Very low accuracy temperaments

Todo: intro, cleanup what are the criteria for inclusion here?

Below are listed some very low accuracy temperaments.

Antitonic

This temperament is characterized by 9/8 being tempering out, and has been termed a "troll temperament". It is named on account of 4/3 and 3/2 both being represented by the 600 cent half octave, which, in terms of diatonic function, serves as an Antitonic. Surprisingly, it has extensions all the way up to the 11-limit, as confirmed by the data from x31eq. The original 5-limit is basically the 3-limit music of 2edo with the addition of harmonic 5 represented by an independent generator.

Comma list: 9/8

POTE generator: ~5/4 = 313.6898 or ~6/5 = 286.3102

Mapping: [⟨2 3 0], ⟨0 0 1]]

Mapping generators: ~3/2, ~5

Badness: 0.0216

7-limit

Comma list: 9/8, 15/14

POTE generator: ~5/4 = 301.9970 or ~6/5 = 298.0030

Mapping: [⟨2 3 0 1], ⟨0 0 1 1]]

Mapping generators: ~3/2, ~5

Badness: 0.0194

11-limit

Comma list: 9/8, 12/11, 21/20

POTE generator: ~5/4 = 340.2928 or ~6/5 = 259.7072

Mapping: [⟨2 3 0 1 7], ⟨0 0 1 1 0]]

Mapping generators: ~3/2, ~5

Badness: 0.0218

Antaeus

Comma list: 9/8, 35/32

POTE generator: ~5/4 = 315.962 or 6/5 = 284.038

Mapping: [⟨2 3 0 10], ⟨0 0 1 -1]]

Wedgie: ⟨⟨ 0 2 -2 3 -3 -10 ]]

Badness: 0.0375

11-limit

Comma list: 9/8, 12/11, 35/32

POTE generator:

Mapping:

Mapping generators:

Vals:

Badness:

Alteraugment

Like augmented, but the generator provides 5/4 instead of 3/2.

Comma list: 32/27

POTE generator: ~10/9 = 59.9349 cents

Mapping: [⟨3 5 7], ⟨0 0 1]]

Badness: 0.0780

Brutus

Comma list: 10/9, 28/25

POTE generator: ~3/2 = 848.221

Mapping: [⟨1 0 -1 -4], ⟨0 1 2 4]]

Wedgie: ⟨⟨ 1 2 4 1 4 4 ]]

Badness: 0.0534

Geryon

Comma list: 8/7, 25/21

POTE generator: ~5/4 = 385.440

Mapping: [⟨1 1 2 3], ⟨0 2 1 0]]

Wedgie: ⟨⟨ 2 1 0 -3 -6 -3 ]]

Vals: ⟨19 31 44 57], ⟨22 36 51 66]

Badness: 0.0510

Phlegyas

Comma list: 10/9, 35/32

POTE generator: ~3/2 = 743.135

Mapping: [⟨1 0 -1 6], ⟨0 1 2 -2]]

Wedgie: ⟨⟨ 1 2 -2 1 -6 -10 ]]

Badness: 0.0513

Malacoda

Comma list: 15/14, 35/32

POTE generator: ~8/7 = 276.283

Mapping: [⟨1 0 3 2], ⟨0 2 -1 1]]

Wedgie: ⟨⟨ 2 -1 1 -6 -4 5 ]]

Badness: 0.0372

Ugolino

Comma list: 15/14, 27/25

POTE generator: ~6/5 = 278.360

Mapping: [⟨1 0 0 -1], ⟨0 2 3 5]]

Wedgie: ⟨⟨ 2 3 5 0 2 3 ]]

Badness: 0.0438

Charon

Comma list: 10/9, 49/45

POTE generator: ~3/2 = 782.604

Mapping: [⟨2 0 -2 -1], ⟨0 1 2 2]]

Wedgie: ⟨⟨ 2 4 4 2 1 -2 ]]

Badness: 0.0564

Nessus

Comma list: 10/9, 49/48

POTE generator: ~8/7 = 213.117

Mapping: [⟨1 0 -1 2], ⟨0 2 4 1]]

Wedgie: ⟨⟨ 2 4 1 2 -4 -9 ]]

Badness: 0.0591

Medusa

Comma list: 15/14, 64/63

POTE generator: ~3/2 = 685.632

Mapping: [⟨1 0 7 6], ⟨0 1 -3 -2]]

Wedgie: ⟨⟨ 1 -3 -2 -7 -6 4 ]]

Badness: 0.0427