Greenwoodmic temperaments
This is a collection of rank-2 temperaments tempering out the greenwoodma, 405/392 ([-3 4 1 -2⟩).
Temperaments discussed elsewhere are
- Sidi (+25/24) → Dicot family
- August (+36/35) → Augmented family
- Superpelog (+49/48) → Semaphoresmic clan
- Injera (+50/49 or 81/80) → Meantone family
- Schism (+64/63) → Archytas clan
- Greenwood (+1323/1280) → Whitewood family
Secund
Subgroup: 2.3.5.7
Comma list: 405/392, 525/512
Mapping: [⟨1 1 3 2], ⟨0 5 -6 7]]
- mapping generaators: ~2, ~16/15
Wedgie: ⟨⟨ 5 -6 7 -21 -3 33 ]]
- CTE: ~2 = 1200.000, ~16/15 = 138.454
- error map: ⟨0.000 -9.684 -17.038 +0.353]
- POTE: ~2 = 1200.000, ~16/15 = 137.958
- error map: ⟨0.000 -12.167 -14.059 -3.123]
Optimal ET sequence: 9, 17, 26, 61bc, 87bcc
Badness (Smith): 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 tunings:
- CTE: ~2 = 1200.000, ~12/11 = 138.420
- POTE: ~2 = 1200.000, ~12/11 = 137.900
Optimal ET sequence: 9, 17, 26, 61bc
Badness (Smith): 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 tunings:
- CTE: ~2 = 1200.000, ~12/11 = 137.455
- POTE: ~2 = 1200.000, ~12/11 = 136.937
Badness (Smith): 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 tunings:
- CTE: ~2 = 1200.000, ~13/12 = 138.583
- POTE: ~2 = 1200.000, ~13/12 = 137.917
Optimal ET sequence: 9, 17, 26, 61bcf
Badness (Smith): 0.026212
Semishallowtone
Subgroup: 2.3.5.7
Comma list: 405/392, 35721/32768
Mapping: [⟨2 0 36 15], ⟨0 1 -10 -3]]
- mapping generators: ~189/128, ~3
- CTE: ~189/128 = 600.000, ~3/2 = 681.532 (~64/63 = 81.532)
- error map: ⟨0.000 -20.423 -1.629 -13.421]
- CWE: ~189/128 = 600.000, ~3/2 = 682.650 (~64/63 = 82.650)
- error map: ⟨0.000 -19.305 -12.811 -16.775]
Optimal ET sequence: 14c, 44bd, 58bcd
- Smith: 0.333
- Dirichlet: 8.420
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 99/98, 35721/32768
Mapping: [⟨2 0 36 15 32], ⟨0 1 -10 -3 -8]]
Optimal tunings:
- CTE: ~189/128 = 600.000, ~3/2 = 681.438 (~64/63 = 81.438)
- CWE: ~189/128 = 600.000, ~3/2 = 682.724 (~64/63 = 82.724)
Optimal ET sequence: 14c, 44bd, 58bcde, 72bbccddee
Badness:
- Smith: 0.125
- Dirichlet: 4.148
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 45/44, 99/98, 35721/32768
Mapping: [⟨2 0 36 15 32 -2], ⟨0 1 -10 -3 -8 3]]
Optimal tunings:
- CTE: ~91/64 = 600.000, ~3/2 = 681.406 (~64/63 = 81.406)
- CWE: ~91/64 = 600.000, ~3/2 = 682.168 (~64/63 = 82.168)
Badness:
- Smith: 0.106
- Dirichlet: 4.377