Septisemi temperaments
These are very low complexity temperaments tempering out the septimal minor semitone, 21/20, and hence equating 5/3 with 7/4, and 10/7 with 3/2.
Temperaments discussed elsewhere are:
- Mother, {16/15, 21/20} → Father family #Mother
- Flat, {21/20, 25/24} → Dicot family #Flat
- Beep, {21/20, 27/25} → Bug family #Beep
- Sharptone, {21/20, 28/27} → Meantone family #Sharptone
- Pelogic, {21/20, 135/128} → Pelogic family #Pelogic
- Gidorah, {21/20, 144/125} → Gamelismic clan #Gidorah
Considered below are fluorine, sodium and oxygen.
Fluorine
5-limit (avila)
Subgroup: 2.3.5
Comma list: 729/640
Mapping: [⟨1 0 -7], ⟨0 1 6]]
POTE generator: ~3/2 = 661.593
Optimal GPV sequence: 2c, 7c, 9, 20b, 29b
Badness: 0.181941
7-limit
Subgroup: 2.3.5.7
Comma list: 21/20, 243/224
Mapping: [⟨1 0 -7 -5], ⟨0 1 6 5]]
Wedgie: ⟨⟨1 6 5 7 5 -5]]
POTE generator: ~3/2 = 663.059
Optimal GPV sequence: 9, 20bdd, 29bdd
Badness: 0.055623
Sodium
Subgroup: 2.3.5.7
Comma list: 21/20, 54/49
Mapping: [⟨1 1 1 2], ⟨0 2 5 3]]
Wedgie: ⟨⟨2 5 3 3 -1 -7]]
POTE generator: ~7/6 = 320.182
Optimal GPV sequence: 4, 11, 15b
Badness: 0.055814
Oxygen
- See also: Porcupine family
Subgroup: 2.3.5.7
Comma list: 21/20, 175/162
Mapping: [⟨1 2 3 3], ⟨0 -3 -5 -2]]
Wedgie: ⟨⟨3 5 2 1 -5 -9]]
POTE generator: ~7/6 = 169.112
Badness: 0.059866