Mint temperaments: Difference between revisions

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== 5-limit ==
== 5-limit ==


Period: 1\1
[[Comma list]]: 3456/3125


Optimal ([[POTE]]) generators: ~25/24 = 140.995
[[Mapping]]: [{{val| 1 1 2 }}, {{val| 0 5 3 }}]


EDO generators: [[8edo|1\8]], [[9edo|1\9]], [[17edo|2\17]]
[[POTE generator]]: ~25/24 = 140.995
 
Scales:
 
<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">
 
Comma list: 3456/3125
 
POTE generator: ~25/24 = 140.995
 
Mapping: [{{val| 1 1 2 }}, {{val| 0 5 3 }}]


{{Val list|legend=1| 8, 9, 17c }}
{{Val list|legend=1| 8, 9, 17c }}


Badness: 0.2005
[[Badness]]: 0.2005
 
</div></div>


== 7-limit ==
== 7-limit ==


Period: 1\1
[[Comma list]]: 36/35, 392/375


Optimal ([[POTE]]) generators: ~15/14 = 140.927
[[Mapping]]: [{{val| 1 1 2 2 }}, {{val| 0 5 3 7 }}]


EDO generators: [[8edo|1\8]], [[9edo|1\9]], [[17edo|2\17]]
{{Multival|legend=1| 5 3 7 -7 -3 8 }}


Scales:  
[[POTE generator]]: ~15/14 = 140.927
 
<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">
 
Comma list: 36/35, 392/375
 
Mapping: [{{val| 1 1 2 2 }}, {{val| 0 5 3 7 }}]
 
Wedgie: {{wedgie| 5 3 7 -7 -3 8 }}


{{Val list|legend=1| 8d, 9, 17c }}
{{Val list|legend=1| 8d, 9, 17c }}


Badness: 0.0484
[[Badness]]: 0.0484
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~12/11 = 140.747
EDO generators: [[8edo|1\8]], [[9edo|1\9]], [[17edo|2\17]]
Scales:
<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">


Comma list: 36/35, 56/55, 77/75
Comma list: 36/35, 56/55, 77/75


Mapping: [{{val| 1 1 2 2 3 }}, {{val| 0 5 3 7 4 }}]
Mapping: [{{val| 1 1 2 2 3 }}, {{val| 0 5 3 7 4 }}]
POTE generators: ~12/11 = 140.747


{{Val list|legend=1| 8d, 9, 17c }}
{{Val list|legend=1| 8d, 9, 17c }}


Badness: 0.0261
Badness: 0.0261
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~13/12 = 140.751
EDO generators: [[8edo|1\8]], [[9edo|1\9]], [[17edo|2\17]]
Scales:
<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">


Comma list: 26/25, 36/35, 56/55, 66/65
Comma list: 26/25, 36/35, 56/55, 66/65


Mapping: [{{val| 1 1 2 2 3 3 }}, {{val| 0 5 3 7 4 6 }}]
Mapping: [{{val| 1 1 2 2 3 3 }}, {{val| 0 5 3 7 4 6 }}]
POTE generators: ~13/12 = 140.751


{{Val list|legend=1| 8d, 9, 17c }}
{{Val list|legend=1| 8d, 9, 17c }}


Badness: 0.0182
Badness: 0.0182
</div></div>


== 17-limit ==
== 17-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~13/12 = 141.404
EDO generators: [[8edo|1\8]], [[9edo|1\9]], [[17edo|2\17]]
Scales:
<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">


Comma list: 26/25, 36/35, 51/50, 56/55, 66/65
Comma list: 26/25, 36/35, 51/50, 56/55, 66/65


Mapping: [{{val| 1 1 2 2 3 3 4 }}, {{val| 0 5 3 7 4 6 1 }}]
Mapping: [{{val| 1 1 2 2 3 3 4 }}, {{val| 0 5 3 7 4 6 1 }}]
POTE generators: ~13/12 = 141.404


{{Val list|legend=1| 8d, 9, 17cg }}
{{Val list|legend=1| 8d, 9, 17cg }}


Badness: 0.0167
Badness: 0.0167
</div></div>


== 19-limit ==
== 19-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~13/12 = 140.479
EDO generators: [[8edo|1\8]], [[9edo|1\9]], [[17edo|2\17]]
Scales:
<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">


Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65
Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65


Mapping: [{{val| 1 1 2 2 3 3 4 4 }}, {{val| 0 5 3 7 4 6 1 2 }}]
Mapping: [{{val| 1 1 2 2 3 3 4 4 }}, {{val| 0 5 3 7 4 6 1 2 }}]
POTE generators: ~13/12 = 140.479


{{Val list|legend=1| 8d, 9, 17cg, 94… }}
{{Val list|legend=1| 8d, 9, 17cg, 94… }}


Badness: 0.0168
Badness: 0.0168
</div></div>


= Ripple =
= Ripple =
{{see also| Ripple family #Ripple }}
{{see also| Ripple family #Ripple }}


Period: 1\1
[[Comma list]]: 36/35, 2560/2401
 
Optimal ([[POTE]]) generators: ~21/20 = 99.483
 
EDO generators: [[11edo|1\11]], [[12edo|1\12]], [[13edo|1\13]]
 
Scales:
 
<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">


Comma list: 36/35, 2560/2401
[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -5 -8 -2 }}]
 
Mapping: [{{val| 1 2 3 3 }}, {{val| 0 -5 -8 -2 }}]


{{Multival|legend=1| 5 8 2 1 -11 -18 }}
{{Multival|legend=1| 5 8 2 1 -11 -18 }}


{{Val list|legend=1| 11c, 12 }}
[[POTE generator]]: ~21/20 = 99.483


Badness: 0.0597
{{Val list|legend=1| 12 }}


</div></div>
[[Badness]]: 0.0597


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~21/20 = 99.385
EDO generators: [[11edo|1\11]], [[12edo|1\12]], [[13edo|1\13]]
Scales:
<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">


Comma list: 36/35, 80/77, 126/121
Comma list: 36/35, 80/77, 126/121


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -5 -8 -2 -6 }}]
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -5 -8 -2 -6 }}]
POTE generator: ~21/20 = 99.385


{{Val list|legend=1| 12 }}
{{Val list|legend=1| 12 }}


Badness: 0.0388
Badness: 0.0388
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~21/20 = 98.572
EDO generators: [[11edo|1\11]], [[12edo|1\12]], [[13edo|1\13]]
Scales:
<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">


Comma list: 36/35, 40/39, 66/65, 147/143
Comma list: 36/35, 40/39, 66/65, 147/143


Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -5 -8 -2 -6 -3 }}]
Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -5 -8 -2 -6 -3 }}]
POTE generator: ~21/20 = 98.572


{{Val list|legend=1| 12f }}
{{Val list|legend=1| 12f }}


Badness: 0.0316
Badness: 0.0316
</div></div>


= Smate =
= Smate =
== 5-limit ==
== 5-limit ==


Period: 1\1
[[Comma list]]: 2048/1875
 
Optimal ([[POTE]]) generators: ~5/4 = 420.855
 
EDO generators: [[14edo|5\14]], [[17edo|6\17]], [[20edo|7\20]]
 
Scales:
 
<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">


Comma list: 2048/1875
[[Mapping]]: [{{val| 1 3 2 }}, {{val| 0 -4 1 }}]


Mapping: [{{val| 1 3 2 }}, {{val| 0 -4 1 }}]
[[POTE generator]]: ~5/4 = 420.855


{{Val list|legend=1| 11, 14, 17c, 20c, 37c }}
{{Val list|legend=1| 11, 14, 17c, 20c, 37c }}


Badness: 0.179
[[Badness]]: 0.179
 
</div></div>


== 7-limit ==
== 7-limit ==


Period: 1\1
[[Comma list]]: 36/35, 2048/1875
 
Optimal ([[POTE]]) generators: ~5/4 = 422.275
 
EDO generators: [[14edo|5\14]], [[17edo|6\17]], [[20edo|7\20]]
 
Scales:


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[Mapping]]: [{{val| 1 3 2 6 }}, {{val| 0 -4 1 -9 }}]
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Comma list: 36/35, 2048/1875
{{Multival|legend=1| 4 -1 9 -11 3 24 }}


Mapping: [{{val| 1 3 2 6 }}, {{val| 0 -4 1 -9 }}]
[[POTE generator]]: ~5/4 = 422.275
 
Wedgie: {{wedgie| 4 -1 9 -11 3 24 }}


{{Val list|legend=1| 14, 17c, 37cd }}
{{Val list|legend=1| 14, 17c, 37cd }}


Badness: 0.0779
[[Badness]]: 0.0779
 
</div></div>


=== 11-limit ===
=== 11-limit ===
Period: 1\1
Optimal ([[POTE]]) generators: ~5/4 = 422.217
EDO generators: [[14edo|5\14]], [[17edo|6\17]], [[20edo|7\20]]
Scales:
<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">


Comma list: 36/35, 56/55, 243/242
Comma list: 36/35, 56/55, 243/242


Mapping: [{{val| 1 3 2 6 7 }}, {{val| 0 -4 1 -9 -10 }}]
Mapping: [{{val| 1 3 2 6 7 }}, {{val| 0 -4 1 -9 -10 }}]
POTE generator: ~5/4 = 422.217


{{Val list|legend=1| 14, 17c, 37cde }}
{{Val list|legend=1| 14, 17c, 37cde }}


Badness: 0.0425
Badness: 0.0425
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generators: ~5/4 = 423.020
EDO generators: [[14edo|5\14]], [[17edo|6\17]], [[20edo|7\20]]
Scales:
<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">


Comma list: 26/25, 36/35, 56/55, 243/242  
Comma list: 26/25, 36/35, 56/55, 243/242  


Mapping: [{{val| 1 3 2 6 7 3 }}, {{val| 0 -4 1 -9 -10 2 }}]
Mapping: [{{val| 1 3 2 6 7 3 }}, {{val| 0 -4 1 -9 -10 2 }}]
POTE generator: ~5/4 = 423.020


{{Val list|legend=1| 14, 17c }}
{{Val list|legend=1| 14, 17c }}


Badness: 0.0368
Badness: 0.0368
</div></div>


== Hemismate ==
== Hemismate ==
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 210.452
EDO generators: [[11edo|2\11]], [[17edo|3\17]], [[23edo|4\23]]
Scales:
<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">


Comma list: 256/245, 392/375  
Comma list: 256/245, 392/375  
Line 342: Line 172:
Mapping: [{{val| 1 3 2 3 }}, {{val| 0 -8 2 -1 }}]
Mapping: [{{val| 1 3 2 3 }}, {{val| 0 -8 2 -1 }}]


Wedgie: {{wedgie| 8 -2 1 -22 -21 8 }}
{{Multival|legend=1| 8 -2 1 -22 -21 8 }}
 
POTE generator: ~8/7 = 210.452


{{Val list|legend=1| 6, 11, 17c, 40bcd }}
{{Val list|legend=1| 6, 11, 17c, 40bcd }}


Badness: 0.1543
Badness: 0.1543
</div></div>


=== 11-limit ===
=== 11-limit ===
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 210.481
EDO generators: [[11edo|2\11]], [[17edo|3\17]], [[23edo|4\23]]
Scales:
<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">


Comma list: 56/55, 77/75, 256/245
Comma list: 56/55, 77/75, 256/245


Mapping: [{{val| 1 3 2 3 4 }}, {{val| 0 -8 2 -1 -3 }}]
Mapping: [{{val| 1 3 2 3 4 }}, {{val| 0 -8 2 -1 -3 }}]
POTE generator: ~8/7 = 210.481


{{Val list|legend=1| 6, 11, 17c, 40bcde }}
{{Val list|legend=1| 6, 11, 17c, 40bcde }}


Badness: 0.0655
Badness: 0.0655
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 210.974
EDO generators: [[11edo|2\11]], [[17edo|3\17]], [[23edo|4\23]]
Scales:
<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">


Comma list: 26/25, 56/55, 77/75, 256/245
Comma list: 26/25, 56/55, 77/75, 256/245


Mapping: [{{val| 1 3 2 3 4 3 }}, {{val| 0 -8 2 -1 -3 4 }}]
Mapping: [{{val| 1 3 2 3 4 3 }}, {{val| 0 -8 2 -1 -3 4 }}]
POTE generators: ~8/7 = 210.974


{{Val list|legend=1| 6, 11, 17c }}
{{Val list|legend=1| 6, 11, 17c }}


Badness: 0.0505
Badness: 0.0505
</div></div>


= Subklei =
= Subklei =
== 5-limit ==
== 5-limit ==


Period: 1\1
[[Comma list]]: 17496/15625
 
Optimal ([[POTE]]) generators: ~6/5 = 284.293
 
EDO generators: [[17edo|4\17]], [[21edo|5\21]]
 
Scales:
 
<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">


Comma list: 17496/15625
[[Mapping]]: [{{val| 1 3 4 }}, {{val| 0 -6 -7 }}]


Mapping: [{{val| 1 3 4 }}, {{val| 0 -6 -7 }}]
[[POTE generator]]: ~6/5 = 284.293


{{Val list|legend=1| 4, 17c, 21, 38c }}
{{Val list|legend=1| 4, 17c, 21, 38c }}


Badness: 0.3559
[[Badness]]: 0.3559
 
</div></div>


== 7-limit ==
== 7-limit ==


Period: 1\1
[[Comma list]]: 36/35, 1029/1000


Optimal ([[POTE]]) generators: ~6/5 = 284.219
[[Mapping]]: [{{val| 1 3 4 4 }}, {{val| 0 -6 -7 -5 }}]


EDO generators: [[17edo|4\17]], [[21edo|5\21]]
{{Multival|legend=1| 6 7 5 -3 -9 -8 }}


Scales:
[[POTE generator]]: ~6/5 = 284.219
 
<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">
 
Comma list: 36/35, 1029/1000
 
Mapping: [{{val| 1 3 4 4 }}, {{val| 0 -6 -7 -5 }}]
 
Wedgie: {{wedgie| 6 7 5 -3 -9 -8 }}


{{Val list|legend=1| 4, 17c, 21, 38c }}
{{Val list|legend=1| 4, 17c, 21, 38c }}


Badness: 0.0611
[[Badness]]: 0.0611
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~6/5 = 283.253
EDO generators: [[17edo|4\17]], [[21edo|5\21]]
Scales:
<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">


Comma list: 36/35, 77/75, 352/343
Comma list: 36/35, 77/75, 352/343


Mapping: [{{val| 1 3 4 4 7 }}, {{val| 0 -6 -7 -5 -15 }}]
Mapping: [{{val| 1 3 4 4 7 }}, {{val| 0 -6 -7 -5 -15 }}]
POTE generator: ~6/5 = 283.253


{{Val list|legend=1| 17c, 55cd }}
{{Val list|legend=1| 17c, 55cd }}


Badness: 0.0447
Badness: 0.0447
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generators: ~6/5 = 282.856
EDO generators: [[17edo|4\17]], [[21edo|5\21]]
Scales:
<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">


Comma list: 26/25, 36/35, 66/65, 352/343  
Comma list: 26/25, 36/35, 66/65, 352/343  
Line 492: Line 250:


Mapping: [{{val| 1 3 4 4 7 7 }}, {{val| 0 -6 -7 -5 -15 -14 }}]
Mapping: [{{val| 1 3 4 4 7 7 }}, {{val| 0 -6 -7 -5 -15 -14 }}]
POTE generator: ~6/5 = 282.856


{{Val list|legend=1| 17c }}
{{Val list|legend=1| 17c }}


Badness: 0.0323
Badness: 0.0323
</div></div>


== Subkla ==
== Subkla ==
Period: 1\1
Optimal ([[POTE]]) generators: ~6/5 = 283.822
EDO generators: [[17edo|4\17]], [[21edo|5\21]]
Scales:
<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">


Comma list: 36/35, 56/55, 1029/1000
Comma list: 36/35, 56/55, 1029/1000


Mapping: [{{val| 1 3 4 4 3 }}, {{val| 0 -6 -7 -5 2 }}]
Mapping: [{{val| 1 3 4 4 3 }}, {{val| 0 -6 -7 -5 2 }}]
POTE generator: ~6/5 = 283.822


{{Val list|legend=1| 4, 17c, 21, 38ce, 55cde }}
{{Val list|legend=1| 4, 17c, 21, 38ce, 55cde }}


Badness: 0.0472
Badness: 0.0472
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generators: ~6/5 = 283.882
EDO generators: [[17edo|4\17]], [[21edo|5\21]]
Scales:
<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">


Comma list: 36/35, 56/55, 66/65, 640/637
Comma list: 36/35, 56/55, 66/65, 640/637


Mapping: [{{val| 1 3 4 4 3 3 }}, {{val| 0 -6 -7 -5 2 3 }}]
Mapping: [{{val| 1 3 4 4 3 3 }}, {{val| 0 -6 -7 -5 2 3 }}]
POTE generator: ~6/5 = 283.882


{{Val list|legend=1| 4, 17c, 21, 38ce, 55cde }}
{{Val list|legend=1| 4, 17c, 21, 38ce, 55cde }}


Badness: 0.0367
Badness: 0.0367
</div></div>


= Slurpee =
= Slurpee =
== 5-limit ==
== 5-limit ==


Period: 1\1
[[Comma list]]: 177147/156250


Optimal ([[POTE]]) generators: ~27/25 = 72.742
[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -7 -11 }}]


EDO generators: [[16edo|1\16]], [[17edo|1\17]], [[33edo|2\33]]
[[POTE generator]]: ~27/25 = 72.742
 
Scales:  
 
<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">
 
Comma list: 177147/156250
 
Mapping: [{{val| 1 2 3 }}, {{val| 0 -7 -11 }}]


{{Val list|legend=1| 16, 17c, 33 }}
{{Val list|legend=1| 16, 17c, 33 }}


Badness: 0.6893
[[Badness]]: 0.6893
 
</div></div>


== 7-limit ==
== 7-limit ==


Period: 1\1
[[Comma list]]: 36/35, 51200/50421
 
Optimal ([[POTE]]) generators: ~21/20 = 72.303
 
EDO generators: [[16edo|1\16]], [[17edo|1\17]], [[33edo|2\33]]
 
Scales:
 
<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">


Comma list: 36/35, 51200/50421
[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -7 -11 -3 }}]


Mapping: [{{val| 1 2 3 3 }}, {{val| 0 -7 -11 -3 }}]
{{Multival|legend=1| 7 11 3 1 -15 -24 }}


Wedgie: {{wedgie| 7 11 3 1 -15 -24 }}
[[POTE generator]]: ~21/20 = 72.303


{{Val list|legend=1| 16, 17c, 33, 50cd, 83bcd }}
{{Val list|legend=1| 16, 17c, 33, 50cd, 83bcd }}


Badness: 0.1149
[[Badness]]: 0.1149
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~21/20 = 72.297
EDO generators: [[16edo|1\16]], [[17edo|1\17]], [[33edo|2\33]]
Scales:
<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">


Comma list: 36/35, 121/120, 352/343  
Comma list: 36/35, 121/120, 352/343  


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -7 -11 -3 -9 }}]
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -7 -11 -3 -9 }}]
POTE generator: ~21/20 = 72.297


{{Val list|legend=1| 16, 17c, 33, 50cd, 83bcd }}
{{Val list|legend=1| 16, 17c, 33, 50cd, 83bcd }}


Badness: 0.0505
Badness: 0.0505
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~21/20 = 72.409
EDO generators: [[16edo|1\16]], [[17edo|1\17]], [[33edo|2\33]]
Scales:
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
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Comma list: 36/35. 66/65, 143/140, 352/343
Comma list: 36/35. 66/65, 143/140, 352/343


Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -7 -11 -3 -9 -5 }}]
Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -7 -11 -3 -9 -5 }}]
POTE generator: ~21/20 = 72.409


{{Val list|legend=1| 16, 17c, 33, 83bcd }}
{{Val list|legend=1| 16, 17c, 33, 83bcd }}


Badness: 0.0331
Badness: 0.0331
</div></div>


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

Revision as of 10:03, 28 March 2021

These are low complexity, high error temperaments tempering out the septimal quarter-tone, 36/35. 36 is both a square and a triangular number, and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo.

Progression

5-limit

Comma list: 3456/3125

Mapping: [⟨1 1 2], ⟨0 5 3]]

POTE generator: ~25/24 = 140.995

Template:Val list

Badness: 0.2005

7-limit

Comma list: 36/35, 392/375

Mapping: [⟨1 1 2 2], ⟨0 5 3 7]]

Wedgie: ⟨⟨ 5 3 7 -7 -3 8 ]]

POTE generator: ~15/14 = 140.927

Template:Val list

Badness: 0.0484

11-limit

Comma list: 36/35, 56/55, 77/75

Mapping: [⟨1 1 2 2 3], ⟨0 5 3 7 4]]

POTE generators: ~12/11 = 140.747

Template:Val list

Badness: 0.0261

13-limit

Comma list: 26/25, 36/35, 56/55, 66/65

Mapping: [⟨1 1 2 2 3 3], ⟨0 5 3 7 4 6]]

POTE generators: ~13/12 = 140.751

Template:Val list

Badness: 0.0182

17-limit

Comma list: 26/25, 36/35, 51/50, 56/55, 66/65

Mapping: [⟨1 1 2 2 3 3 4], ⟨0 5 3 7 4 6 1]]

POTE generators: ~13/12 = 141.404

Template:Val list

Badness: 0.0167

19-limit

Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65

Mapping: [⟨1 1 2 2 3 3 4 4], ⟨0 5 3 7 4 6 1 2]]

POTE generators: ~13/12 = 140.479

Template:Val list

Badness: 0.0168

Ripple

See also: Ripple family § Ripple

Comma list: 36/35, 2560/2401

Mapping: [⟨1 2 3 3], ⟨0 -5 -8 -2]]

Wedgie: ⟨⟨ 5 8 2 1 -11 -18 ]]

POTE generator: ~21/20 = 99.483

Template:Val list

Badness: 0.0597

11-limit

Comma list: 36/35, 80/77, 126/121

Mapping: [⟨1 2 3 3 4], ⟨0 -5 -8 -2 -6]]

POTE generator: ~21/20 = 99.385

Template:Val list

Badness: 0.0388

13-limit

Comma list: 36/35, 40/39, 66/65, 147/143

Mapping: [⟨1 2 3 3 4 4], ⟨0 -5 -8 -2 -6 -3]]

POTE generator: ~21/20 = 98.572

Template:Val list

Badness: 0.0316

Smate

5-limit

Comma list: 2048/1875

Mapping: [⟨1 3 2], ⟨0 -4 1]]

POTE generator: ~5/4 = 420.855

Template:Val list

Badness: 0.179

7-limit

Comma list: 36/35, 2048/1875

Mapping: [⟨1 3 2 6], ⟨0 -4 1 -9]]

Wedgie: ⟨⟨ 4 -1 9 -11 3 24 ]]

POTE generator: ~5/4 = 422.275

Template:Val list

Badness: 0.0779

11-limit

Comma list: 36/35, 56/55, 243/242

Mapping: [⟨1 3 2 6 7], ⟨0 -4 1 -9 -10]]

POTE generator: ~5/4 = 422.217

Template:Val list

Badness: 0.0425

13-limit

Comma list: 26/25, 36/35, 56/55, 243/242

Mapping: [⟨1 3 2 6 7 3], ⟨0 -4 1 -9 -10 2]]

POTE generator: ~5/4 = 423.020

Template:Val list

Badness: 0.0368

Hemismate

Comma list: 256/245, 392/375

Mapping: [⟨1 3 2 3], ⟨0 -8 2 -1]]

Wedgie: ⟨⟨ 8 -2 1 -22 -21 8 ]]

POTE generator: ~8/7 = 210.452

Template:Val list

Badness: 0.1543

11-limit

Comma list: 56/55, 77/75, 256/245

Mapping: [⟨1 3 2 3 4], ⟨0 -8 2 -1 -3]]

POTE generator: ~8/7 = 210.481

Template:Val list

Badness: 0.0655

13-limit

Comma list: 26/25, 56/55, 77/75, 256/245

Mapping: [⟨1 3 2 3 4 3], ⟨0 -8 2 -1 -3 4]]

POTE generators: ~8/7 = 210.974

Template:Val list

Badness: 0.0505

Subklei

5-limit

Comma list: 17496/15625

Mapping: [⟨1 3 4], ⟨0 -6 -7]]

POTE generator: ~6/5 = 284.293

Template:Val list

Badness: 0.3559

7-limit

Comma list: 36/35, 1029/1000

Mapping: [⟨1 3 4 4], ⟨0 -6 -7 -5]]

Wedgie: ⟨⟨ 6 7 5 -3 -9 -8 ]]

POTE generator: ~6/5 = 284.219

Template:Val list

Badness: 0.0611

11-limit

Comma list: 36/35, 77/75, 352/343

Mapping: [⟨1 3 4 4 7], ⟨0 -6 -7 -5 -15]]

POTE generator: ~6/5 = 283.253

Template:Val list

Badness: 0.0447

13-limit

Comma list: 26/25, 36/35, 66/65, 352/343

POTE generator: ~6/5 = 282.856

Mapping: [⟨1 3 4 4 7 7], ⟨0 -6 -7 -5 -15 -14]]

POTE generator: ~6/5 = 282.856

Template:Val list

Badness: 0.0323

Subkla

Comma list: 36/35, 56/55, 1029/1000

Mapping: [⟨1 3 4 4 3], ⟨0 -6 -7 -5 2]]

POTE generator: ~6/5 = 283.822

Template:Val list

Badness: 0.0472

13-limit

Comma list: 36/35, 56/55, 66/65, 640/637

Mapping: [⟨1 3 4 4 3 3], ⟨0 -6 -7 -5 2 3]]

POTE generator: ~6/5 = 283.882

Template:Val list

Badness: 0.0367

Slurpee

5-limit

Comma list: 177147/156250

Mapping: [⟨1 2 3], ⟨0 -7 -11]]

POTE generator: ~27/25 = 72.742

Template:Val list

Badness: 0.6893

7-limit

Comma list: 36/35, 51200/50421

Mapping: [⟨1 2 3 3], ⟨0 -7 -11 -3]]

Wedgie: ⟨⟨ 7 11 3 1 -15 -24 ]]

POTE generator: ~21/20 = 72.303

Template:Val list

Badness: 0.1149

11-limit

Comma list: 36/35, 121/120, 352/343

Mapping: [⟨1 2 3 3 4], ⟨0 -7 -11 -3 -9]]

POTE generator: ~21/20 = 72.297

Template:Val list

Badness: 0.0505

13-limit

Comma list: 36/35. 66/65, 143/140, 352/343

Mapping: [⟨1 2 3 3 4 4], ⟨0 -7 -11 -3 -9 -5]]

POTE generator: ~21/20 = 72.409

Template:Val list

Badness: 0.0331

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