Keemic temperaments: Difference between revisions

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These temper out the keema, {{monzo| -5 -3 3 1 }} = [[875/864]]. Keemic temperaments include [[Magic family #Magic|magic]], [[Kleismic family #Keemun|keemun]], [[Meantone family #Flattone|flattone]], [[Porcupine family #Porcupine|porcupine]], [[Jubilismic clan #Doublewide|doublewide]], [[Gamelismic clan #Superkleismic|superkleismic]], and [[Sycamore family #Sycamore|sycamore]]. Discussed below are quasitemp and barbad.
These temper out the keema, {{monzo| -5 -3 3 1 }} = [[875/864]]. Keemic temperaments include [[Jubilismic clan #Doublewide|doublewide]], [[Meantone family #Flattone|flattone]], [[Porcupine family #Porcupine|porcupine]], [[Gamelismic clan #Superkleismic|superkleismic]], [[Magic family #Magic|magic]], [[Kleismic family #Keemun|keemun]], and [[Sycamore family #Sycamore|sycamore]]. Discussed below are quasitemp and barbad.


= Quasitemp =
= Quasitemp =
Comma: 6103515625/5804752896
== 5-limit ==
Comma list: 6103515625/5804752896


POTE generator: ~3125/2592 = 292.702
POTE generator: ~3125/2592 = 292.702


Map: [<1 5 5|, <0 -14 -11|]
Mapping: [{{val| 1 5 5 }}, {{val| 0 -14 -11 }}]


{{EDOs|legend=1| 4, 37, 41 }}
{{Val list|legend=1| 4, …, 37, 41 }}


Badness: 0.7678
Badness: 0.7678


== 7-limit ==
== 7-limit ==
Commas: 875/864, 2401/2400
Comma list: 875/864, 2401/2400


POTE generator ~25/21 = 292.710
POTE generator ~25/21 = 292.710


Map: [<1 5 5 5|, <0 -14 -11 -9|]
Mapping: [{{val| 1 5 5 5 }}, {{val| 0 -14 -11 -9 }}]


Wedgie: <<14 11 9 -15 -25 -10||
{{Multival|legend=1| 14 11 9 -15 -25 -10 }}


{{EDOs|legend=1| 4, 37, 41 }}
{{Val list|legend=1| 4, …, 37, 41 }}


Badness: 0.0603
Badness: 0.0603


== 11-limit ==
== 11-limit ==
Commas: 100/99, 385/384, 1375/1372
Comma list: 100/99, 385/384, 1375/1372


POTE generator: ~25/21 = 292.547
POTE generator: ~25/21 = 292.547


Map: [<1 5 5 5 2|, <0 -14 -11 -9 6|]
Mapping: [{{val| 1 5 5 5 2 }}, {{val| 0 -14 -11 -9 6 }}]


{{EDOs|legend=1| 4, 37, 41, 119 }}
{{Val list|legend=1| 37, 41, 119 }}


Badness: 0.0432
Badness: 0.0432


=== 13-limit ===
=== 13-limit ===
Commas: 100/99, 196/195, 275/273, 385/384
Comma list: 100/99, 196/195, 275/273, 385/384


POTE generator: ~13/11 = 292.457
POTE generator: ~13/11 = 292.457


Map: [<1 5 5 5 2 2|, <0 -14 -11 -9 6 7|]
Mapping: [{{val| 1 5 5 5 2 2 }}, {{val| 0 -14 -11 -9 6 7 }}]


{{EDOs|legend=1| 4, 37, 41, 78, 119f }}
{{Val list|legend=1| 37, 41, 78, 119f }}


Badness: 0.0329
Badness: 0.0329


== Quato ==
== Quato ==
Commas: 243/242, 441/440, 625/616
Comma list: 243/242, 441/440, 625/616


POTE generator: ~25/21 = 292.851
POTE generator: ~25/21 = 292.851


Map: [<1 5 5 5 12|, <0 -14 -11 -9 -35|]
Mapping: [{{val| 1 5 5 5 12 }}, {{val| 0 -14 -11 -9 -35 }}]


{{EDOs|legend=1| 41, 127cd, 168cd }}
{{Val list|legend=1| 41, 127cd, 168cd }}


Badness: 0.0412
Badness: 0.0412


=== 13-limit ===
=== 13-limit ===
Commas: 105/104, 243/242, 275/273, 325/324
Comma list: 105/104, 243/242, 275/273, 325/324


POTE generator: ~13/11 = 292.928
POTE generator: ~13/11 = 292.928


Map: [<1 5 5 5 12 12|, <0 -14 -11 -9 -35 -34|]
Mapping: [{{val| 1 5 5 5 12 12 }}, {{val| 0 -14 -11 -9 -35 -34 }}]


{{EDOs|legend=1| 41, 86ce, 127cd }}
{{Val list|legend=1| 41, 86ce, 127cd }}


Badness: 0.0301
Badness: 0.0301


= Barbad =
= Barbad =
Commas: 875/864, 16875/16807
Comma list: 875/864, 16875/16807


POTE generator: ~75/49 = 468.331
POTE generator: ~75/49 = 468.331


Map: [<1 9 7 11|, <0 -19 -12 -21|]
Mapping: [{{val| 1 9 7 11 }}, {{val| 0 -19 -12 -21 }}]


Wedgie: <<19 12 21 -25 -20 15||
{{Multival|legend=1| 19 12 21 -25 -20 15 }}


{{EDOs|legend=1| 18, 23d, 41 }}
{{Val list|legend=1| 18, 23d, 41 }}


Badness: 0.1104
Badness: 0.1104


== 11-limit ==
== 11-limit ==
Commas: 245/242, 540/539, 625/616
Comma list: 245/242, 540/539, 625/616


POTE generator: ~98/75 = 468.367
POTE generator: ~98/75 = 468.367


Map: [<1 9 7 11 14|, <0 -19 -12 -21 -27|]
Mapping: [{{val| 1 9 7 11 14 }}, {{val| 0 -19 -12 -21 -27 }}]


{{EDOs|legend=1| 18e, 23de, 41, 228ccdd }}
{{Val list|legend=1| 18e, 23de, 41, 228ccdd }}


Badness: 0.0501
Badness: 0.0501


== 13-limit ==
== 13-limit ==
Commas: 144/143, 196/195, 245/242, 275/273
Comma list: 144/143, 196/195, 245/242, 275/273


POTE generator: ~13/10 = 468.270
POTE generator: ~13/10 = 468.270


Map: [<1 9 7 11 14 8|, <0 -19 -12 -21 -27 -11|]
Mapping: [{{val| 1 9 7 11 14 8 }}, {{val| 0 -19 -12 -21 -27 -11 }}]


{{EDOs|legend=1| 18e, 23de, 41 }}
{{Val list|legend=1| 18e, 23de, 41 }}


Badness: 0.0392
Badness: 0.0392

Revision as of 06:20, 21 March 2021

These temper out the keema, [-5 -3 3 1⟩ = 875/864. Keemic temperaments include doublewide, flattone, porcupine, superkleismic, magic, keemun, and sycamore. Discussed below are quasitemp and barbad.

Quasitemp

5-limit

Comma list: 6103515625/5804752896

POTE generator: ~3125/2592 = 292.702

Mapping: [⟨1 5 5], ⟨0 -14 -11]]

Template:Val list

Badness: 0.7678

7-limit

Comma list: 875/864, 2401/2400

POTE generator ~25/21 = 292.710

Mapping: [⟨1 5 5 5], ⟨0 -14 -11 -9]]

Wedgie: ⟨⟨ 14 11 9 -15 -25 -10 ]]

Template:Val list

Badness: 0.0603

11-limit

Comma list: 100/99, 385/384, 1375/1372

POTE generator: ~25/21 = 292.547

Mapping: [⟨1 5 5 5 2], ⟨0 -14 -11 -9 6]]

Template:Val list

Badness: 0.0432

13-limit

Comma list: 100/99, 196/195, 275/273, 385/384

POTE generator: ~13/11 = 292.457

Mapping: [⟨1 5 5 5 2 2], ⟨0 -14 -11 -9 6 7]]

Template:Val list

Badness: 0.0329

Quato

Comma list: 243/242, 441/440, 625/616

POTE generator: ~25/21 = 292.851

Mapping: [⟨1 5 5 5 12], ⟨0 -14 -11 -9 -35]]

Template:Val list

Badness: 0.0412

13-limit

Comma list: 105/104, 243/242, 275/273, 325/324

POTE generator: ~13/11 = 292.928

Mapping: [⟨1 5 5 5 12 12], ⟨0 -14 -11 -9 -35 -34]]

Template:Val list

Badness: 0.0301

Barbad

Comma list: 875/864, 16875/16807

POTE generator: ~75/49 = 468.331

Mapping: [⟨1 9 7 11], ⟨0 -19 -12 -21]]

Wedgie: ⟨⟨ 19 12 21 -25 -20 15 ]]

Template:Val list

Badness: 0.1104

11-limit

Comma list: 245/242, 540/539, 625/616

POTE generator: ~98/75 = 468.367

Mapping: [⟨1 9 7 11 14], ⟨0 -19 -12 -21 -27]]

Template:Val list

Badness: 0.0501

13-limit

Comma list: 144/143, 196/195, 245/242, 275/273

POTE generator: ~13/10 = 468.270

Mapping: [⟨1 9 7 11 14 8], ⟨0 -19 -12 -21 -27 -11]]

Template:Val list

Badness: 0.0392

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