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 = | |||
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. | ||
Comma list: 9/8 | Comma list: [[9/8]] | ||
POTE generator: ~5/4 = 313.6898 or ~6/5 = 286.3102 | POTE generator: ~5/4 = 313.6898 or ~6/5 = 286.3102 | ||
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Badness: | Badness: | ||
== 7-limit == | |||
Comma list: 9/8, 15/14 | Comma list: 9/8, 15/14 | ||
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Badness: | Badness: | ||
== Brutus | == Antaeus == | ||
Comma list: 9/8, 35/32 | |||
POTE generator: ~5/4 = 315.962 or 6/5 = 284.038 | |||
Mapping: [{{val| 2 3 0 10 }}, {{val| 0 0 1 -1 }}] | |||
{{Multival|legend=1| 0 2 -2 3 -3 -10 }} | |||
{{Val list|legend=1| 2d, 4 }} | |||
Badness: 0.0375 | |||
= 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: [{{val| 3 5 7 }}, {{val| 0 0 1 }}] | |||
{{Val list|legend=1| 3, 12bcc }} | |||
= Brutus = | |||
Comma list: 10/9, 28/25 | Comma list: 10/9, 28/25 | ||
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Badness: 0.0534 | Badness: 0.0534 | ||
= Geryon = | |||
Comma list: 8/7, 25/21 | Comma list: 8/7, 25/21 | ||
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Badness: 0.0510 | Badness: 0.0510 | ||
= Phlegyas = | |||
Comma list: 10/9, 35/32 | Comma list: 10/9, 35/32 | ||
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Badness: 0.0513 | Badness: 0.0513 | ||
= Malacoda = | |||
Comma list: 15/14, 35/32 | Comma list: 15/14, 35/32 | ||
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Badness: 0.0372 | Badness: 0.0372 | ||
= Ugolino = | |||
Comma list: 15/14, 27/25 | Comma list: 15/14, 27/25 | ||
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Badness: 0.0438 | Badness: 0.0438 | ||
= Charon = | |||
Comma list: 10/9, 49/45 | Comma list: 10/9, 49/45 | ||
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Badness: 0.0564 | Badness: 0.0564 | ||
= Nessus = | |||
Comma list: 10/9, 49/48 | Comma list: 10/9, 49/48 | ||
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Badness: 0.0591 | Badness: 0.0591 | ||
= Medusa = | |||
Comma list: 15/14, 64/63 | Comma list: 15/14, 64/63 | ||