Septisemi temperaments

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular 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 (+128/125) → Augmented family
• Gidorah (+144/125) → Gamelismic clan
• Oxygen (+175/162) → Very low accuracy temperaments

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:

• WE: ~2 = 1210.600 ¢, ~3/2 = 667.437 ¢

error map: ⟨+10.600 -23.917 +7.711]

• CWE: ~2 = 1200.000 ¢, ~3/2 = 663.474 ¢

error map: ⟨0.000 -38.481 -5.472]

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

Badness (Sintel): 4.27

7-limit

Subgroup: 2.3.5.7

Comma list: 21/20, 243/224

Mapping: [⟨1 0 -7 -5], ⟨0 1 6 5]]

Optimal tunings:

• WE: ~2 = 1211.420 ¢, ~3/2 = 669.369 ¢

error map: ⟨+11.420 -21.165 +18.481 -21.980]

• CWE: ~2 = 1200.000 ¢, ~3/2 = 665.210 ¢

error map: ⟨0.000 -36.745 +4.945 -42.777]

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

Badness (Sintel): 1.41

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

Optimal tunings:

• WE: ~2 = 1207.624 ¢, ~7/6 = 322.216 ¢

error map: ⟨+7.624 -49.898 +32.393 +13.072]

• CWE: ~2 = 1200.000 ¢, ~7/6 = 322.210 ¢

error map: ⟨0.000 -57.535 +24.737 -2.196]

Optimal ET sequence: 4, 11

Badness (Sintel): 1.41