Subgroup temperaments: Difference between revisions
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→2.….19/7.… subgroups: add a temperament |
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[[Subgroup]]: 2.3.19/7 | [[Subgroup]]: 2.3.19/7 | ||
[[Comma list]]: [[57/56]] ({{ | [[Comma list]]: [[57/56]] ({{Monzo| -3 1 1 }}) | ||
{{Mapping|legend=2| 1 0 3 | 0 1 -1 }} | {{Mapping|legend=2| 1 0 3 | 0 1 -1 }} | ||
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[[Badness]] (Sintel): 0.082 | [[Badness]] (Sintel): 0.082 | ||
=== Supramin === | |||
This is a remarkable low-complexity microtemperament that contains the 14:17:19 triad within just four generator steps. An excellent tuning is [[25edo]], which provides an accurate yet tone-efficient tuning of this temperament. It was named by [[User:Overthink|Overthink]] in 2026 after the fact that the generator is a [[17/14]] supraminor third, two of which reach [[28/19]]. | |||
[[Subgroup]]: 2.17/7.19/7 | |||
[[Comma list]]: [[5491/5488]] ({{Monzo| -4 2 1 }}) | |||
{{Mapping|legend=2| 1 0 4 | 0 1 -2 }} | |||
: mapping generators: ~2, ~17/7 | |||
[[Optimal tuning]]s: | |||
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1200.022{{c}}, ~17/14 = 335.793{{c}} | |||
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.000{{c}}, ~17/14 = 335.785{{c}} | |||
{{Optimal ET sequence|legend=1| 7, 18, 25 }} | |||
[[Badness]] (Sintel): 0.005 | |||
==== Supramine ==== | |||
This extension approximates the 14:17:19:23:25 pentad in just six generator steps, at the cost of some accuracy. 25edo remains a strong tuning. | |||
Subgroup: 2.17/7.19/7.23/7 | |||
Comma list: [[323/322]], [[392/391]] | |||
Subgroup-val mapping: {{Mapping| 1 0 4 3 | 0 1 -2 -1 }} | |||
Optimal tunings: | |||
* Subgroup WE: ~2 = 1199.871{{c}}, ~17/14 = 336.243{{c}} | |||
* Subgroup CWE: ~2 = 1200.000{{c}}, ~17/14 = 336.296{{c}} | |||
{{Optimal ET sequence|legend=0| 7, 18, 25 }} | |||
Badness (Sintel): 0.029 | |||
==== 2.25/7.17/7.19/7.23/7 subgroup ==== | |||
Subgroup: 2.25/7.17/7.19/7.23/7 | |||
Comma list: [[323/322]], [[392/391]], [[476/475]] | |||
Subgroup-val mapping: {{Mapping| 1 -2 0 4 3 | 0 3 1 -2 -1 }} | |||
Optimal tunings: | |||
* Subgroup WE: ~2 = 1199.757{{c}}, ~17/14 = 335.428{{c}} | |||
* Subgroup CWE: ~2 = 1200.000{{c}}, ~17/14 = 335.479{{c}} | |||
{{Optimal ET sequence|legend=0| 7, 18, 25 }} | |||
Badness (Sintel): 0.053 | |||
== 3/2.5/2.… subgroups == | == 3/2.5/2.… subgroups == | ||