Stearnsmic clan: Difference between revisions
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The '''stearnsmic clan''' tempers out the stearnsma, the no-fives comma {{monzo| 1 10 0 -6 }} = 118098/117649. Stearnsmic temperaments not listed include [[ | The '''stearnsmic clan''' tempers out the stearnsma, the no-fives comma {{monzo| 1 10 0 -6 }} = 118098/117649. Stearnsmic temperaments not listed include: | ||
* ''[[Hedgehog]]'', {50/49, 245/243} → [[Porcupine family #Hedgehog|Porcupine family]] | |||
* [[Wizard]], {225/224, 118098/117649} → [[Marvel temperaments #Wizard|Marvel temperaments]] | |||
* ''[[Echidna]]'', {1728/1715, 2048/2025} → [[Diaschismic family #Echidna|Diaschismic family]] | |||
* [[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]] | |||
* ''[[Pogo]]'', {32805/32768, 118098/117649} → [[Schismatic family #Pogo|Schismatic family]] | |||
* ''[[Septisuperfourth]]'', {6144/6125, 118098/117649} → [[Porwell temperaments #Septisuperfourth|Porwell temperaments]] | |||
== No-five stearnsmic == | == No-five stearnsmic == | ||
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== Decistearn == | == Decistearn == | ||
{{See also| Trisedodge family }} | |||
The ''decistearn'' temperament (80&130) has a period of 1/10 octave and tempers out the [[3136/3125|hemimean comma]], 3136/3125 as well as the [[15/14ths equal temperament|linus comma]]. | The ''decistearn'' temperament (80&130) has a period of 1/10 octave and tempers out the [[3136/3125|hemimean comma]], 3136/3125 as well as the [[15/14ths equal temperament|linus comma]]. | ||
Revision as of 13:10, 2 November 2021
The stearnsmic clan tempers out the stearnsma, the no-fives comma [1 10 0 -6⟩ = 118098/117649. Stearnsmic temperaments not listed include:
- Hedgehog, {50/49, 245/243} → Porcupine family
- Wizard, {225/224, 118098/117649} → Marvel temperaments
- Echidna, {1728/1715, 2048/2025} → Diaschismic family
- Harry, {2401/2400, 19683/19600} → Gravity family and Breedsmic temperaments
- Octoid, {4375/4374, 16875/16807} → Ragismic microtemperaments
- Pogo, {32805/32768, 118098/117649} → Schismatic family
- Septisuperfourth, {6144/6125, 118098/117649} → Porwell temperaments
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
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
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
Vals: 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
Vals: 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
Vals: 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]]
Wedgie: ⟨⟨ 36 66 60 21 -6 -46 ]]
POTE generator: ~245/243 = 16.942
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: ~245/243 = 16.950
Vals: 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
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
Vals: 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
Vals: 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
Vals: Template:Val list
Badness: 0.027608
Decistearn
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
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
Vals: 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
Vals: 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
Vals: 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
Vals: Template:Val list
Badness: 0.018232