No-threes subgroup temperaments: Difference between revisions
Normalize mapping |
Move llywelyn/shoe back here, as the clan is unnecessary |
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* Didacus ([[3136/3125]]) → [[Hemimean clan #Didacus|Hemimean clan]] | * Didacus ([[3136/3125]]) → [[Hemimean clan #Didacus|Hemimean clan]] | ||
* Mercy ([[823543/819200]]) → [[Quince clan #Mercy|Quince clan]] | * Mercy ([[823543/819200]]) → [[Quince clan #Mercy|Quince clan]] | ||
* Sidewalk ([[823543/800000]]) → [[2023/2000 #Sidewalk]] | * Sidewalk ([[823543/800000]]) → [[2023/2000 #Sidewalk]] | ||
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[[Badness]] (Sintel): 0.156 | [[Badness]] (Sintel): 0.156 | ||
=== Llywelyn a.k.a. shoe === | |||
Llywelyn a.k.a. shoe is the common [[restriction]] of [[gamelismic clan #Gorgo|gorgo]] (16 & 21), [[breedsmic temperaments #Gorgik|gorgik]] (21 & 37), and [[gariboh clan #Semaja|semaja]] (16 & 37). It can be described as 16 & 21, and tempers out the [[llywelynsma]]. Its generator is a flattened [[~]][[8/7]] whole tone, seven of which give the interval class of [[5/1|5]]. Its [[ploidacot]] is alpha-heptaseph. [[Weak extension]]s to the full 7-limit include [[marvel temperaments #Misneb|misneb]] (21 & 32), which splits 8/7 into two for [[15/14]]~[[16/15]] each, [[archytas clan #Ultrapyth|ultrapyth (32 & 37)]], which splits [[16/7]] into two for a [[3/2|perfect fifth]], and [[buzzardsmic clan #Septimal buzzard|buzzard]] (53 & 58), which splits 16/7 into three, each for [[21/16]]. | |||
; Scales | |||
* [[Shoe5]], [[Shoe6]], [[Shoe11]], [[Shoe16]] | |||
[[Subgroup]]: 2.5.7 | |||
[[Comma list]]: 4194304/4117715 | |||
{{Mapping|legend=3| 1 1 3 | 0 7 -1 }} | |||
{{Mapping|legend=5| 1 0 1 3 | 0 0 7 -1 }} | |||
: mapping generators: ~2, ~8/7 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.1974{{c}}, ~8/7 = 226.7586{{c}} | |||
: [[error map]]: {{val| -0.803 +0.194 +2.008 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 226.8388{{c}} | |||
: error map: {{val| 0.000 +1.558 +4.335 }} | |||
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37, 164d }} | |||
[[Badness]] (Sintel): 2.06 | |||
==== 2.5.7.11 subgroup ==== | |||
Subgroup: 2.5.7.11 | |||
Comma list: 176/175, 1310720/1294139 | |||
{{Mapping|legend=2| 1 1 3 1 | 0 7 -1 13 }} | |||
{{Mapping|legend=4| 1 0 1 3 1 | 0 0 7 -1 13 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.1784{{c}}, ~8/7 = 226.9582{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.0438{{c}} | |||
{{Optimal ET sequence|legend=0| 16, 21, 37, 206cd, 243cd, …, 354ccdd }} | |||
Badness (Sintel): 0.651 | |||
==== 2.5.7.11.13 subgroup ==== | |||
Subgroup: 2.5.7.11.13 | |||
Comma list: 176/175, 640/637, 847/845 | |||
{{Mapping|legend=2| 1 1 3 1 2 | 0 7 -1 13 9 }} | |||
{{Mapping|legend=4| 1 0 1 3 1 2 | 0 0 7 -1 13 9 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.1643{{c}}, ~8/7 = 226.9495{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.0315{{c}} | |||
{{Optimal ET sequence|legend=0| 16, 21, 37, 206cdf, 243cdf, …, 354ccddff }} | |||
Badness (Sintel): 0.319 | |||
==== 2.5.7.11.13.17 subgroup ==== | |||
Subgroup: 2.5.7.11.13.17 | |||
Comma list: 176/175, 221/220, 640/637, 847/845 | |||
{{Mapping|legend=2| 1 1 3 1 2 2 | 0 7 -1 13 9 11 }} | |||
{{Mapping|legend=4| 1 0 1 3 1 2 2 | 0 0 7 -1 13 9 11 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.3162{{c}}, ~8/7 = 227.1125{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.1774{{c}} | |||
{{Optimal ET sequence|legend=0| 16, 21, 37, 95 }} | |||
Badness (Sintel): 0.458 | |||
=== Huntington === | === Huntington === | ||