Wizardharry clan

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.

The wizardharry clan of rank-3 temperaments tempers out the wizardharry comma, 4000/3993, the amount by which a stack of three 11/10's falls short of the fourth, 4/3.

Homalic

Subgroup: 2.3.5.11

Comma list: 4000/3993

Subgroup-val mapping: [⟨1 2 0 1], ⟨0 -3 0 1], ⟨0 0 1 1]]

Mapping generators: ~2, ~11/10, ~5

Optimal tunings:

• WE: ~2 = 1199.917 ¢, ~11/10 = 165.946 ¢, ~5/4 = 386.212 ¢
• CWE: ~2 = 1200.000 ¢, ~11/10 = 165.977 ¢, ~5/4 = 386.130 ¢

Optimal ET sequence: 7, 8, 15, 22, 50, 58, 65, 72

Badness (Sintel): 0.247

Overview to extensions

The second comma in the comma list determines how we extend the no-7 subgroup temperament to include the harmonic 7. Hanuman adds 3025/3024, history adds 441/440, and moctpine adds 1375/1372. Hades adds 540/539 as well as 9801/9800, splitting the octave in two.

Discussed elsewhere are:

• Hanuman (+3025/3024) → Lehmerismic temperaments
• History (+441/440) → Werckismic temperaments
• Hades (+540/539 or 9801/9800) → Swetismic temperaments

Considered below are moctpine and naiad, besides the no-7 subgroup temperament.

Moctpine

See also: Moctdelismic clan

Named by Xenllium in 2026, moctpine tempers out 1375/1372 and 4000/3993.

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 4000/3993

Mapping: [⟨1 2 1 1 2], ⟨0 -3 -1 -1 0], ⟨0 0 3 4 3]]

Mapping generators: ~2, ~11/10, ~7/5

Optimal tunings:

• WE: ~2 = 1199.9745 ¢, ~11/10 = 165.9846 ¢, ~7/5 = 583.8721 ¢

error map: ⟨-0.025 +0.040 -0.707 +0.652 +0.247]

• CWE: ~2 = 1200.0000 ¢, ~11/10 = 165.9939 ¢, ~7/5 = 583.8766 ¢

error map: ⟨0.000 +0.063 -0.678 +0.686 +0.312]

Optimal ET sequence: 29, 37, 43, 72, 152, 224, 629, 781, 853c

Badness (Sintel): 1.28

Naiad

For the 7-limit version of this temperament, see Miscellaneous 7-limit temperaments #Naiad.

Named by Xenllium in 2026, naiad tempers out 3773/3750 and 5488/5445 in the 11-limit. It can be extended to the 13-limit by adding 196/195, 364/363, or 1001/1000 to the comma basis.

Subgroup: 2.3.5.7.11

Comma list: 3773/3750, 4000/3993

Mapping: [⟨1 5 0 2 0], ⟨0 -9 0 -4 3], ⟨0 0 1 1 1]]

Mapping generators: ~2, ~98/75, ~5

Optimal tunings:

• WE: ~2 = 1199.723 ¢, ~98/75 = 455.134 ¢, ~5/4 = 387.934 ¢
• CWE: ~2 = 1200.000 ¢, ~98/75 = 455.259 ¢, ~5/4 = 387.694 ¢

Optimal ET sequence: 8d, 21, 29, 37, 50, 58, 87, 145

Badness (Sintel): 3.098

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 364/363, 1001/1000

Mapping: [⟨1 5 0 2 0 1], ⟨0 -9 0 -4 3 1], ⟨0 0 1 1 1 1]]

Optimal tunings:

• WE: ~2 = 1199.622 ¢, ~13/10 = 455.074 ¢, ~5/4 = 387.918 ¢
• CWE: ~2 = 1200.000 ¢, ~13/10 = 455.243 ¢, ~5/4 = 387.576 ¢

Optimal ET sequence: 8d, 21, 29, 37, 50, 58, 87, 145

Badness (Sintel): 1.182

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 170/169, 196/195, 221/220, 364/363

Mapping: [⟨1 5 0 2 0 1 1], ⟨0 -9 0 -4 3 1 2], ⟨0 0 1 1 1 1 1]]

Optimal tunings:

• WE: ~2 = 1200.088 ¢, ~13/10 = 455.350 ¢, ~5/4 = 387.578 ¢
• CWE: ~2 = 1200.000 ¢, ~13/10 = 455.311 ¢, ~5/4 = 387.658 ¢

Optimal ET sequence: 8d, 21, 29g, 50, 58, 87g

Badness (Sintel): 1.337