Luna family

The Luna family tempers out the Luna comma; 274877906944/274658203125, which has a monzo of |38 -2 -15>

Luna

Comma: 274877906944/274658203125

POTE generator: ~262144/234375 = 193.201

Map: [<1 4 2|, <0 -15 2|]

EDOs: 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559

Badness: 0.0206

Hemithirds

Main article: Hemithirds

See also: Hemimean clan § Hemithirds

Subgroup: 2.3.5.7

Comma list: 1029/1024, 3136/3125

Mapping: [⟨1 4 2 2], ⟨0 -15 2 5]]

Wedgie: ⟨⟨ 15 -2 -5 -38 -50 -6 ]]

POTE generator: ~28/25 = 193.244

Minimax tuning:

• 7-odd-limit

[[1 0 0 0⟩, [5/2 3/4 0 -3/4⟩, [11/5 -1/10 0 1/10⟩, [5/2 -1/4 0 1/4⟩]

Eigenmonzos: 2, 7/6

• 9-odd-limit

[[1 0 0 0⟩, [10/7 6/7 0 -3/7⟩, [82/35 -4/35 0 2/35⟩, [20/7 -2/7 0 1/7⟩]

Eigenmonzos: 2, 7/6

Badness: 0.0443

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 3136/3125

Mapping: [⟨1 4 2 2 7], ⟨0 -15 2 5 -22]]

POTE generator: ~28/25 = 193.227

Minimax tuning:

• 11-odd-limit

[[1 0 0 0 0⟩, [11/9 0 0 -5/9 5/9⟩, [64/27 0 0 2/27 -2/27⟩, [79/27 0 0 5/27 -5/27⟩, [79/27 0 0 -22/27 22/27⟩]

Eigenmonzos: 2, 11/7

Badness: 0.0190

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 385/384, 625/624

Mapping: [⟨1 4 2 2 7 0], ⟨0 -15 2 5 -22 23]]

POTE generator: ~28/25 = 193.166

Badness: 0.0217

Lunatic

Commas: 4375/4374, 274877906944/274658203125

POTE generator: ~262144/234375 = 193.196

Map: [<1 4 2 2|, <0 -15 2 -113|]

Wedgie: <<15 -2 113 -38 137 268||

EDOs: 87d, 118, 323, 441, 1205, 1646

Badness: 0.0380

Semiluna

See also: Canousmic temperaments § Semiluna

Commas: 4802000/4782969, 95703125/95551488

POTE generator: ~2187/1960 = 193.1725

Map: [<2 8 4 23|, <0 -15 2 -54|]

EDOs: 56d, 118, 292, 410

Badness: 0.1922

11-limit

Commas: 5632/5625, 9801/9800, 14641/14580

POTE generator: ~121/108 = 193.1732

Map: [<2 8 4 23 14|, <0 -15 2 -54 -22|]

EDOs: 56d, 118, 292, 410

Badness: 0.0678