Mint temperaments: Difference between revisions

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= Progression =
= Progression =
== 5-limit ==
== 5-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~25/24 = 140.995
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: 3456/3125
Comma list: 3456/3125


Line 12: Line 25:


Badness: 0.2005
Badness: 0.2005
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~15/14 = 140.927
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, 392/375
Comma list: 36/35, 392/375
POTE generator: ~15/14 = 140.927


Mapping: [{{val| 1 1 2 2 }}, {{val| 0 5 3 7 }}]
Mapping: [{{val| 1 1 2 2 }}, {{val| 0 5 3 7 }}]
Line 25: Line 51:


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
[[POTE generator]]: ~12/11 = 140.747


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 }}]
Line 36: Line 75:


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
[[POTE generator]]: ~13/12 = 140.751


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 }}]
Line 47: Line 99:


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
[[POTE generator]]: ~13/12 = 141.404


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 }}]
Line 58: Line 123:


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
[[POTE generator]]: ~13/12 = 140.479


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 }}]
Line 69: Line 147:


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


= Ripple =
= Ripple =
== 5-limit ==
== 5-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~27/25 = 100.838
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: 6561/6250
Comma list: 6561/6250
POTE generator: ~27/25 = 100.838


Mapping: [{{val| 1 2 3 }}, {{val| 0 -5 -8 }}]
Mapping: [{{val| 1 2 3 }}, {{val| 0 -5 -8 }}]
Line 81: Line 172:


Badness: 0.1389
Badness: 0.1389
</div></div>


== 7-limit ==
== 7-limit ==
{{see also| Slendro clan #Hemiripple }}
{{see also| Slendro clan #Hemiripple }}
{{see also| Sensamagic clan #Cohemiripple }}
{{see also| Sensamagic clan #Cohemiripple }}
Period: 1\1
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
Comma list: 36/35, 2560/2401
[[POTE generator]]: ~21/20 = 99.483


Mapping: [{{val| 1 2 3 3 }}, {{val| 0 -5 -8 -2 }}]
Mapping: [{{val| 1 2 3 3 }}, {{val| 0 -5 -8 -2 }}]
Line 97: Line 200:


Badness: 0.0597
Badness: 0.0597
</div></div>


== 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
POTE generator: ~21/20 = 99.385


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 }}]
Line 108: Line 224:


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
POTE generator: ~21/20 = 98.572


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 }}]
Line 119: Line 248:


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


= Smate =
= Smate =
== 5-limit ==
Period: 1\1
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
Comma list: 2048/1875
POTE generator: ~5/4 = 420.855


Mapping: [{{val| 1 3 2 }}, {{val| 0 -4 1 }}]
Mapping: [{{val| 1 3 2 }}, {{val| 0 -4 1 }}]
Line 130: Line 273:


Badness: 0.179
Badness: 0.179
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
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;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Comma list: 36/35, 2048/1875
Comma list: 36/35, 2048/1875
POTE generator: ~5/4 = 422.275


Mapping: [{{val| 1 3 2 6 }}, {{val| 0 -4 1 -9 }}]
Mapping: [{{val| 1 3 2 6 }}, {{val| 0 -4 1 -9 }}]
Line 143: Line 299:


Badness: 0.0779
Badness: 0.0779
</div></div>


=== 11-limit ===
=== 11-limit ===
Comma list: 36/35 56/55 243/242


POTE generator: ~5/4 = 422.217
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


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 }}]
Line 154: Line 323:


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  
POTE generator: ~5/4 = 423.020


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 }}]
Line 165: Line 347:


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  
POTE generator: ~8/7 = 210.452


Mapping: [{{val| 1 3 2 3 }}, {{val| 0 -8 2 -1 }}]
Mapping: [{{val| 1 3 2 3 }}, {{val| 0 -8 2 -1 }}]
Line 178: Line 373:


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
POTE generator: ~8/7 =  210.481


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 }}]
Line 189: Line 397:


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
POTE generator: ~8/7 = 210.974


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 }}]
Line 200: Line 421:


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


= Subklei =
= Subklei =
== 5-limit ==
Period: 1\1
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
Comma list: 17496/15625
POTE generator: ~6/5 = 284.293


Mapping: [{{val| 1 3 4 }}, {{val| 0 -6 -7 }}]
Mapping: [{{val| 1 3 4 }}, {{val| 0 -6 -7 }}]
Line 211: Line 446:


Badness: 0.3559
Badness: 0.3559
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~6/5 = 284.219
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, 1029/1000
Comma list: 36/35, 1029/1000
POTE generator: ~6/5 = 284.219


Mapping: [{{val| 1 3 4 4 }}, {{val| 0 -6 -7 -5 }}]
Mapping: [{{val| 1 3 4 4 }}, {{val| 0 -6 -7 -5 }}]
Line 224: Line 472:


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
POTE generator: ~6/5 = 283.253


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 }}]
Line 235: Line 496:


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 246: Line 522:


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
POTE generator: ~6/5 = 283.822


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 }}]
Line 257: Line 546:


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
POTE generator: ~6/5 = 283.882


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 }}]
Line 268: Line 570:


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


= Slurpee =
= Slurpee =
== 5-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~27/25 = 72.742
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: 177147/156250  
Comma list: 177147/156250  
POTE generator: ~27/25 = 72.742


Mapping: [{{val| 1 2 3 }}, {{val| 0 -7 -11 }}]
Mapping: [{{val| 1 2 3 }}, {{val| 0 -7 -11 }}]
Line 279: Line 595:


Badness: 0.6893
Badness: 0.6893
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
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
Comma list: 36/35, 51200/50421
POTE generator: ~21/20 = 72.303


Mapping: [{{val| 1 2 3 3 }}, {{val| 0 -7 -11 -3 }}]
Mapping: [{{val| 1 2 3 3 }}, {{val| 0 -7 -11 -3 }}]
Line 292: Line 621:


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  
POTE generator: ~21/20 = 72.297


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 }}]
Line 303: Line 645:


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>
<div class="mw-collapsible-content">
Comma list: 36/35. 66/65, 143/140, 352/343
Comma list: 36/35. 66/65, 143/140, 352/343
POTE generator: ~21/20 = 72.409


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 }}]
Line 314: Line 669:


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


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

Revision as of 13:22, 3 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

Period: 1\1

Optimal (POTE) generators: ~25/24 = 140.995

EDO generators: 1\8, 1\9, 2\17

Scales:

Technical data

Comma list: 3456/3125

POTE generator: ~25/24 = 140.995

Mapping: [⟨1 1 2], ⟨0 5 3]]

Template:Val list

Badness: 0.2005

7-limit

Period: 1\1

Optimal (POTE) generators: ~15/14 = 140.927

EDO generators: 1\8, 1\9, 2\17

Scales:

Technical data

Comma list: 36/35, 392/375

Mapping: [⟨1 1 2 2], ⟨0 5 3 7]]

Wedgie: ⟨⟨5 3 7 -7 -3 8]]

Template:Val list

Badness: 0.0484

11-limit

Period: 1\1

Optimal (POTE) generators: ~12/11 = 140.747

EDO generators: 1\8, 1\9, 2\17

Scales:

Technical data

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

Mapping: [⟨1 1 2 2 3], ⟨0 5 3 7 4]]

Template:Val list

Badness: 0.0261

13-limit

Period: 1\1

Optimal (POTE) generators: ~13/12 = 140.751

EDO generators: 1\8, 1\9, 2\17

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0182

17-limit

Period: 1\1

Optimal (POTE) generators: ~13/12 = 141.404

EDO generators: 1\8, 1\9, 2\17

Scales:

Technical data

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]]

Template:Val list

Badness: 0.0167

19-limit

Period: 1\1

Optimal (POTE) generators: ~13/12 = 140.479

EDO generators: 1\8, 1\9, 2\17

Scales:

Technical data

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]]

Template:Val list

Badness: 0.0168

Ripple

5-limit

Period: 1\1

Optimal (POTE) generators: ~27/25 = 100.838

EDO generators: 1\8, 1\9, 2\17

Scales:

Technical data

Comma list: 6561/6250

Mapping: [⟨1 2 3], ⟨0 -5 -8]]

Template:Val list

Badness: 0.1389

7-limit

See also: Slendro clan § Hemiripple
See also: Sensamagic clan § Cohemiripple

Period: 1\1

Optimal (POTE) generators: ~21/20 = 99.483

EDO generators: 1\11, 1\12, 1\13

Scales:

Technical data

Comma list: 36/35, 2560/2401

Mapping: [⟨1 2 3 3], ⟨0 -5 -8 -2]]

Wedgie: ⟨⟨5 8 2 1 -11 -18]]

Template:Val list

Badness: 0.0597

11-limit

Period: 1\1

Optimal (POTE) generators: ~21/20 = 99.385

EDO generators: 1\11, 1\12, 1\13

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0388

13-limit

Period: 1\1

Optimal (POTE) generators: ~21/20 = 98.572

EDO generators: 1\11, 1\12, 1\13

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0316

Smate

5-limit

Period: 1\1

Optimal (POTE) generators: ~5/4 = 420.855

EDO generators: 5\14, 6\17, 7\20

Scales:

Technical data

Comma list: 2048/1875

Mapping: [⟨1 3 2], ⟨0 -4 1]]

Template:Val list

Badness: 0.179

7-limit

Period: 1\1

Optimal (POTE) generators: ~5/4 = 422.275

EDO generators: 5\14, 6\17, 7\20

Scales:

Technical data

Comma list: 36/35, 2048/1875

Mapping: [⟨1 3 2 6], ⟨0 -4 1 -9]]

Wedgie: ⟨⟨4 -1 9 -11 3 24]]

Template:Val list

Badness: 0.0779

11-limit

Period: 1\1

Optimal (POTE) generators: ~5/4 = 422.217

EDO generators: 5\14, 6\17, 7\20

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0425

13-limit

Period: 1\1

Optimal (POTE) generators: ~5/4 = 423.020

EDO generators: 5\14, 6\17, 7\20

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0368

Hemismate

Period: 1\1

Optimal (POTE) generators: ~8/7 = 210.452

EDO generators: 2\11, 3\17, 4\23

Scales:

Technical data

Comma list: 256/245, 392/375

Mapping: [⟨1 3 2 3], ⟨0 -8 2 -1]]

Wedgie: ⟨⟨8 -2 1 -22 -21 8]]

Template:Val list

Badness: 0.1543

11-limit

Period: 1\1

Optimal (POTE) generators: ~8/7 = 210.481

EDO generators: 2\11, 3\17, 4\23

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0655

13-limit

Period: 1\1

Optimal (POTE) generators: ~8/7 = 210.974

EDO generators: 2\11, 3\17, 4\23

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0505

Subklei

5-limit

Period: 1\1

Optimal (POTE) generators: ~6/5 = 284.293

EDO generators: 4\17, 5\21

Scales:

Technical data

Comma list: 17496/15625

Mapping: [⟨1 3 4], ⟨0 -6 -7]]

Template:Val list

Badness: 0.3559

7-limit

Period: 1\1

Optimal (POTE) generators: ~6/5 = 284.219

EDO generators: 4\17, 5\21

Scales:

Technical data

Comma list: 36/35, 1029/1000

Mapping: [⟨1 3 4 4], ⟨0 -6 -7 -5]]

Wedgie: ⟨⟨6 7 5 -3 -9 -8]]

Template:Val list

Badness: 0.0611

11-limit

Period: 1\1

Optimal (POTE) generators: ~6/5 = 283.253

EDO generators: 4\17, 5\21

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0447

13-limit

Period: 1\1

Optimal (POTE) generators: ~6/5 = 282.856

EDO generators: 4\17, 5\21

Scales:

Technical data

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]]

Template:Val list

Badness: 0.0323

Subkla

Period: 1\1

Optimal (POTE) generators: ~6/5 = 283.822

EDO generators: 4\17, 5\21

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0472

13-limit

Period: 1\1

Optimal (POTE) generators: ~6/5 = 283.882

EDO generators: 4\17, 5\21

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0367

Slurpee

5-limit

Period: 1\1

Optimal (POTE) generators: ~27/25 = 72.742

EDO generators: 1\16, 1\17, 2\33

Scales:

Technical data

Comma list: 177147/156250

Mapping: [⟨1 2 3], ⟨0 -7 -11]]

Template:Val list

Badness: 0.6893

7-limit

Period: 1\1

Optimal (POTE) generators: ~21/20 = 72.303

EDO generators: 1\16, 1\17, 2\33

Scales:

Technical data

Comma list: 36/35, 51200/50421

Mapping: [⟨1 2 3 3], ⟨0 -7 -11 -3]]

Wedgie: ⟨⟨7 11 3 1 -15 -24]]

Template:Val list

Badness: 0.1149

11-limit

Period: 1\1

Optimal (POTE) generators: ~21/20 = 72.297

EDO generators: 1\16, 1\17, 2\33

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0505

13-limit

Period: 1\1

Optimal (POTE) generators: ~21/20 = 72.409

EDO generators: 1\16, 1\17, 2\33

Scales:

Technical data

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

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

Template:Val list

Badness: 0.0331

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