Stearnsmic clan: Difference between revisions

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* [[Harry]], {2401/2400, 19683/19600} → [[Gravity family #Harry|Gravity family]] and [[Breedsmic temperaments #Harry|Breedsmic temperaments]]
* [[Harry]], {2401/2400, 19683/19600} → [[Gravity family #Harry|Gravity family]] and [[Breedsmic temperaments #Harry|Breedsmic temperaments]]
* ''[[Octoid]]'', {4375/4374, 16875/16807} → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
* ''[[Octoid]]'', {4375/4374, 16875/16807} → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
* ''[[Septisuperfourth]]'', {6144/6125, 118098/117649} → [[Escapade family #Septisuperfourth aka biscapade|Escapade family]]
* ''[[Septisuperfourth]]'', {6144/6125, 118098/117649} → [[Escapade family #Septisuperfourth|Escapade family]]
* ''[[Pogo]]'', {32805/32768, 118098/117649} → [[Schismatic family #Pogo|Schismatic family]]
* ''[[Pogo]]'', {32805/32768, 118098/117649} → [[Schismatic family #Pogo|Schismatic family]]


Line 49: Line 49:
POTE generator: ~9/7 = 434.217
POTE generator: ~9/7 = 434.217


Vals: {{Val list| 58, 94, 152 }}
Optimal GPV sequence: {{Val list| 58, 94, 152 }}


Badness: 0.028240
Badness: 0.028240
Line 62: Line 62:
POTE generator: ~9/7 = 434.221
POTE generator: ~9/7 = 434.221


Vals: {{Val list| 58, 94, 152f }}
Optimal GPV sequence: {{Val list| 58, 94, 152f }}


Badness: 0.021645
Badness: 0.021645
Line 75: Line 75:
POTE generator: ~9/7 = 434.181
POTE generator: ~9/7 = 434.181


Vals: {{Val list| 58, 94, 152f }}
Optimal GPV sequence: {{Val list| 58, 94, 152f }}


Badness: 0.021316
Badness: 0.021316
Line 105: Line 105:
POTE generator: ~567/500 = 216.950
POTE generator: ~567/500 = 216.950


Vals: {{Val list| 72, 282, 354 }}
Optimal GPV sequence: {{Val list| 72, 282, 354 }}


Badness: 0.032096
Badness: 0.032096
Line 135: Line 135:
POTE generator: ~5/4 = 386.5968
POTE generator: ~5/4 = 386.5968


Vals: {{Val list| 94, 282, 376, 658de }}
Optimal GPV sequence: {{Val list| 94, 282, 376, 658de }}


Badness: 0.082255
Badness: 0.082255
Line 148: Line 148:
POTE generator: ~5/4 = 386.8141
POTE generator: ~5/4 = 386.8141


Vals: {{Val list| 94, 282 }}
Optimal GPV sequence: {{Val list| 94, 282 }}


Badness: 0.045941
Badness: 0.045941
Line 161: Line 161:
POTE generator: ~5/4 = 386.8420
POTE generator: ~5/4 = 386.8420


Vals: {{Val list| 94, 282 }}
Optimal GPV sequence: {{Val list| 94, 282 }}


Badness: 0.027608
Badness: 0.027608
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POTE generator: ~6/5 = 314.079
POTE generator: ~6/5 = 314.079


Vals: {{Val list| 50, 80, 130, 210e, 340ce }}
Optimal GPV sequence: {{Val list| 50, 80, 130, 210e, 340ce }}


Badness: 0.038556
Badness: 0.038556
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POTE generator: ~6/5 = 313.947
POTE generator: ~6/5 = 313.947


Vals: {{Val list| 50, 80, 130 }}
Optimal GPV sequence: {{Val list| 50, 80, 130 }}


Badness: 0.026895
Badness: 0.026895
Line 219: Line 219:
POTE generator: ~6/5 = 313.931
POTE generator: ~6/5 = 313.931


Vals: {{Val list| 50, 80, 130 }}
Optimal GPV sequence: {{Val list| 50, 80, 130 }}


Badness: 0.024234
Badness: 0.024234
Line 232: Line 232:
POTE generator: ~6/5 = 313.949
POTE generator: ~6/5 = 313.949


Vals: {{Val list| 50, 80, 130 }}
Optimal GPV sequence: {{Val list| 50, 80, 130 }}


Badness: 0.018232
Badness: 0.018232

Revision as of 12:52, 29 December 2021

The stearnsmic clan tempers out the stearnsma, the no-fives comma [1 10 0 -6⟩ = 118098/117649.

Stearnsmic temperaments not listed include:

Considered below are supers, stearnscape, garistearn and decistearn.

No-five stearnsmic

Subgroup: 2.3.7

Comma list: 118098/117649

Sval mapping: [⟨2 1 2], ⟨0 3 5]]

Gencom mapping: [⟨2 1 0 2], ⟨0 3 0 5]]

POTE generator: ~9/7 = 433.888

Template:Val list

Supers

Subgroup: 2.3.5.7

Comma list: 5120/5103, 118098/117649

Mapping: [⟨2 1 -12 2], ⟨0 3 23 5]]

Wedgie: ⟨⟨ 6 46 10 59 -1 -106 ]]

POTE generator: ~9/7 = 434.218

Template:Val list

Badness: 0.092748

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 5120/5103

Mapping: [⟨2 1 -12 2 -9], ⟨0 3 23 5 22]]

POTE generator: ~9/7 = 434.217

Optimal GPV sequence: Template:Val list

Badness: 0.028240

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 729/728, 1575/1573

Mapping: [⟨2 1 -12 2 -9 -2], ⟨0 3 23 5 22 13]]

POTE generator: ~9/7 = 434.221

Optimal GPV sequence: Template:Val list

Badness: 0.021645

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 170/169, 289/288, 352/351, 442/441, 561/560

Mapping: [⟨2 1 -12 2 -9 -2 6], ⟨0 3 23 5 22 13 3]]

POTE generator: ~9/7 = 434.181

Optimal GPV sequence: Template:Val list

Badness: 0.021316

Stearnscape

Subgroup: 2.3.5.7

Comma list: 118098/117649, 250047/250000

Mapping: [⟨6 3 2 6], ⟨0 6 11 10]]

Mapping generators: ~2450/2187, ~567/500

Wedgie: ⟨⟨ 36 66 60 21 -6 -46 ]]

POTE generator: ~567/500 = 216.942

Template:Val list

Badness: 0.090467

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 137781/137500

Mapping: [⟨6 3 2 6 11], ⟨0 6 11 10 9]]

POTE generator: ~567/500 = 216.950

Optimal GPV sequence: Template:Val list

Badness: 0.032096

Garistearn

The garistearn temperament (94&282) has a period of 1/94 octave and tempers out 118098/117649 and garischisma, 33554432/33480783.

Subgroup: 2.3.5.7

Comma list: 118098/117649, 33554432/33480783

Mapping: [⟨94 149 0 264], ⟨0 0 1 0]]

Wedgie: ⟨⟨ 0 94 0 149 0 -264 ]]

POTE generator: ~5/4 = 386.7805

Template:Val list

Badness: 0.307043

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 33554432/33480783

Mapping: [⟨94 149 0 264 107], ⟨0 0 1 0 1]]

POTE generator: ~5/4 = 386.5968

Optimal GPV sequence: Template:Val list

Badness: 0.082255

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1575/1573, 28672/28561

Mapping: [⟨94 149 0 264 107 348], ⟨0 0 1 0 1 0]]

POTE generator: ~5/4 = 386.8141

Optimal GPV sequence: Template:Val list

Badness: 0.045941

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873

Mapping: [⟨94 149 0 264 107 348 166], ⟨0 0 1 0 1 0 1]]

POTE generator: ~5/4 = 386.8420

Optimal GPV sequence: Template:Val list

Badness: 0.027608

Decistearn

See also: Trisedodge family

The decistearn temperament (80&130) has a period of 1/10 octave and tempers out the hemimean comma, 3136/3125 as well as the linus comma.

Subgroup: 2.3.5.7

Comma list: 3136/3125, 118098/117649

Mapping: [⟨10 17 24 30], ⟨0 -3 -2 -5]]

Wedgie: ⟨⟨ 30 20 50 -38 -5 60 ]]

POTE generator: ~6/5 = 313.960

Template:Val list

Badness: 0.095543

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 3136/3125, 4000/3993

Mapping: [⟨10 17 24 30 35], ⟨0 -3 -2 -5 -1]]

POTE generator: ~6/5 = 314.079

Optimal GPV sequence: Template:Val list

Badness: 0.038556

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 364/363, 540/539, 3136/3125

Mapping: [⟨10 17 24 30 35 37], ⟨0 -3 -2 -5 -1 0]]

POTE generator: ~6/5 = 313.947

Optimal GPV sequence: Template:Val list

Badness: 0.026895

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 221/220, 289/288, 351/350, 540/539, 1632/1625

Mapping: [⟨10 17 24 30 35 37 42], ⟨0 -3 -2 -5 -1 0 -3]]

POTE generator: ~6/5 = 313.931

Optimal GPV sequence: Template:Val list

Badness: 0.024234

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 221/220, 289/288, 351/350, 361/360, 456/455, 476/475

Mapping: [⟨10 17 24 30 35 37 42 44], ⟨0 -3 -2 -5 -1 0 -3 -4]]

POTE generator: ~6/5 = 313.949

Optimal GPV sequence: Template:Val list

Badness: 0.018232

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