Greenwoodmic temperaments

This is a collection of rank-2 temperaments tempering out the greenwoodma, [-3 4 1 -2⟩ = 405/392.

Considered below is secund. 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