Very low accuracy temperaments

From Xenharmonic Wiki
(Redirected from Medusa)
Jump to navigation Jump to search

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, 32/27, or 15/14, equating wildly different interval sizes. All temperaments listed temper out an interval of at least size 15/14.

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.

Subgroup: 2.3.5

Comma: 9/8

Mapping: [2 3 0], 0 0 1]]

Mapping generators: ~3/2, ~5

POTE generator: ~5/4 = 313.690 or ~6/5 = 286.310

Optimal ET sequence2, 4

Badness: 0.021647

7-limit

Subgroup: 2.3.5.7

Comma list: 9/8, 15/14

Mapping: [2 3 0 1], 0 0 1 1]]

POTE generator: ~5/4 = 301.997 or ~6/5 = 298.003

Optimal ET sequence2, 4

Badness: 0.019373

11-limit

Subgroup: 2.3.5.7.11

Comma list: 9/8, 12/11, 15/14

Mapping: [2 3 0 1 7], 0 0 1 1 0]]

POTE generator: ~5/4 = 340.293 or ~6/5 = 259.707

Optimal ET sequence2, 4

Badness: 0.021810

Antietam

Subgroup: 2.3.5.7.11

Comma list: 9/8, 11/10, 15/14

Mapping: [2 3 0 1 2], 0 0 1 1 1]]

POTE generator: ~5/4 = 322.080 or ~6/5 = 277.920

Optimal ET sequence2, 4e

Badness: 0.018993

Antaeus

Subgroup: 2.3.5.7

Comma list: 9/8, 35/32

Mapping: [2 3 0 10], 0 0 1 -1]]

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

Optimal ET sequence2d, 4

Badness: 0.037537

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [2 3 0 10 7], 0 0 1 -1 0]]

POTE generator: ~5/4 = 318.173 or ~6/5 = 281.827

Optimal ET sequence2d, 4

Badness: 0.033786

Music

short composition by Wensik in POTE-tuned 5-limit antitonic using an 8-note ternary scale.

Alteraugment

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

Subgroup: 2.3.5

Comma: 32/27

Mapping: [3 5 7], 0 0 1]]

POTE generator: ~10/9 = 59.935

Optimal ET sequence3, 12bcc, 15bbcc, 18bbcc

Badness: 0.078042

Vector Graphics suggests the name kinsborough for this temperament.

Yo (2c&3)

This temperament family is characterized by the yo 2nd 10/9 being tempering out.

Subgroup: 2.3.5

Comma list: 10/9

Mapping: [1 0 -1], 0 1 2]]

POTE generator: ~3/2 = 775.970

Optimal ET sequence3, 11bc, 14bc, 17bb

Badness: 0.016712

Brutus

Subgroup: 2.3.5.7

Comma list: 10/9, 28/25

Mapping: [1 0 -1 -4], 0 1 2 4]]

POTE generator: ~3/2 = 848.221

Optimal ET sequence3, 7bc, 10bc

Badness: 0.053389

Phlegyas

Subgroup: 2.3.5.7

Comma list: 10/9, 35/32

Mapping: [1 0 -1 6], 0 1 2 -2]]

POTE generator: ~3/2 = 743.135

Optimal ET sequence3, 5c, 8c, 13bcc

Badness: 0.051293

Charon

Subgroup: 2.3.5.7

Comma list: 10/9, 49/45

Mapping: [2 0 -2 -1], 0 1 2 2]]

POTE generator: ~3/2 = 782.604 (or ~15/14 = 182.604)

Optimal ET sequence6, 14bc, 20bb

Badness: 0.056404

Nessus

Subgroup: 2.3.5.7

Comma list: 10/9, 49/48

Mapping: [1 0 -1 2], 0 2 4 1]]

POTE generator: ~7/6 = 213.117

Optimal ET sequence5c, 6, 11bc, 17bb

Badness: 0.059070

Geryon

Subgroup: 2.3.5.7

Comma list: 8/7, 25/21

Mapping: [1 1 2 3], 0 2 1 0]]

POTE generator: ~5/4 = 385.440

Optimal ET sequence3d, 16 26 37 48], 19 31 44 57], 22 36 51 66]

Badness: 0.051009

Malacoda

Subgroup: 2.3.5.7

Comma list: 15/14, 35/32

Mapping: [1 0 3 2], 0 2 -1 1]]

POTE generator: ~7/6 = 276.283

Optimal ET sequence1, 4, 9c, 13bcc

Badness: 0.037207

Ugolino

Subgroup: 2.3.5.7

Comma list: 15/14, 27/25

Mapping: [1 0 0 -1], 0 2 3 5]]

POTE generator: ~6/5 = 278.360

Optimal ET sequence4, 9d, 13bd

Badness: 0.043758

Uncle

Subgroup: 2.3.5

Comma list: 4096/3645

Mapping: [1 1 6], 0 1 -6]]

Optimal tuning (CWE): ~2 = 1\1, ~3/2 = 731.732

Supporting ETs: 5, 8c, 13, 18, 23bc, 28bc, 33bcc, 41bbc, 51bbccc

Badness (Sintel): 6.332

Medusa

Subgroup: 2.3.5.7

Comma list: 15/14, 64/63

Mapping: [1 0 7 6], 0 1 -3 -2]]

POTE generator: ~3/2 = 685.632

Optimal ET sequence2, 5c, 7

Badness: 0.042712

11-limit

Subgroup: 2.3.5.7.11

Comma list: 15/14, 22/21, 33/32

Mapping: [1 0 7 6 5], 0 1 -3 -2 -1]]

POTE generator: ~3/2 = 685.809

Optimal ET sequence2, 5c, 7

Badness: 0.026828

Plutus

Subgroup: 2.3.5.7

Comma list: 15/14, 81/80

Mapping: [1 0 -4 -5], 0 1 4 5]]

POTE generator: ~3/2 = 682.895

Optimal ET sequence2cd, 5d, 7

Badness: 0.045275

11-limit

Subgroup: 2.3.5.7.11

Comma list: 15/14, 22/21, 81/80

Mapping: [1 0 -4 -5 -6], 0 1 4 5 6]]

POTE generator: ~3/2 = 685.234

Optimal ET sequence2cde, 5de, 7

Badness: 0.032521

Involution

Subgroup: 2.3.5

Comma list: 45/32

Mapping: [1 1 3], 0 1 -2]]

CTE generator: ~3/2 = 509.892

Optimal ET sequence: None aside from extremely absurd alternative ETs

Badness: 0.133021

7-limit

Subgroup: 2.3.5.7

Comma list: 45/28, 8/7

Mapping: [1 1 3 3], 0 1 -2 0]]

CTE generator: ~3/2 = 509.892

Optimal ET sequence: None aside from extremely absurd alternative ETs

Badness: 0.118764

Devolution

Subgroup: 3.5.7

Comma list: 35/27

Mapping: [1 1 2], 0 1 -1]]

CTE generator: ~5/3 = 701.863

Optimal ET sequence8cdd, otherwise none aside from extremely absurd alternative ETs

Badness (Sintel): 0.751

Codex

This temperament is named as an abbreviation of "co-decimal", as it resembles decimal in many ways, but exchanges the roles of 5s and 7s. While decimal equates 8/7 and 7/6, as well as 6/5 and 5/4, this equates 10/9 and 6/5, as well as 7/6 and 9/7. It is an extension of bug in the same way decimal is of semaphore.

Subgroup: 2.3.5.7

Comma list: 27/25, 54/49

Mapping: [2 0 0 1], 0 2 3 3]]

CTE generator: ~7/5 = 1\2, ~5/3 = 935.289

Optimal ET sequence10cd, 14d

Badness: 0.077065