Very low accuracy temperaments: Difference between revisions
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Below are listed some very low accuracy temperaments. | Below are listed some very low accuracy temperaments. | ||
= Antitonic = | == 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 [http://x31eq.com/cgi-bin/rt.cgi?limit=11&ets=2_4p&tuning=po x31eq]. The original 5-limit is basically the 3-limit music of [[2edo]] with the addition of harmonic 5 represented by an independent generator. | 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 [http://x31eq.com/cgi-bin/rt.cgi?limit=11&ets=2_4p&tuning=po x31eq]. The original 5-limit is basically the 3-limit music of [[2edo]] with the addition of harmonic 5 represented by an independent generator. | ||
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Badness: 0.0216 | Badness: 0.0216 | ||
== 7-limit == | === 7-limit === | ||
Comma list: 9/8, 15/14 | Comma list: 9/8, 15/14 | ||
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Badness: 0.0194 | Badness: 0.0194 | ||
=== 11-limit === | ==== 11-limit ==== | ||
Comma list: 9/8, 12/11, 21/20 | Comma list: 9/8, 12/11, 21/20 | ||
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Badness: 0.0218 | Badness: 0.0218 | ||
== Antaeus == | === Antaeus === | ||
Comma list: 9/8, 35/32 | Comma list: 9/8, 35/32 | ||
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Badness: 0.0375 | Badness: 0.0375 | ||
=== 11-limit === | ==== 11-limit ==== | ||
Comma list: 9/8, 12/11, 35/32 | Comma list: 9/8, 12/11, 35/32 | ||
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Badness: | Badness: | ||
= Alteraugment = | == Alteraugment == | ||
Like [[augmented]], but the generator provides 5/4 instead of 3/2. | Like [[augmented]], but the generator provides 5/4 instead of 3/2. | ||
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Badness: 0.0780 | Badness: 0.0780 | ||
= Brutus = | == Brutus == | ||
Comma list: 10/9, 28/25 | Comma list: 10/9, 28/25 | ||
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Badness: 0.0534 | Badness: 0.0534 | ||
= Geryon = | == Geryon == | ||
Comma list: 8/7, 25/21 | Comma list: 8/7, 25/21 | ||
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Badness: 0.0510 | Badness: 0.0510 | ||
= Phlegyas = | == Phlegyas == | ||
Comma list: 10/9, 35/32 | Comma list: 10/9, 35/32 | ||
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Badness: 0.0513 | Badness: 0.0513 | ||
= Malacoda = | == Malacoda == | ||
Comma list: 15/14, 35/32 | Comma list: 15/14, 35/32 | ||
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Badness: 0.0372 | Badness: 0.0372 | ||
= Ugolino = | == Ugolino == | ||
Comma list: 15/14, 27/25 | Comma list: 15/14, 27/25 | ||
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Badness: 0.0438 | Badness: 0.0438 | ||
= Charon = | == Charon == | ||
Comma list: 10/9, 49/45 | Comma list: 10/9, 49/45 | ||
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Badness: 0.0564 | Badness: 0.0564 | ||
= Nessus = | == Nessus == | ||
Comma list: 10/9, 49/48 | Comma list: 10/9, 49/48 | ||
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Badness: 0.0591 | Badness: 0.0591 | ||
= Medusa = | == Medusa == | ||
Comma list: 15/14, 64/63 | Comma list: 15/14, 64/63 | ||
Revision as of 19:16, 3 June 2021
|
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