Mint temperaments: Difference between revisions

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= Progression =
= Progression =
== 5-limit ==
[[Comma list]]: 3456/3125
[[Comma list]]: 3456/3125


Line 12: Line 10:
{{Val list|legend=1| 8, 9, 17c }}
{{Val list|legend=1| 8, 9, 17c }}


[[Badness]]: 0.2005
[[Badness]]: 0.200483


== 7-limit ==
== 7-limit ==
[[Comma list]]: 36/35, 392/375
[[Comma list]]: 36/35, 392/375


Line 26: Line 23:
{{Val list|legend=1| 8d, 9, 17c }}
{{Val list|legend=1| 8d, 9, 17c }}


[[Badness]]: 0.0484
[[Badness]]: 0.048356


== 11-limit ==
== 11-limit ==
Comma list: 36/35, 56/55, 77/75
Comma list: 36/35, 56/55, 77/75


Line 38: Line 34:
{{Val list|legend=1| 8d, 9, 17c }}
{{Val list|legend=1| 8d, 9, 17c }}


Badness: 0.0261
Badness: 0.026050


== 13-limit ==
== 13-limit ==
Comma list: 26/25, 36/35, 56/55, 66/65
Comma list: 26/25, 36/35, 56/55, 66/65


Line 50: Line 45:
{{Val list|legend=1| 8d, 9, 17c }}
{{Val list|legend=1| 8d, 9, 17c }}


Badness: 0.0182
Badness: 0.018158


== 17-limit ==
== 17-limit ==
Comma list: 26/25, 36/35, 51/50, 56/55, 66/65
Comma list: 26/25, 36/35, 51/50, 56/55, 66/65


Line 62: Line 56:
{{Val list|legend=1| 8d, 9, 17cg }}
{{Val list|legend=1| 8d, 9, 17cg }}


Badness: 0.0167
Badness: 0.016743


== 19-limit ==
== 19-limit ==
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


Line 72: Line 65:
POTE generators: ~13/12 = 140.479
POTE generators: ~13/12 = 140.479


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


Badness: 0.0168
Badness: 0.016841


= Ripple =
= Ripple =
Line 87: Line 80:
[[POTE generator]]: ~21/20 = 99.483
[[POTE generator]]: ~21/20 = 99.483


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


[[Badness]]: 0.0597
[[Badness]]: 0.059735


== 11-limit ==
== 11-limit ==
Comma list: 36/35, 80/77, 126/121
Comma list: 36/35, 80/77, 126/121


Line 99: Line 91:
POTE generator: ~21/20 = 99.385
POTE generator: ~21/20 = 99.385


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


Badness: 0.0388
Badness: 0.038811


== 13-limit ==
== 13-limit ==
Comma list: 36/35, 40/39, 66/65, 147/143
Comma list: 36/35, 40/39, 66/65, 147/143


Line 111: Line 102:
POTE generator: ~21/20 = 98.572
POTE generator: ~21/20 = 98.572


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


Badness: 0.0316
Badness: 0.031639


= Smate =
= Smate =
Line 128: Line 119:
{{Val list|legend=1| 3d, 11d, 14, 17c, 37cd }}
{{Val list|legend=1| 3d, 11d, 14, 17c, 37cd }}


[[Badness]]: 0.0779
[[Badness]]: 0.077871


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


Line 140: Line 130:
{{Val list|legend=1| 14, 17c, 37cde }}
{{Val list|legend=1| 14, 17c, 37cde }}


Badness: 0.0425
Badness: 0.042518


== 13-limit ==
== 13-limit ==
Comma list: 26/25, 36/35, 56/55, 243/242  
Comma list: 26/25, 36/35, 56/55, 243/242  


Line 152: Line 141:
{{Val list|legend=1| 14, 17c }}
{{Val list|legend=1| 14, 17c }}


Badness: 0.0368
Badness: 0.036836


= Subklei =
= Subklei =
== 5-limit ==
[[Comma list]]: 17496/15625
[[Comma list]]: 17496/15625


Line 165: Line 152:
{{Val list|legend=1| 4, 17c, 21, 38c }}
{{Val list|legend=1| 4, 17c, 21, 38c }}


[[Badness]]: 0.3559
[[Badness]]: 0.355937


== 7-limit ==
== 7-limit ==
[[Comma list]]: 36/35, 1029/1000
[[Comma list]]: 36/35, 1029/1000


Line 179: Line 165:
{{Val list|legend=1| 4, 17c, 21, 38c }}
{{Val list|legend=1| 4, 17c, 21, 38c }}


[[Badness]]: 0.0611
[[Badness]]: 0.061101


== 11-limit ==
== 11-limit ==
Comma list: 36/35, 77/75, 352/343
Comma list: 36/35, 77/75, 352/343


Line 191: Line 176:
{{Val list|legend=1| 17c, 55cd }}
{{Val list|legend=1| 17c, 55cd }}


Badness: 0.0447
Badness: 0.044651


=== 13-limit ===
=== 13-limit ===
Comma list: 26/25, 36/35, 66/65, 352/343  
Comma list: 26/25, 36/35, 66/65, 352/343  


Line 205: Line 189:
{{Val list|legend=1| 17c }}
{{Val list|legend=1| 17c }}


Badness: 0.0323
Badness: 0.032324


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


Line 217: Line 200:
{{Val list|legend=1| 4, 17c, 21, 38ce, 55cde }}
{{Val list|legend=1| 4, 17c, 21, 38ce, 55cde }}


Badness: 0.0472
Badness: 0.047247


=== 13-limit ===
=== 13-limit ===
Comma list: 36/35, 56/55, 66/65, 640/637
Comma list: 36/35, 56/55, 66/65, 640/637


Line 229: Line 211:
{{Val list|legend=1| 4, 17c, 21, 38ce, 55cde }}
{{Val list|legend=1| 4, 17c, 21, 38ce, 55cde }}


Badness: 0.0367
Badness: 0.036701


= Slurpee =
= Slurpee =
== 5-limit ==
[[Comma list]]: 177147/156250  
[[Comma list]]: 177147/156250  


Line 242: Line 222:
{{Val list|legend=1| 16, 17c, 33 }}
{{Val list|legend=1| 16, 17c, 33 }}


[[Badness]]: 0.6893
[[Badness]]: 0.689274


== 7-limit ==
== 7-limit ==
[[Comma list]]: 36/35, 51200/50421
[[Comma list]]: 36/35, 51200/50421


Line 256: Line 235:
{{Val list|legend=1| 16, 17c, 33, 50cd, 83bcd }}
{{Val list|legend=1| 16, 17c, 33, 50cd, 83bcd }}


[[Badness]]: 0.1149
[[Badness]]: 0.114869


== 11-limit ==
== 11-limit ==
Comma list: 36/35, 121/120, 352/343  
Comma list: 36/35, 121/120, 352/343  


Line 268: Line 246:
{{Val list|legend=1| 16, 17c, 33, 50cd, 83bcd }}
{{Val list|legend=1| 16, 17c, 33, 50cd, 83bcd }}


Badness: 0.0505
Badness: 0.050514


== 13-limit ==
== 13-limit ==
Comma list: 36/35. 66/65, 143/140, 352/343
Comma list: 36/35. 66/65, 143/140, 352/343


Line 280: Line 257:
{{Val list|legend=1| 16, 17c, 33, 83bcd }}
{{Val list|legend=1| 16, 17c, 33, 83bcd }}


Badness: 0.0331
Badness: 0.033102
 
= Penta =
[[Comma list]]: 144/125
 
[[Mapping]]: [{{val| 1 1 2 }}, {{val| 0 3 2 }}]
 
[[POTE generator]]: ~6/5 = 235.442
 
{{Val list|legend=1| 1b, 5 }}
 
[[Badness]]: 0.101806
 
== 7-limit ==
[[Comma list]]: 36/35, 28/25
 
[[Mapping]]: [{{val| 1 1 2 2 }}, {{val| 0 3 2 4 }}]
 
{{Multival|legend=1| 3 2 4 -4 -2 4 }}
 
[[POTE generator]]: ~6/5 = 239.977
 
{{Val list|legend=1| 1bd, 5 }}
 
[[Badness]]: 0.046882


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]

Revision as of 03:34, 9 April 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

Comma list: 3456/3125

Mapping: [⟨1 1 2], ⟨0 5 3]]

POTE generator: ~25/24 = 140.995

Template:Val list

Badness: 0.200483

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: 0.048356

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: 0.026050

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: 0.018158

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: 0.016743

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: 0.016841

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: 0.059735

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: 0.038811

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: 0.031639

Smate

See also: Smate family § Smate

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: 0.077871

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: 0.042518

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: 0.036836

Subklei

Comma list: 17496/15625

Mapping: [⟨1 3 4], ⟨0 -6 -7]]

POTE generator: ~6/5 = 284.293

Template:Val list

Badness: 0.355937

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: 0.061101

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: 0.044651

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: 0.032324

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: 0.047247

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: 0.036701

Slurpee

Comma list: 177147/156250

Mapping: [⟨1 2 3], ⟨0 -7 -11]]

POTE generator: ~27/25 = 72.742

Template:Val list

Badness: 0.689274

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: 0.114869

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: 0.050514

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: 0.033102

Penta

Comma list: 144/125

Mapping: [⟨1 1 2], ⟨0 3 2]]

POTE generator: ~6/5 = 235.442

Template:Val list

Badness: 0.101806

7-limit

Comma list: 36/35, 28/25

Mapping: [⟨1 1 2 2], ⟨0 3 2 4]]

Wedgie: ⟨⟨ 3 2 4 -4 -2 4 ]]

POTE generator: ~6/5 = 239.977

Template:Val list

Badness: 0.046882

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