No-twos subgroup temperaments

(WIP, catalog of 3.5.7 subgroup rank two temperaments will eventually be redirected here)

This is a collection of subgroup temperaments which omit the prime harmonic of 2. Because of the absence of octaves, these are all nonoctave scales using a period of a tritave, or if harmonic 3 is also excluded, 5/1.

Izar

Subgroup: 3.5.7

Comma list: 13841287201/13839609375

Subgroup-val mapping: [⟨1 7 5], ⟨0 -12 -7]]

Sval mapping generators: ~3, ~16807/10125

Optimal tuning (CTE): ~3 = 1\1edt, ~16807/10125 = 877.280

Supporting ETs: b13, b11cd, b193, b15cd, b180, b24c, b167, b37c, b154, 141, b50c, b28cd, b128, b63c

Canopus

Subgroup: 3.5.7

Comma list: 16875/16807

Subgroup-val mapping: [⟨1 3 3], ⟨0 -5 -4]]

Sval mapping generators: ~3, ~7/5

Optimal tuning (CTE): ~3 = 1\1edt, ~7/5 = 584.017

Supporting ETs: b13, b10, b75, b62, b23, b49, b36, b16, b7cd, 29, b42c, b19cd, b33cd, b55c

BPS

Subgroup: 3.5.7

Comma list: 245/243

Sval mapping: [⟨1 1 2], ⟨0 -2 1]]

Sval mapping generators: ~3, ~9/7

Optimal tuning (POTE): ~3 = 1\1edt, ~9/7 = 440.4881

Optimal ET sequence: b4, b9, b13, b56, b69, b82, b95

No-twos-or-threes subgroup temperaments

Juggernaut

Subgroup: 5.7.11

Comma list: 125/121

Subgroup-val mapping: [⟨2 4 3], ⟨0 1 0]]

Mapping generators: ~11/5, ~7/25

Optimal tuning (CTE): ~11/5 = 1\2ed5, ~7/5 = 582.512

Supporting ETs: c14, c10, c6, c18, c24, c22, c32, c16, c38, c8d, c34, c26d, c46, c52e

No-twos-or-threes 13-limit

Subgroup: 5.7.11.13

Comma list: 125/121, 637/625

Subgroup-val mapping: [⟨2 4 3 0], ⟨0 1 0 -2]]

Mapping generators: ~11/5, ~7/25

Optimal tuning (CTE): ~11/5 = 1\2ed5, ~7/5 = 582.512

Supporting ETs: c10, c14, c6, c24, c34, c16f, c44, c18f, c38, c26f, c54, c64

Antipyth

Subgroup: 5.7.11

Comma list: 859375/823543

Subgroup-val mapping: [⟨1 2 7], ⟨0 1 7]]

Mapping generators: ~5, ~7/25

Optimal tuning (CTE): ~5 = 1\1ed5, ~7/5 = 592.728

Supporting ETs: c14, c5, c19, c33, c47, c9e, c61, c75, c23e, c24e, c52e, c80e, c89e, c37e