Wizmic microtemperaments: Difference between revisions

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Line 23: Line 23:
[[Comma list]]: 420175/419904, 703125/702464
[[Comma list]]: 420175/419904, 703125/702464


[[Mapping]]: [{{val| 1 -14 -3 -20 }}, {{val| 0 41 14 60 }}]
[[Mapping]]: [{{val| 1 27 11 40 }}, {{val| 0 -41 -14 -60 }}]
 
Mapping generators: ~2, ~192/125


{{Multival|legend=1| 41 14 60 -73 -20 100 }}
{{Multival|legend=1| 41 14 60 -73 -20 100 }}


[[POTE generator]]: ~125/96 = 456.144
[[POTE generator]]: ~192/125 = 743.856


{{Val list|legend=1| 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd }}
{{Val list|legend=1| 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd }}
Line 38: Line 40:
[[Comma list]]: 420175/419904, 5250987/5242880
[[Comma list]]: 420175/419904, 5250987/5242880


[[Mapping]]: [{{val| 1 -1 -11 4 }}, {{val| 0 13 67 -6 }}]
[[Mapping]]: [{{val| 1 12 56 -2 }}, {{val| 0 -13 -67 6 }}]
 
Mapping generators: ~2, ~256/147


{{Multival|legend=1| 13 67 -6 76 -46 -202 }}
{{Multival|legend=1| 13 67 -6 76 -46 -202 }}


[[POTE generator]]: ~147/128 = 238.599
[[POTE generator]]: ~256/147 = 961.401


{{Val list|legend=1| 5, 161c, 166, 171, 1544d, 1715d, 1886d, 2057d, 2228d, 2399d, 2570d, 2741d, 2912dd, 3083cdd }}
{{Val list|legend=1| 5, 161c, 166, 171, 1544d, 1715d, 1886d, 2057d, 2228d, 2399d, 2570d, 2741d, 2912dd, 3083cdd }}
Line 55: Line 59:
[[Comma list]]: 420175/419904, 29360128/29296875
[[Comma list]]: 420175/419904, 29360128/29296875


[[Mapping]]: [{{val| 1 -4 2 -6 }}, {{val| 0 52 3 82 }}]
[[Mapping]]: [{{val| 1 48 5 76 }}, {{val| 0 -52 -3 -82 }}]
 
Mapping generators: ~2, ~6272/3375


{{Multival|legend=1| 52 3 82 -116 -16 182 }}
{{Multival|legend=1| 52 3 82 -116 -16 182 }}


[[POTE generator]]: ~3375/3136 = 128.8879
[[POTE generator]]: ~6272/3375 = 1071.1121


{{Val list|legend=1| 121, 149, 270, 2309c, 2579c, 2849c, 3119bc, 3389bc, 3659bcc, 3929bcc, 4199bcc }}
{{Val list|legend=1| 121, 149, 270, 2309c, 2579c, 2849c, 3119bc, 3389bc, 3659bcc, 3929bcc, 4199bcc }}
Line 70: Line 76:
Comma list: 3025/3024, 5632/5625, 117649/117612
Comma list: 3025/3024, 5632/5625, 117649/117612


Mapping: [{{val| 1 -4 2 -6 -9 }}, {{val| 0 52 3 82 116 }}]
Mapping: [{{val| 1 48 5 76 107 }}, {{val| 0 -52 -3 -82 -116 }}]


POTE generator: ~264/245 = 128.8898
POTE generator: ~245/132 = 1071.1102


Vals: {{Val list| 121, 149, 270, 2551bc, 2821bc, 3091bc, 3361bc, 3631bbcc, 3901bbccd, 4171bbccd, 4441bbccd, 4711bbccd }}
Vals: {{Val list| 121, 149, 270, 2551bc, 2821bc, 3091bc, 3361bc, 3631bbcc, 3901bbccd, 4171bbccd, 4441bbccd, 4711bbccd }}
Line 83: Line 89:
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224


Mapping: [{{val| 1 -4 2 -6 -9 -5 }}, {{val| 0 52 3 82 116 81 }}]
Mapping: [{{val| 1 48 5 76 107 76 }}, {{val| 0 -52 -3 -82 -116 -81 }}]


POTE generator: ~14/13 = 128.8902
POTE generator: ~13/7 = 1071.1098


Vals: {{Val list| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}
Vals: {{Val list| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}
Line 96: Line 102:
Comma list: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224
Comma list: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224


Mapping: [{{val| 1 -4 2 -6 -9 -5 -3 }}, {{val| 0 52 3 82 116 81 66 }}]
Mapping: [{{val| 1 48 5 76 107 76 63 }}, {{val| 0 -52 -3 -82 -116 -81 -66 }}]


POTE generator: ~14/13 = 128.8912
POTE generator: ~13/7 = 1071.1088


Vals: {{Val list| 121, 149, 270 }}
Vals: {{Val list| 121, 149, 270 }}
Line 113: Line 119:
[[Comma list]]: 420175/419904, 1600000/1594323
[[Comma list]]: 420175/419904, 1600000/1594323


[[Mapping]]: [{{val| 1 -7 -20 -2 }}, {{val| 0 25 65 14 }}
[[Mapping]]: [{{val| 1 18 45 12 }}, {{val| 0 -25 -65 -14 }}
 
Mapping generators: ~2, ~63/40


{{Multival|legend=1| 25 65 14 45 -48 -150 }}
{{Multival|legend=1| 25 65 14 45 -48 -150 }}


[[POTE generator]]: ~80/63 = 412.098
[[POTE generator]]: ~63/40 = 787.902


{{Val list|legend=1| 99, 265, 364, 463, 562, 1025 }}
{{Val list|legend=1| 99, 265, 364, 463, 562, 1025 }}
Line 128: Line 136:
Comma list: 9801/9800, 41503/41472, 585640/583443
Comma list: 9801/9800, 41503/41472, 585640/583443


Mapping: [{{val|2 11 25 10 16}}, {{val|0 -25 -65 -14 -29}}]
Mapping: [{{val| 2 11 25 10 16 }}, {{val| 0 -25 -65 -14 -29 }}]
 
Mapping generators: ~99/70, ~49/44


POTE generator: ~49/44 = 187.904
POTE generator: ~49/44 = 187.904
Line 141: Line 151:
Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280
Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280


Mapping: [{{val|2 11 25 10 16 24}}, {{val|0 -25 -65 -14 -29 -53}}]
Mapping: [{{val| 2 11 25 10 16 24 }}, {{val| 0 -25 -65 -14 -29 -53 }}]


POTE generator: ~39/35 = 187.904
POTE generator: ~39/35 = 187.904
Line 154: Line 164:
Comma list: 3025/3024, 117649/117612, 1600000/1594323
Comma list: 3025/3024, 117649/117612, 1600000/1594323


Mapping: [{{val|1 18 45 12 -10}}, {{val|0 -50 -130 -28 41}}]
Mapping: [{{val| 1 18 45 12 -10 }}, {{val| 0 -50 -130 -28 41 }}]
 
Mapping generators: ~2, ~1120/891


POTE generator: ~1120/891 = 393.950
POTE generator: ~1120/891 = 393.950
Line 167: Line 179:
Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323
Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323


Mapping: [{{val|1 18 45 12 -10 71}}, {{val|0 -50 -130 -28 41 -205}}]
Mapping: [{{val| 1 18 45 12 -10 71 }}, {{val| 0 -50 -130 -28 41 -205 }}]


POTE generator: ~1120/891 = 393.948
POTE generator: ~1120/891 = 393.948
Line 180: Line 192:
Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561
Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561


Mapping: [{{val|1 18 45 12 -10 6}}, {{val|0 -50 -130 -28 41 -7}}]
Mapping: [{{val| 1 18 45 12 -10 6 }}, {{val| 0 -50 -130 -28 41 -7 }}]


POTE generator: ~49/39 = 393.949
POTE generator: ~49/39 = 393.949

Revision as of 15:54, 31 December 2021

This is a collection of microtemperaments which tempers out the wizma, [-6 -8 2 5⟩ = 420175/419904.

Discussed elsewhere are:

Qak

Subgroup: 2.3.5.7

Comma list: 420175/419904, 703125/702464

Mapping: [⟨1 27 11 40], ⟨0 -41 -14 -60]]

Mapping generators: ~2, ~192/125

Wedgie: ⟨⟨ 41 14 60 -73 -20 100 ]]

POTE generator: ~192/125 = 743.856

Template:Val list

Badness: 0.029267

Tokko

Subgroup: 2.3.5.7

Comma list: 420175/419904, 5250987/5242880

Mapping: [⟨1 12 56 -2], ⟨0 -13 -67 6]]

Mapping generators: ~2, ~256/147

Wedgie: ⟨⟨ 13 67 -6 76 -46 -202 ]]

POTE generator: ~256/147 = 961.401

Template:Val list

Badness: 0.044417

Tertiathirds

The tertiathirds temperament (121&270) tempers out the quasiorwellisma, 29360128/29296875 in the 7-limit, as well as the wizma. This temperament splits the interval of 5/4 into three 14/13 generators.

Subgroup: 2.3.5.7

Comma list: 420175/419904, 29360128/29296875

Mapping: [⟨1 48 5 76], ⟨0 -52 -3 -82]]

Mapping generators: ~2, ~6272/3375

Wedgie: ⟨⟨ 52 3 82 -116 -16 182 ]]

POTE generator: ~6272/3375 = 1071.1121

Template:Val list

Badness: 0.093005

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 5632/5625, 117649/117612

Mapping: [⟨1 48 5 76 107], ⟨0 -52 -3 -82 -116]]

POTE generator: ~245/132 = 1071.1102

Vals: Template:Val list

Badness: 0.033322

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224

Mapping: [⟨1 48 5 76 107 76], ⟨0 -52 -3 -82 -116 -81]]

POTE generator: ~13/7 = 1071.1098

Vals: Template:Val list

Badness: 0.019494

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224

Mapping: [⟨1 48 5 76 107 76 63], ⟨0 -52 -3 -82 -116 -81 -66]]

POTE generator: ~13/7 = 1071.1088

Vals: Template:Val list

Badness: 0.019107

Witch

See also: Amity family

The witch temperament (99&166) tempers out wizma (420175/419904) and the amity comma (1600000/1594323) as well as the hemfiness comma (4096000/4084101, saquinru-atriyo).

Subgroup: 2.3.5.7

Comma list: 420175/419904, 1600000/1594323

Mapping: [⟨1 18 45 12], ⟨0 -25 -65 -14]

Mapping generators: ~2, ~63/40

Wedgie: ⟨⟨ 25 65 14 45 -48 -150 ]]

POTE generator: ~63/40 = 787.902

Template:Val list

Badness: 0.080608

Semiwitch

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 41503/41472, 585640/583443

Mapping: [⟨2 11 25 10 16], ⟨0 -25 -65 -14 -29]]

Mapping generators: ~99/70, ~49/44

POTE generator: ~49/44 = 187.904

Vals: Template:Val list

Badness: 0.088189

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280

Mapping: [⟨2 11 25 10 16 24], ⟨0 -25 -65 -14 -29 -53]]

POTE generator: ~39/35 = 187.904

Vals: Template:Val list

Badness: 0.038009

Hitch

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 117649/117612, 1600000/1594323

Mapping: [⟨1 18 45 12 -10], ⟨0 -50 -130 -28 41]]

Mapping generators: ~2, ~1120/891

POTE generator: ~1120/891 = 393.950

Vals: Template:Val list

Badness: 0.093482

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323

Mapping: [⟨1 18 45 12 -10 71], ⟨0 -50 -130 -28 41 -205]]

POTE generator: ~1120/891 = 393.948

Vals: Template:Val list

Badness: 0.060716

Hitcher

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561

Mapping: [⟨1 18 45 12 -10 6], ⟨0 -50 -130 -28 41 -7]]

POTE generator: ~49/39 = 393.949

Vals: Template:Val list

Badness: 0.059591

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