Very low accuracy temperaments: Difference between revisions

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


Commas: [[32/27]]
Comma list: [[32/27]]


POTE generator: ~10/9 = 59.9349 cents
POTE generator: ~10/9 = 59.9349 cents
Line 13: Line 13:
Mapping: [{{val| 3 5 7 }}, {{val| 0 0 1 }}]
Mapping: [{{val| 3 5 7 }}, {{val| 0 0 1 }}]


{{Val list|legend=1| 3, 6 }}
{{Val list|legend=1| 3, 12bcc }}
 
[http://x31eq.com/cgi-bin/rt.cgi?ets=3_3cc&limit=5 The temperament finder - 5-limit 3 & 3cc]


== Antitonic (2 & 4p) ==
== Antitonic (2 & 4p) ==
Line 59: Line 57:


== Brutus ==
== Brutus ==
Commas: 10/9, 28/25
Comma list: 10/9, 28/25


POTE generator: ~3/2 = 848.221
POTE generator: ~3/2 = 848.221


Map: [<1 0 -1 -4|, <0 1 2 4|]
Mapping: [{{val| 1 0 -1 -4 }}, {{val| 0 1 2 4 }}]


Wedgie: <<1 2 4 1 4 4||
{{Multival|legend=1| 1 2 4 1 4 4 }}


EDOs: 3, 10bc
{{Val list|legend=1| 3, 10bc }}


Badness: 0.0534
Badness: 0.0534


== Geryon ==
== Geryon ==
Commas: 8/7, 25/21
Comma list: 8/7, 25/21


POTE generator: ~5/4 = 385.440
POTE generator: ~5/4 = 385.440


Map: [<1 1 2 3|, <0 2 1 0|]
Mapping: [{{val| 1 1 2 3 }}, {{val| 0 2 1 0 }}]


Wedgie: <<2 1 0 -3 -6 -3||
{{Multival|legend=1| 2 1 0 -3 -6 -3 }}


EDOs: <19 31 44 57|, <22 36 51 66|
[[Val]]s: {{val| 19 31 44 57 }}, {{val| 22 36 51 66 }}


Badness: 0.0510
Badness: 0.0510


== Antaeus ==
== Antaeus ==
Commas: 9/8, 35/32
Comma list: 9/8, 35/32


POTE generator: ~5/4 = 315.962
POTE generator: ~5/4 = 315.962


Map: [<2 3 0 10|, <0 0 1 -1|]
Mapping: [{{val| 2 3 0 10 }}, {{val| 0 0 1 -1 }}]


Wedgie: <<0 2 -2 3 -3 -10||
{{Multival|legend=1| 0 2 -2 3 -3 -10 }}


EDOs: 4, 10bd, 12bcd
{{Val list|legend=1| 4, 10bd, 12bcd }}


Badness: 0.0375
Badness: 0.0375


== Phlegyas ==
== Phlegyas ==
Commas: 10/9, 35/32
Comma list: 10/9, 35/32


POTE generator: ~3/2 = 743.135
POTE generator: ~3/2 = 743.135


Map: [<1 0 -1 6|, <0 1 2 -2|]
Mapping: [{{val| 1 0 -1 6 }}, {{val| 0 1 2 -2 }}]


Wedgie: <<1 2 -2 1 -6 -10||
{{Multival|legend=1| 1 2 -2 1 -6 -10 }}


EDOs: 3, 10c, 11bcd, 13c
{{Val list|legend=1| 3, 10c, 11bcd, 13c }}


Badness: 0.0513
Badness: 0.0513


== Malacoda ==
== Malacoda ==
Commas: 15/14, 35/32
Comma list: 15/14, 35/32


POTE generator: ~8/7 = 276.283
POTE generator: ~8/7 = 276.283


Map: [<1 0 3 2|, <0 2 -1 1|]
Mapping: [{{val| 1 0 3 2 }}, {{val| 0 2 -1 1 }}]


Wedge: <<2 -1 1 -6 -4 5||
{{Multival|legend=1| 2 -1 1 -6 -4 5 }}


EDOs: 1, 4, 13bc
{{Val list|legend=1| 1, 4, 13bc }}


Badness: 0.0372
Badness: 0.0372


== Ugolino ==
== Ugolino ==
Commas: 15/14, 27/25
Comma list: 15/14, 27/25


POTE generator: ~6/5 = 278.360
POTE generator: ~6/5 = 278.360


Map: [<1 0 0 -1|, <0 2 3 5|]
Mapping: [{{val| 1 0 0 -1 }}, {{val| 0 2 3 5 }}]


Wedgie: <<2 3 5 0 2 3||
{{Multival|legend=1| 2 3 5 0 2 3 }}


EDOs: 4, 13bd
{{Val list|legend=1| 4, 13bd }}


Badness: 0.0438
Badness: 0.0438


== Charon ==
== Charon ==
Commas: 10/9, 49/45
Comma list: 10/9, 49/45


POTE generator: ~3/2 = 782.604
POTE generator: ~3/2 = 782.604


Map: [<2 0 -2 -1|, <0 1 2 2|]
Mapping: [{{val| 2 0 -2 -1 }}, {{val| 0 1 2 2 }}]


Wedgie: <<2 4 4 2 1 -2||
{{Multival|legend=1| 2 4 4 2 1 -2 }}


EDOs: 6, 13bd
{{Val list|legend=1| 6, 13bd }}


Badness: 0.0564
Badness: 0.0564


== Nessus ==
== Nessus ==
Commas: 10/9, 49/48
Comma list: 10/9, 49/48


POTE generator: ~8/7 = 213.117
POTE generator: ~8/7 = 213.117


Map: [<1 0 -1 2|, <0 2 4 1|]
Mapping: [{{val| 1 0 -1 2 }}, {{val| 0 2 4 1 }}]


Wedgie: <<2 4 1 2 -4 -9||
{{Multival|legend=1| 2 4 1 2 -4 -9 }}


EDOs: 6, 11bc, 17b
{{Val list|legend=1| 6, 11bc, 17b }}


Badness: 0.0591
Badness: 0.0591


== Medusa ==
== Medusa ==
Commas: 15/14, 64/63
Comma list: 15/14, 64/63


POTE generator: ~3/2 = 685.632
POTE generator: ~3/2 = 685.632


Map: [<1 0 7 6|, <0 1 -3 -2|]
Mapping: [{{val| 1 0 7 6 }}, {{val| 0 1 -3 -2 }}]


Wedgie: <<1 -3 -2 -7 -6 4||
{{Multival|legend=1| 1 -3 -2 -7 -6 4 }}


EDOs: 2, 7, 12c, 14cd
{{Val list|legend=1| 2, 7, 12c, 14cd }}


Badness: 0.0427
Badness: 0.0427


[[Category:Temperament]]
[[Category:Temperament]]

Revision as of 05:00, 15 March 2021

Todo: intro, cleanup

what are the criteria for inclusion here?

Below are listed some very low accuracy temperaments.

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]]

Template:Val list

Antitonic (2 & 4p)

This temperament is characterized by tempering out 9/8, 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 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:

Mapping:

Mapping generators:

Vals:

Badness:

7-limit

Comma list: 9/8, 21/20

POTE generator:

Mapping:

Mapping generators:

Vals:

Badness:

11-limit

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

POTE generator:

Mapping:

Mapping generators:

Vals:

Badness:

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 ]]

Template:Val list

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

Antaeus

Comma list: 9/8, 35/32

POTE generator: ~5/4 = 315.962

Mapping: [⟨2 3 0 10], ⟨0 0 1 -1]]

Wedgie: ⟨⟨ 0 2 -2 3 -3 -10 ]]

Template:Val list

Badness: 0.0375

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 ]]

Template:Val list

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 ]]

Template:Val list

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 ]]

Template:Val list

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 ]]

Template:Val list

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 ]]

Template:Val list

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 ]]

Template:Val list

Badness: 0.0427

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