User:FloraC/Sandbox

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Proposed temperaments

Ideas welcome!

A 7-limit rank-3 family (80 & 94 & 118)

|4 -14 3 4> = 4802000/4782969 is a 6.9-cent comma which is the difference between a sensamagic and a cataharry, or the sum of a ragisma and a hemimage. It identifies 14/9 by three 81/70's stacked, and 9/5 by four of them stacked. It therefore also features splitting the septimal diesis, 49/48, into three equal parts, making two distinct interseptimal intervals related to the 35th harmonic.

Comma: 4802000/4782969

Map: [<1 0 0 -1|, <0 1 2 2|, <0 0 -4 3|]

Wedgie: <<<4 -3 -14 -4 |||

POTE generators: ~3/2 = 702.373, ~81/70 = 254.625

EDOs: 19, 75, 80, 94, 99, 212, 292, 311, 410, 1131, 1541b

Badness: 1.122 × 10-3

11-limit

Commas: 9801/9800, 14641/14580

Map: [<2 0 0 -2 1|, <0 1 2 2 2|, <0 0 4 -3 1|]

POTE generators: ~3/2 = 702.3850, ~81/70 = 254.6168 or ~11/9 = 345.3832

Edos: 14c, 24, 80, 94, 118, 198, 212, 292, 330e, 410

Badness: 2.197 × 10-3

A 13-limit rank-3 temperament (87 & 94 & 111)

Commas: 352/351, 847/845, 14641/14580

Map: [<1 0 2 12 1 6|, <0 1 2 -4 2 -1|, <0 0 4 4 1 1|]

EDOs: 7, 17c, 24d, 87, 111, 181, 198

Badness: 0.0540 × 10-3

A 13-limit rank-4 temperament (41 & 46 & 53 & 58)

Commas: 352/351, 847/845

Map: [<1 0 0 10 0 5|, <0 1 0 -6 0 -3|, <0 0 1 1 0 0|, <0 0 0 0 1 1|]

Wedgie: <<<<0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5 0||||

POTE generators: ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538

EDOs: 12f, 17c, 29, 41, 46, 53, 58, 87, 111, 140, 198

Badness: 2.550 × 10-6