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) → Father family
• Sharptone (+28/27) → Meantone family
• Pelogic (+135/128) → Pelogic family
• Flat (+25/24) → Dicot family
• Beep (+27/25) → Bug family
• Deflated (+21/20) → Augmented family
• Gidorah (+144/125) → Gamelismic clan
• Oxygen (+175/162) → Porcupine family

Considered below are fluorine and sodium.

Fluorine

5-limit (avila)

Subgroup: 2.3.5

Comma list: 729/640

Mapping: [⟨1 0 -7], ⟨0 1 6]]

mapping generators: ~2, ~3

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 661.593

Optimal ET 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 ]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 663.059

Optimal ET 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 ]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 320.182

Optimal ET sequence: 4, 11, 15b

Badness: 0.055814