Septisemi temperaments

This is a collection of 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) → Mavila family
• Flattie (+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 tunings:

• CTE: ~2 = 1200.000, ~3/2 = 666.499

error map: ⟨0.000 -35.456 +12.682]

• POTE: ~2 = 1200.000, ~3/2 = 661.593

error map: ⟨0.000 -40.362 -16.754]

Optimal ET sequence: 2c, 7c, 9, 20b, 29b

Badness (Smith): 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 tunings:

• CTE: ~2 = 1200.000, ~3/2 = 668.748

error map: ⟨0.000 -33.207 +26.177 -25.084]

• POTE: ~2 = 1200.000, ~3/2 = 663.059

error map: ⟨0.000 -38.896 -7.960 -53.531]

Optimal ET sequence: 2c, 7c, 9, 20bdd, 29bdd

Badness (Smith): 0.055623

Sodium

Subgroup: 2.3.5.7

Comma list: 21/20, 54/49

Mapping: [⟨1 1 1 2], ⟨0 2 5 3]]

mapping generators: ~2, ~7/6

Wedgie: ⟨⟨ 2 5 3 3 -1 -7 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~7/6 = 325.425

error map: ⟨0.000 -51.104 +40.813 +7.450]

• POTE: ~2 = 1200.000, ~7/6 = 320.182

error map: ⟨0.000 -61.591 +14.597 -8.280]

Optimal ET sequence: 4, 11, 15b

Badness (Smith): 0.055814