Very low accuracy temperaments

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

Below are listed some very low accuracy temperaments. Temperaments with exceedingly low accuracy such as these tend to temper out very large “commas” such as 9/8, 10/9, or 15/14, equating wildly different interval sizes.

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