Keemic temperaments: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Databoxified (with data reviewed)
Revert databoxes
Line 5: Line 5:
== 5-limit ==
== 5-limit ==


Period: 1\1
Subgroup: 2.3.5
 
Optimal ([[POTE]]) generator: ~3125/2592 = 292.702
 
EDO generator: [[37edo|9\37]], [[41edo|10\41]], [[45edo|11\45]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5
[[Comma list]]: 6103515625/5804752896


Comma list: 6103515625/5804752896
[[Mapping]]: [{{val| 1 5 5 }}, {{val| 0 -14 -11 }}]


Mapping: [{{val| 1 5 5 }}, {{val| 0 -14 -11 }}]
[[POTE generator]]: ~3125/2592 = 292.702


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


Badness: 0.7678
[[Badness]]: 0.7678
 
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~25/21 = 292.710
EDO generator: [[37edo|9\37]], [[41edo|10\41]], [[45edo|11\45]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 875/864, 2401/2400
[[Comma list]]: 875/864, 2401/2400


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


{{Multival|legend=1| 14 11 9 -15 -25 -10 }}
{{Multival|legend=1| 14 11 9 -15 -25 -10 }}
[[POTE generator]]: ~25/21 = 292.710


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


Badness: 0.0603
[[Badness]]: 0.0603
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~25/21 = 292.547
EDO generator: [[37edo|9\37]], [[41edo|10\41]], [[78edo|19\78]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 76: Line 40:


Mapping: [{{val| 1 5 5 5 2 }}, {{val| 0 -14 -11 -9 6 }}]
Mapping: [{{val| 1 5 5 5 2 }}, {{val| 0 -14 -11 -9 6 }}]
POTE generator: ~25/21 = 292.547


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


Badness: 0.0432
Badness: 0.0432
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~25/21 = 292.457
EDO generator: [[37edo|9\37]], [[41edo|10\41]], [[78edo|19\78]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 104: Line 56:


Mapping: [{{val| 1 5 5 5 2 2 }}, {{val| 0 -14 -11 -9 6 7 }}]
Mapping: [{{val| 1 5 5 5 2 2 }}, {{val| 0 -14 -11 -9 6 7 }}]
POTE generator: ~25/21 = 292.457


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


Badness: 0.0329
Badness: 0.0329
</div></div>


== Quato ==
== Quato ==
Period: 1\1
Optimal ([[POTE]]) generator: ~25/21 = 292.851
EDO generator: [[41edo|10\41]], [[45edo|11\45]], [[86edo|21\86]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 130: Line 70:


Mapping: [{{val| 1 5 5 5 12 }}, {{val| 0 -14 -11 -9 -35 }}]
Mapping: [{{val| 1 5 5 5 12 }}, {{val| 0 -14 -11 -9 -35 }}]
POTE generator: ~25/21 = 292.851


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


Badness: 0.0412
Badness: 0.0412
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~13/11 = 292.928
EDO generator: [[41edo|10\41]], [[45edo|11\45]], [[86edo|21\86]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 156: Line 84:


Mapping: [{{val| 1 5 5 5 12 12 }}, {{val| 0 -14 -11 -9 -35 -34 }}]
Mapping: [{{val| 1 5 5 5 12 12 }}, {{val| 0 -14 -11 -9 -35 -34 }}]
POTE generator: ~13/11 = 292.928


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


Badness: 0.0301
Badness: 0.0301
</div></div>


= Barbad =
= Barbad =


Period: 1\1
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generator: ~98/75 = 468.331
 
EDO generator: [[18edo|7\18]], [[23edo|9\23]], [[41edo|16\41]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
[[Comma list]]: 875/864, 16875/16807


Comma list: 875/864, 16875/16807
[[Mapping]]: [{{val| 1 9 7 11 }}, {{val| 0 -19 -12 -21 }}]


Mapping: [{{val| 1 9 7 11 }}, {{val| 0 -19 -12 -21 }}]
[[POTE generator]]: ~98/75 = 468.331


{{Multival|legend=1| 19 12 21 -25 -20 15 }}
{{Multival|legend=1| 19 12 21 -25 -20 15 }}
Line 187: Line 105:
{{Val list|legend=1| 18, 23d, 41 }}
{{Val list|legend=1| 18, 23d, 41 }}


Badness: 0.1104
[[Badness]]: 0.1104
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~98/75 = 468.367
EDO generator: [[18edo|7\18]], [[23edo|9\23]], [[41edo|16\41]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 210: Line 114:


Mapping: [{{val| 1 9 7 11 14 }}, {{val| 0 -19 -12 -21 -27 }}]
Mapping: [{{val| 1 9 7 11 14 }}, {{val| 0 -19 -12 -21 -27 }}]
POTE generator: ~98/75 = 468.367


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


Badness: 0.0501
Badness: 0.0501
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~13/10 = 468.270
EDO generator: [[18edo|7\18]], [[23edo|9\23]], [[41edo|16\41]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 236: Line 128:


Mapping: [{{val| 1 9 7 11 14 8 }}, {{val| 0 -19 -12 -21 -27 -11 }}]
Mapping: [{{val| 1 9 7 11 14 8 }}, {{val| 0 -19 -12 -21 -27 -11 }}]
POTE generator: ~13/10 = 468.270


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


Badness: 0.0392
Badness: 0.0392
</div></div>


[[Category:Theory]]
[[Category:Theory]]

Revision as of 10:17, 28 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

Subgroup: 2.3.5

Comma list: 6103515625/5804752896

Mapping: [⟨1 5 5], ⟨0 -14 -11]]

POTE generator: ~3125/2592 = 292.702

Template:Val list

Badness: 0.7678

7-limit

Subgroup: 2.3.5.7

Comma list: 875/864, 2401/2400

Mapping: [⟨1 5 5 5], ⟨0 -14 -11 -9]]

Wedgie: ⟨⟨ 14 11 9 -15 -25 -10 ]]

POTE generator: ~25/21 = 292.710

Template:Val list

Badness: 0.0603

11-limit

Subgroup: 2.3.5.7.11

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

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

POTE generator: ~25/21 = 292.547

Template:Val list

Badness: 0.0432

13-limit

Subgroup: 2.3.5.7.11.13

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]]

POTE generator: ~25/21 = 292.457

Template:Val list

Badness: 0.0329

Quato

Subgroup: 2.3.5.7.11

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

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

POTE generator: ~25/21 = 292.851

Template:Val list

Badness: 0.0412

13-limit

Subgroup: 2.3.5.7.11.13

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

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

POTE generator: ~13/11 = 292.928

Template:Val list

Badness: 0.0301

Barbad

Subgroup: 2.3.5.7

Comma list: 875/864, 16875/16807

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

POTE generator: ~98/75 = 468.331

Wedgie: ⟨⟨ 19 12 21 -25 -20 15 ]]

Template:Val list

Badness: 0.1104

11-limit

Subgroup: 2.3.5.7.11

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

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

POTE generator: ~98/75 = 468.367

Template:Val list

Badness: 0.0501

13-limit

Subgroup: 2.3.5.7.11.13

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

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

POTE generator: ~13/10 = 468.270

Template:Val list

Badness: 0.0392

Retrieved from "https://en.xen.wiki/index.php?title=Keemic_temperaments&oldid=64938"