Dicot family: Difference between revisions
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1206.283{{c}}, ~ | * [[WE]]: ~2 = 1206.283{{c}}, ~5/4 = 350.420{{c}} | ||
: [[error map]]: {{val| +6.283 +5.167 -23.328 }} | : [[error map]]: {{val| +6.283 +5.167 -23.328 }} | ||
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 351.086{{c}} | * [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 351.086{{c}} | ||
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In the 11-limit, we have the identity 25/24 = ([[45/44]])⋅([[55/54]]), so it makes sense to temper out all of them. This leads to the very natural subgroup temperament where [[11/9]]~[[27/22]] is mapped to the neutral third. As such, this is also the path that most of the septimal extensions take to get their 11-limit versions. | In the 11-limit, we have the identity 25/24 = ([[45/44]])⋅([[55/54]]), so it makes sense to temper out all of them. This leads to the very natural subgroup temperament where [[11/9]]~[[27/22]] is mapped to the neutral third. As such, this is also the path that most of the septimal extensions take to get their 11-limit versions. | ||
=== 2.3.5.11 | An alternative identity 25/24 = ([[33/32]])⋅([[100/99]]) also makes sense to temper out in the 11-limit, leading to some undecimal extensions as eudicot. | ||
=== 2.3.5.11 dicot === | |||
Subgroup: 2.3.5.11 | Subgroup: 2.3.5.11 | ||
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Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1206.750{{c}}, ~ | * WE: ~2 = 1206.750{{c}}, ~5/4 = 348.684{{c}} | ||
* CWE: ~2 = 1200.000{{c}}, ~ | * CWE: ~2 = 1200.000{{c}}, ~5/4 = 348.954{{c}} | ||
{{Optimal ET sequence|legend=0| 3e, 4e, 7, 24c, 31c }} | {{Optimal ET sequence|legend=0| 3e, 4e, 7, 24c, 31c }} | ||
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Badness (Sintel): 0.536 | Badness (Sintel): 0.536 | ||
=== 2.3.5.11 eudicot === | |||
Subgroup: 2.3.5.11 | |||
Comma list: 25/24, 33/32 | |||
Subgroup val mapping: {{mapping| 1 1 2 4 | 0 2 1 -2 }} | |||
Gencom mapping: {{mapping| 1 1 2 0 4 | 0 2 1 0 -2 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1209.224{{c}}, ~5/4 = 347.612{{c}} | |||
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 346.056{{c}} | |||
{{Optimal ET sequence|legend=0| 3, 4, 7 }} | |||
Badness (Sintel): 0.493 | |||
==== 2.3.5.11.13 subgroup ==== | |||
Subgroup: 2.3.5.11.13 | |||
Comma list: 25/24, 33/32, 40/39 | |||
Subgroup val mapping: {{mapping| 1 1 2 4 4 | 0 2 1 -2 -1 }} | |||
Gencom mapping: {{mapping| 1 1 2 0 4 4 | 0 2 1 0 -2 -1 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1205.934{{c}}, ~5/4 = 349.530{{c}} | |||
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 348.213{{c}} | |||
{{Optimal ET sequence|legend=0| 3, 4, 7 }} | |||
Badness (Sintel): 0.575 | |||
== Septimal dicot == | == Septimal dicot == | ||