Mint temperaments: Difference between revisions

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=== 13-limit ===
=== 13-limit ===
Commas: 26/25, 56/55, 77/75, 256/245
Comma list: 26/25, 56/55, 77/75, 256/245


POTE generator: ~8/7 = 210.974
POTE generator: ~8/7 = 210.974
Line 201: Line 201:
Badness: 0.0505
Badness: 0.0505


=Subklei=
= Subklei =
Comma: 17496/15625
Comma list: 17496/15625


POTE generator: ~6/5 = 284.293
POTE generator: ~6/5 = 284.293


Map: [<1 3 4|, <0 -6 -7|]
Mapping: [{{val| 1 3 4 }}, {{val| 0 -6 -7 }}]


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


Badness: 0.3559
Badness: 0.3559


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


POTE generator: ~6/5 = 284.219
POTE generator: ~6/5 = 284.219


Map: [<1 3 4 4|, <0 -6 -7 -5|]
Mapping: [{{val| 1 3 4 4 }}, {{val| 0 -6 -7 -5 }}]


Wedgie: <<6 7 5 -3 -9 -8||
Wedgie: {{wedgie| 6 7 5 -3 -9 -8 }}


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


Badness: 0.0611
Badness: 0.0611


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


POTE generator: ~6/5 = 283.253
POTE generator: ~6/5 = 283.253


Map: [<1 3 4 4 7|, <0 -6 -7 -5 -15|]
Mapping: [{{val| 1 3 4 4 7 }}, {{val| 0 -6 -7 -5 -15 }}]


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


Badness: 0.0447
Badness: 0.0447


==Subkla==
=== 13-limit ===
Commas: 36/35, 56/55, 1029/1000
Comma list: 26/25, 36/35, 66/65, 352/343


POTE generator: ~6/5 = 283.822
POTE generator: ~6/5 = 282.856


Map: [<1 3 4 4 3|, <0 -6 -7 -5 2|]
Mapping: [{{val| 1 3 4 4 7 7 }}, {{val| 0 -6 -7 -5 -15 -14 }}]


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


Badness: 0.0472
Badness: 0.0323


===13-limit===
== Subkla ==
Commas: 36/35, 56/55, 66/65, 640/637
Comma list: 36/35, 56/55, 1029/1000


POTE generator: ~6/5 = 283.882
POTE generator: ~6/5 = 283.822


Map: [<1 3 4 4 3 3|, <0 -6 -7 -5 2 3|]
Mapping: [{{val| 1 3 4 4 3 }}, {{val| 0 -6 -7 -5 2 }}]


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


Badness: 0.0367
Badness: 0.0472


==13-limit==
=== 13-limit ===
Commas: 26/25, 36/35, 66/65, 352/343
Comma list: 36/35, 56/55, 66/65, 640/637


POTE generator: ~6/5 = 282.856
POTE generator: ~6/5 = 283.882


Map: [<1 3 4 4 7 7|, <0 -6 -7 -5 -15 -14|]
Mapping: [{{val| 1 3 4 4 3 3 }}, {{val| 0 -6 -7 -5 2 3 }}]


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


Badness: 0.0323
Badness: 0.0367


=Slurpee=
= Slurpee =
Comma: 177147/156250  
Comma list: 177147/156250  


POTE generator: ~27/25 = 72.742
POTE generator: ~27/25 = 72.742


Map: [<1 2 3|, <0 -7 -11|]
Mapping: [{{val| 1 2 3 }}, {{val| 0 -7 -11 }}]


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


Badness: 0.6893
Badness: 0.6893


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


POTE generator: ~21/20 = 72.303
POTE generator: ~21/20 = 72.303


Map: [<1 2 3 3|, <0 -7 -11 -3|]
Mapping: [{{val| 1 2 3 3 }}, {{val| 0 -7 -11 -3 }}]


Wedgie: <<7 11 3 1 -15 -24||
Wedgie: {{wedgie| 7 11 3 1 -15 -24 }}


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


Badness: 0.1149
Badness: 0.1149


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


POTE generator: ~21/20 = 72.297
POTE generator: ~21/20 = 72.297


Map: [<1 2 3 3 4|, <0 -7 -11 -3 -9|]
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -7 -11 -3 -9 }}]


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


Badness: 0.0505
Badness: 0.0505


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


POTE generator: ~21/20 = 72.409
POTE generator: ~21/20 = 72.409


Map: [<1 2 3 3 4 4|, <0 -7 -11 -3 -9 -5|]
Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -7 -11 -3 -9 -5 }}]


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


Badness: 0.0331
Badness: 0.0331

Revision as of 10:17, 28 February 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

POTE generator: ~25/24 = 140.995

Mapping: [⟨1 1 2], ⟨0 5 3]]

Template:Val list

Badness: 0.2005

7-limit

Comma list: 36/35, 392/375

POTE generator: ~15/14 = 140.927

Mapping: [⟨1 1 2 2], ⟨0 5 3 7]]

Wedgie: ⟨⟨5 3 7 -7 -3 8]]

Template:Val list

Badness: 0.0484

11-limit

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

POTE generator: ~12/11 = 140.747

Mapping: [⟨1 1 2 2 3], ⟨0 5 3 7 4]]

Template:Val list

Badness: 0.0261

13-limit

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

POTE generator: ~13/12 = 140.751

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

Template:Val list

Badness: 0.0182

17-limit

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

POTE generator: ~13/12 = 141.404

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

Template:Val list

Badness: 0.0167

19-limit

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

POTE generator: ~13/12 = 140.479

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

Comma list: 6561/6250

POTE generator: ~27/25 = 100.838

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

Comma list: 36/35, 2560/2401

POTE generator: ~21/20 = 99.483

Mapping: [⟨1 2 3 3], ⟨0 -5 -8 -2]]

Wedgie: ⟨⟨5 8 2 1 -11 -18]]

Template:Val list

Badness: 0.0597

11-limit

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

POTE generator: ~21/20 = 99.385

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

Template:Val list

Badness: 0.0388

13-limit

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

POTE generator: ~21/20 = 98.572

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

Template:Val list

Badness: 0.0316

Smate

Comma list: 2048/1875

POTE generator: ~5/4 = 420.855

Mapping: [⟨1 3 2], ⟨0 -4 1]]

Template:Val list

Badness: 0.179

7-limit

Comma list: 36/35, 2048/1875

POTE generator: ~5/4 = 422.275

Mapping: [⟨1 3 2 6], ⟨0 -4 1 -9]]

Wedgie: ⟨⟨4 -1 9 -11 3 24]]

Template:Val list

Badness: 0.0779

11-limit

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

POTE generator: ~5/4 = 422.217

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

Template:Val list

Badness: 0.0425

13-limit

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

POTE generator: ~5/4 = 423.020

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

Template:Val list

Badness: 0.0368

Hemismate

Comma list: 256/245, 392/375

POTE generator: ~8/7 = 210.452

Mapping: [⟨1 3 2 3], ⟨0 -8 2 -1]]

Wedgie: ⟨⟨8 -2 1 -22 -21 8]]

Template:Val list

Badness: 0.1543

11-limit

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

POTE generator: ~8/7 = 210.481

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

Template:Val list

Badness: 0.0655

13-limit

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

POTE generator: ~8/7 = 210.974

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

Template:Val list

Badness: 0.0505

Subklei

Comma list: 17496/15625

POTE generator: ~6/5 = 284.293

Mapping: [⟨1 3 4], ⟨0 -6 -7]]

Template:Val list

Badness: 0.3559

7-limit

Comma list: 36/35, 1029/1000

POTE generator: ~6/5 = 284.219

Mapping: [⟨1 3 4 4], ⟨0 -6 -7 -5]]

Wedgie: ⟨⟨6 7 5 -3 -9 -8]]

Template:Val list

Badness: 0.0611

11-limit

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

POTE generator: ~6/5 = 283.253

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

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]]

Template:Val list

Badness: 0.0323

Subkla

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

POTE generator: ~6/5 = 283.822

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

Template:Val list

Badness: 0.0472

13-limit

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

POTE generator: ~6/5 = 283.882

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

Template:Val list

Badness: 0.0367

Slurpee

Comma list: 177147/156250

POTE generator: ~27/25 = 72.742

Mapping: [⟨1 2 3], ⟨0 -7 -11]]

Template:Val list

Badness: 0.6893

7-limit

Comma list: 36/35, 51200/50421

POTE generator: ~21/20 = 72.303

Mapping: [⟨1 2 3 3], ⟨0 -7 -11 -3]]

Wedgie: ⟨⟨7 11 3 1 -15 -24]]

Template:Val list

Badness: 0.1149

11-limit

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

POTE generator: ~21/20 = 72.297

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

Template:Val list

Badness: 0.0505

13-limit

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

POTE generator: ~21/20 = 72.409

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

Template:Val list

Badness: 0.0331

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