, ~12/11 = 136.937 | |||
{{Optimal ET sequence|legend=0| 9, 26f, 35 }} | |||
Badness: 0.049684 | Badness (Smith): 0.049684 | ||
==== Secundly ==== | ==== Secundly ==== | ||
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Mapping: {{mapping| 1 1 3 2 3 3 | 0 5 -6 7 4 6 }} | Mapping: {{mapping| 1 1 3 2 3 3 | 0 5 -6 7 4 6 }} | ||
Optimal | Optimal tunings: | ||
* POTE: ~2 = 1200.000, ~12/11 = 137.917 | |||
{{Optimal ET sequence|legend=0| 9, 17, 26, 61bcf, 87bccf }} | |||
Badness: 0.026212 | Badness (Smith): 0.026212 | ||
== Semishallowtone == | == Semishallowtone == | ||
{{See also|Shallowtone}} | {{See also| Shallowtone }} | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 405/392, 35721/32768 | [[Comma list]]: 405/392, 35721/32768 | ||
{{Mapping|legend=1| 2 2 16 9|0 1 -10 -3}} | {{Mapping|legend=1| 2 2 16 9 | 0 1 -10 -3 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~189/128 = 600.000, ~3/2 = 681.532 | |||
[[Support]]ing [[ET]]s: {{EDOs|14c, 30b, 44bd, 58bcd, 72bbccdd}} | [[Support]]ing [[ET]]s: {{EDOs| 14c, 30b, 44bd, 58bcd, 72bbccdd }} | ||
[[Badness]] (Dirichlet): 8.420 | |||
=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 45/44, 99/98, 43659/40960 | |||
{{ | Mapping: {{mapping| 2 2 16 9 16 | 0 1 -10 -3 -8}} | ||
Optimal tunings: | |||
* CTE: ~189/128 = 600.000, ~3/2 = 681.438 | |||
Supporting ETs: {{EDOs| 14c, 30b, 44bd, 58bcde, 72bbccddee }} | |||
Dirichlet | Badness (Dirichlet): 4.148 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 45/44, 27/26, 99/98, 35721/32768 | |||
{{ | Mapping: {{mapping| 2 2 16 9 16 4 | 0 1 -10 -3 -8 3 }} | ||
Optimal tunings: | |||
* CTE: ~189/128 = 600.000, ~3/2 = 681.406 | |||
Supporting ETs: {{EDOs| 14c, 30b }} | |||
Dirichlet | Badness (Dirichlet): 4.377 | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||