No-threes subgroup temperaments: Difference between revisions
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* Mercy ([[823543/819200]]) → [[Quince clan #Mercy|Quince clan]] | * Mercy ([[823543/819200]]) → [[Quince clan #Mercy|Quince clan]] | ||
* Llywelyn a.k.a. shoe ([[4194304/4117715]]) → [[Llywelynsmic clan #Llywelyn a.k.a. shoe|Llywelynsmic clan]] | * Llywelyn a.k.a. shoe ([[4194304/4117715]]) → [[Llywelynsmic clan #Llywelyn a.k.a. shoe|Llywelynsmic clan]] | ||
* Sidewalk ([[823543/800000]]) → [[2023/2000#Sidewalk]] | |||
=== Frostburn === | === Frostburn === | ||
{{See also| Magic family #Quadrimage | {{See also| Magic family #Quadrimage | Subgroup temperaments #Baldy }} | ||
[[Subgroup]]: 2.5.7 | [[Subgroup]]: 2.5.7 | ||
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{{Main| Bastille }} | {{Main| Bastille }} | ||
Described as the 2.5.7 subgroup 1407 & 1789 temperament, and named after an eponymous historical event which took place on July 14, 1789 (14/07/1789). Extensions discussed elsewhere include [[The Jacobins#Double bastille|double bastille]]. | Described as the 2.5.7 subgroup 1407 & 1789 temperament, and named after an [[wikipedia:Storming of the Bastille|eponymous historical event]] which took place on July 14, 1789 (14/07/1789). Extensions discussed elsewhere include [[The Jacobins#Double bastille|double bastille]]. | ||
Subgroup: 2.5.7 | Subgroup: 2.5.7 | ||
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[[Tp tuning #T2 tuning|RMS error]]: 0.5886 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.5886 cents | ||
=== Pakkanen | === Pakkanen === | ||
[[Subgroup]]: 2.5.7.11 | [[Subgroup]]: 2.5.7.11 | ||
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{{Optimal ET sequence|legend=1| 6, 16, 22, 28, 29, 35, 41, 57, 63, 98c }} | {{Optimal ET sequence|legend=1| 6, 16, 22, 28, 29, 35, 41, 57, 63, 98c }} | ||
[[Badness]] (Sintel): 0.573 | |||
=== No-threes naiad === | |||
{{See also| Wizardharry clan #Naiad | Werckismic temperaments #Seminaiad }} | |||
This temperament can be described as the 21 & 29 & 37 temperament in no-threes subgroups. It expands [[Subgroup temperaments #Tridec|tridec]] and [[Subgroup temperaments #Naiadec|naiadec]]. | |||
[[Subgroup]]: 2.5.7.11 | |||
[[Comma list]]: 5021863/5000000 | |||
{{Mapping|legend=2| 1 0 2 0 | 0 1 1 1 | 0 0 -4 3 }} | |||
: mapping generators: ~2, ~5, ~100/77 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.080¢, ~5 = 2786.820¢, ~100/77 = 454.618¢ | |||
* [[CWE]]: ~2 = 1200.000¢, ~5 = 2786.740¢, ~100/77 = 454.590¢ | |||
{{Optimal ET sequence|legend=1| 16, 21, 29, 37, 50, 58, 66, 87, 103, 124 }} | |||
[[Badness]] (Sintel): 1.862 | |||
==== 2.5.7.11.13 subgroup ==== | |||
Subgroup: 2.5.7.11.13 | |||
Comma list: 847/845, 1001/1000 | |||
Sval mapping: {{Mapping| 1 0 2 0 1 | 0 1 1 1 1 | 0 0 -4 3 1 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1200.034¢, ~5 = 2786.678¢, ~13/10 = 454.569¢ | |||
* CWE: ~2 = 1200.000¢, ~5 = 2786.646¢, ~13/10 = 454.557¢ | |||
{{Optimal ET sequence|legend=0| 16, 21, 29, 37, 50, 58, 66, 87, 103, 124 }} | |||
Badness (Sintel): 0.179 | |||
==== 2.5.7.11.13.17 subgroup ==== | |||
Subgroup: 2.5.7.11.13.17 | |||
Comma list: 170/169, 221/220, 847/845 | |||
Sval mapping: {{Mapping| 1 0 2 0 1 1 | 0 1 1 1 1 1 | 0 0 -4 3 1 2 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1200.407¢, ~5 = 2787.484¢, ~13/10 = 455.036¢ | |||
* CWE: ~2 = 1200.000¢, ~5 = 2787.107¢, ~13/10 = 454.906¢ | |||
{{Optimal ET sequence|legend=0| 16, 21, 29g, 37, 50, 58, 66g, 87g }} | |||
Badness (Sintel): 0.438 | |||
== Higher 2.5 temperaments == | == Higher 2.5 temperaments == | ||
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{{Optimal ET sequence|legend=1|8, 13, 21, 34, 81, 115}} | {{Optimal ET sequence|legend=1|8, 13, 21, 34, 81, 115}} | ||
== No-threes-or-fives subgroup temperaments == | == No-threes-or-fives subgroup temperaments == | ||