Catalog of 3.5.11 subgroup rank two temperaments

This is a catalog of 3.5.11 nonoctave subgroup temperaments.

Polaris

Main article: Polaris

Polaris tempers out the comma 177147/171875, and thus equates 7 5/3's with 15/11, or equivalently 7 9/5's with 11/9.

Subgroup: 3.5.11

Comma list: 177147/171875

Gencom: [3/1 5/3; 177147/171875]

Mapping: [{⟨1 2 1], ⟨0 1 -6]]]

POTE generator: ~5/3 = 892.6

EDTs: 17, 15, 32, 49, 13[+11], 47, 19, 11[+11], 81, 66, 79[+11], 62[+11], 28[+11], 21[-11]

Deneb

Main article: Deneb

Subgroup: 3.5.11

Comma list: 6655/6561

Gencom: [3/1 11/9; 6655/6561]

Mapping: [⟨1 2 2], ⟨0 -3 1]]

POTE generator: ~11/9 = 340.242

EDTs: 28, 11, 17, 6, 39, 5, 67, 45, 50, 16, 23, 73, 61, 62

Alnilam

Effectively a microtemperament, Alnilam takes a generator of an 81/55 flat fifth and equates 9 of them with 11/9. The name was given by CompactStar to continue with the theme of naming no-twos temperaments after proper star names, but also to indirectly reference mavila.

Subgroup: 3.5.11

Comma list: [0 -35 9 0 10⟩

Gencom: [3/1 81/55; [0 -35 9 0 10⟩]

Mapping: [[⟨1 5 -1], ⟨0 -10 9]]

CTE generator: ~81/55 = 672.410

EDTs: 99, 17, 82, 116, 181, 65, 14[-5], 280, 48, 215, 31, 133, 314, 263