Miscellaneous 7-limit 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.

Below are listed some 7-limit rank-3 temperaments that do not belong to some other temperament collection, the majority of which are restrictions to the 7-limit of temperaments that emerge more fully in higher limits or subgroups; they are sorted by TE logflat badness. Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:

• Individual temperament families and clans
• Very low accuracy temperaments
• Very high accuracy temperaments

See also Miscellaneous 5-limit temperaments.

Uniwiz

For extensions, see Keenanismic temperaments #Uniwiz.

Subgroup: 2.3.5.7

Comma list: 1500625/1492992

Mapping: [⟨2 1 0 7], ⟨0 2 0 3], ⟨0 0 1 -1]]

mapping generators: ~1225/864, ~35/24, ~5

Optimal tuning (CTE): ~1225/864 = 600.0000 ¢, ~35/24 = 651.1974 ¢, ~5/4 = 385.6847 ¢

Optimal ET sequence: 22, 46, 68, 72, 118, 140, 212, 330, 470, 542d, 872cdd, 1012cdd, 1414ccddd

Badness (Smith): 0.7042 × 10^-3

Mirwomo

For extensions, see Rastmic rank-3 clan #Mirwomo.

Subgroup: 2.3.5.7

Comma list: 33075/32768

Mapping: [⟨1 1 0 6], ⟨0 2 0 -3], ⟨0 0 1 -1]]

mapping generators: ~2, ~128/105, ~5

Optimal tunings:

• WE: ~2 = 1200.8046 ¢, ~11/9 = 350.3723 ¢, ~5/4 = 384.1239 ¢

error map: ⟨+0.805 -0.406 -0.581 -0.848]

• CWE: ~2 = 1200.0000 ¢, ~11/9 = 350.1448 ¢, ~5/4 = 383.8961 ¢

error map: ⟨0.000 -1.665 -2.418 -3.157]

Optimal ET sequence: 17, 21, 24, 31, 41, 72, 281d, 322cd, 353cd, 425bcdd, 497bcdd

Badness (Sintel): 3.40

Parahemif

For extensions, see Rastmic rank-3 clan #Parahemif.

Subgroup: 2.3.5.7

Comma list: 1605632/1594323

Mapping: [⟨1 1 0 -1], ⟨0 2 0 13], ⟨0 0 1 0]]

mapping generators: ~2, ~896/729, ~5

Optimal tunings:

• WE: ~2 = 1199.7303 ¢, ~896/729 = 351.4056 ¢, ~5/4 = 386.8527 ¢

error map: ⟨-0.270 +0.586 -0.000 -0.284]

• CWE: ~2 = 1200.0000 ¢, ~896/729 = 351.4569 ¢, ~5/4 = 386.6884 ¢

error map: ⟨0.000 +0.959 +0.375 +0.114]

Optimal ET sequence: 17c, 24, 34d, 41, 58, 99, 239, 338

Badness (Sintel): 8.77