Luna family
- 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 luna family of temperaments tempers out the luna comma, 274877906944/274658203125, which has a monzo of [38 -2 -15⟩.
Luna
Luna divides 16/3 into fifteen parts, two of which make 5/4. It also divides 9/8 in five and 3/2 in three.
Subgroup: 2.3.5
Comma list: 274877906944/274658203125
Mapping: [⟨1 4 2], ⟨0 -15 2]]
- mapping generators: ~2, ~262144/234375
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~262144/234375 = 193.201 ¢
Optimal ET sequence: 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559
Badness (Smith): 0.020576
- Music
- "Moongazing" from Lesser Groove (2020) – Bandcamp | YouTube – atmospheric-electro, Luna[25] in 1000edo by Xotla
Overview to extensions
Hemithirds, a strong extension of didacus that tempers out 1029/1024 alongside 3136/3125, might be considered the main 7-limit extension to luna of practical interest, as 7/4 is found at only 5 generators. However, luna is an undoubted microtemperament of the 5-limit in its own right, supported by systems like 118edo and 441edo, and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna.
Temperaments discussed elsewhere include:
- Subneutral (+2401/2400) → Breedsmic temperaments
- Hemithirds (+3136/3125) → Hemimean clan
Lunatic
Subgroup: 2.3.5.7
Comma list: 4375/4374, 274877906944/274658203125
Mapping: [⟨1 4 2 21], ⟨0 -15 2 -113]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~262144/234375 = 193.196 ¢
Optimal ET sequence: 87d, 118, 323, 441, 1205, 1646
Badness (Smith): 0.037966
11-limit
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 12005/11979, 172032/171875
Mapping: [⟨1 4 2 21 14], ⟨0 -15 2 -113 -140]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~352/315 = 193.200 ¢
Optimal ET sequence: 118, 323e, 441, 559, 1000e
Badness (Smith): 0.058588
Hemiluna
Subgroup: 2.3.5.7
Comma list: 48828125/48771072, 67108864/66976875
Mapping: [⟨1 4 2 -5], ⟨0 -30 4 97]]
- mapping generators: ~2, ~200/189
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~200/189 = 96.591 ¢
Optimal ET sequence: 87, 236, 323, 410, 733, 1056, 1789bd, 2845bdd
Badness (Smith): 0.179304
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 14641/14580, 131072/130977
Mapping: [⟨1 4 2 -5 7], ⟨0 -30 4 97 -44]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~200/189 = 96.587 ¢
Optimal ET sequence: 87, 236, 323, 410
Badness (Smith): 0.100077
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580
Mapping: [⟨1 4 2 -5 7 7], ⟨0 -30 4 97 -44 -41]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~143/135 = 96.586 ¢
Optimal ET sequence: 87, 236, 323, 410
Badness (Smith): 0.046151
Semiluna
Subgroup: 2.3.5.7
Comma list: 4802000/4782969, 95703125/95551488
Mapping: [⟨2 8 4 23], ⟨0 -15 2 -54]]
- mapping generators: ~10125/7168, ~2187/1960
Optimal tuning (POTE): ~99/70 = 600.0000 ¢, ~2187/1960 = 193.1725 ¢
Optimal ET sequence: 56d, 118, 292, 410
Badness (Smith): 0.192167
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 14641/14580
Mapping: [⟨2 8 4 23 14], ⟨0 -15 2 -54 -22]]
Optimal tuning (POTE): ~99/70 = 600.0000 ¢, ~121/108 = 193.1732 ¢
Optimal ET sequence: 56d, 118, 292, 410
Badness (Smith): 0.067783