Greenwoodmic temperaments: Difference between revisions
CompactStar (talk | contribs) No edit summary |
CompactStar (talk | contribs) No edit summary |
||
| Line 1: | Line 1: | ||
This is a collection of [[Rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the greenwoodma, {{monzo| -3 4 1 -2 }} = [[405/392]]. | This is a collection of [[Rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the greenwoodma, {{monzo| -3 4 1 -2 }} = [[405/392]]. | ||
Temperaments discussed elsewhere are | |||
* ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi|Dicot family]] | * ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi|Dicot family]] | ||
* ''[[August]]'' (+36/35) → [[Augmented family #August|Augmented family]] | * ''[[August]]'' (+36/35) → [[Augmented family #August|Augmented family]] | ||
| Line 64: | Line 64: | ||
== Semishallowtone == | == Semishallowtone == | ||
{{See also|Syntonic-chromatic equivalence continuum#Shallowtone}} | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
Revision as of 08:35, 19 April 2024
This is a collection of rank-2 temperaments tempering out the greenwoodma, [-3 4 1 -2⟩ = 405/392.
Temperaments discussed elsewhere are
- Sidi (+25/24) → Dicot family
- August (+36/35) → Augmented family
- Superpelog (+49/48) → Slendro clan
- Injera (+50/49 or 81/80) → Meantone family
- Schism (+64/63) → Archytas clan
- Greenwood (+1323/1280) → Apotome family
Secund
Subgroup: 2.3.5.7
Comma list: 405/392, 525/512
Mapping: [⟨1 1 3 2], ⟨0 5 -6 7]]
Wedgie: ⟨⟨ 5 -6 7 -21 -3 33 ]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 137.958
Optimal ET sequence: 9, 17, 26, 61bc, 87bcc
Badness: 0.089840
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 385/384
Mapping: [⟨1 1 3 2 3], ⟨0 5 -6 7 4]]
Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 137.900
Optimal ET sequence: 9, 17, 26, 61bc, 87bcc
Badness: 0.042562
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 45/44, 99/98, 385/384
Mapping: [⟨1 1 3 2 3 2], ⟨0 5 -6 7 4 15]]
Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 136.937
Optimal ET sequence: 9, 26f, 35
Badness: 0.049684
Secundly
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 65/64, 78/77, 99/98
Mapping: [⟨1 1 3 2 3 3], ⟨0 5 -6 7 4 6]]
Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 137.917
Optimal ET sequence: 9, 17, 26, 61bcf, 87bccf
Badness: 0.026212
Semishallowtone
Subgroup: 2.3.5.7
Comma list: 405/392, 35721/32768
Mapping: [⟨2 2 16 9], ⟨0 1 -10 -3]]
Optimal tuning (CTE): ~189/128 = 1\2, ~3/2 = 681.532
Supporting ETs: 14c, 30b, 44bd, 58bcd, 72bbccdd
Dirichlet badness: 8.420
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 43659/40960
Mapping: [⟨2 2 16 9 16], ⟨0 1 -10 -3 -8]]
Optimal tuning (CTE): ~189/128 = 1\2, ~3/2 = 681.438
Supporting ETs: 14c, 30b, 44bd, 58bcde, 72bbccddee
Dirichlet badness: 4.148
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 27/26, 99/98, 35721/32768
Mapping: [⟨2 2 16 9 16 4], ⟨0 1 -10 -3 -8 3]]
Optimal tuning (CTE): ~189/128 = 1\2, ~3/2 = 681.406
Supporting ETs: 14c, 30b
Dirichlet badness: 4.377