Keemic temperaments: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
m Cleanup; edo list reviewed
Databoxified (with data reviewed)
Line 4: Line 4:
= Quasitemp =
= Quasitemp =
== 5-limit ==
== 5-limit ==
Period: 1\1
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
POTE generator: ~3125/2592 = 292.702


Mapping: [{{val| 1 5 5 }}, {{val| 0 -14 -11 }}]
Mapping: [{{val| 1 5 5 }}, {{val| 0 -14 -11 }}]
Line 13: Line 26:


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
Comma list: 875/864, 2401/2400
Comma list: 875/864, 2401/2400
POTE generator ~25/21 = 292.710


Mapping: [{{val| 1 5 5 5 }}, {{val| 0 -14 -11 -9 }}]
Mapping: [{{val| 1 5 5 5 }}, {{val| 0 -14 -11 -9 }}]
Line 26: Line 54:


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
Comma list: 100/99, 385/384, 1375/1372
Comma list: 100/99, 385/384, 1375/1372
POTE generator: ~25/21 = 292.547


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 }}]
Line 37: Line 80:


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


Line 48: Line 108:


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
Comma list: 243/242, 441/440, 625/616
Comma list: 243/242, 441/440, 625/616
POTE generator: ~25/21 = 292.851


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 }}]
Line 59: Line 134:


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
Comma list: 105/104, 243/242, 275/273, 325/324
Comma list: 105/104, 243/242, 275/273, 325/324
POTE generator: ~13/11 = 292.928


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 }}]
Line 70: Line 160:


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


= Barbad =
= Barbad =
Period: 1\1
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
POTE generator: ~75/49 = 468.331


Mapping: [{{val| 1 9 7 11 }}, {{val| 0 -19 -12 -21 }}]
Mapping: [{{val| 1 9 7 11 }}, {{val| 0 -19 -12 -21 }}]
Line 83: Line 188:


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
Comma list: 245/242, 540/539, 625/616
Comma list: 245/242, 540/539, 625/616
POTE generator: ~98/75 = 468.367


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 }}]
Line 94: Line 214:


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
Comma list: 144/143, 196/195, 245/242, 275/273
Comma list: 144/143, 196/195, 245/242, 275/273
POTE generator: ~13/10 = 468.270


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 }}]
Line 105: Line 240:


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


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

Revision as of 06:34, 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

Period: 1\1

Optimal (POTE) generator: ~3125/2592 = 292.702

EDO generator: 9\37, 10\41, 11\45

Scales (Scala files):

Technical data

Subgroup: 2.3.5

Comma list: 6103515625/5804752896

Mapping: [⟨1 5 5], ⟨0 -14 -11]]

Template:Val list

Badness: 0.7678

7-limit

Period: 1\1

Optimal (POTE) generator: ~25/21 = 292.710

EDO generator: 9\37, 10\41, 11\45

Scales (Scala files):

Technical data

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 ]]

Template:Val list

Badness: 0.0603

11-limit

Period: 1\1

Optimal (POTE) generator: ~25/21 = 292.547

EDO generator: 9\37, 10\41, 19\78

Scales (Scala files):

Technical data

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]]

Template:Val list

Badness: 0.0432

13-limit

Period: 1\1

Optimal (POTE) generator: ~25/21 = 292.457

EDO generator: 9\37, 10\41, 19\78

Scales (Scala files):

Technical data

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]]

Template:Val list

Badness: 0.0329

Quato

Period: 1\1

Optimal (POTE) generator: ~25/21 = 292.851

EDO generator: 10\41, 11\45, 21\86

Scales (Scala files):

Technical data

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]]

Template:Val list

Badness: 0.0412

13-limit

Period: 1\1

Optimal (POTE) generator: ~13/11 = 292.928

EDO generator: 10\41, 11\45, 21\86

Scales (Scala files):

Technical data

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]]

Template:Val list

Badness: 0.0301

Barbad

Period: 1\1

Optimal (POTE) generator: ~98/75 = 468.331

EDO generator: 7\18, 9\23, 16\41

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 875/864, 16875/16807

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

Wedgie: ⟨⟨ 19 12 21 -25 -20 15 ]]

Template:Val list

Badness: 0.1104

11-limit

Period: 1\1

Optimal (POTE) generator: ~98/75 = 468.367

EDO generator: 7\18, 9\23, 16\41

Scales (Scala files):

Technical data

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]]

Template:Val list

Badness: 0.0501

13-limit

Period: 1\1

Optimal (POTE) generator: ~13/10 = 468.270

EDO generator: 7\18, 9\23, 16\41

Scales (Scala files):

Technical data

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]]

Template:Val list

Badness: 0.0392

Retrieved from "https://en.xen.wiki/index.php?title=Keemic_temperaments&oldid=63592"