Stearnsmic clan: Difference between revisions

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Stearnsmic temperaments temper out the stearnsma, the no-fives comma {{monzo|1 10 0 -6}} = 118098/117649. Sternismic temperaments not listed include [[Gravity family #Harry|harry]], [[Marvel temperaments #Wizard|wizard]], [[Schismatic family #Pogo|pogo]], [[Porcupine family #Hedgehog|hedgehog]], [[Porwell temperaments #Septisuperfourth|septisuperfourth]], [[Hemifamity temperaments #Supers|supers]], and [[Ragismic microtemperaments #Octoid|octoid]].
The '''stearnsmic clan''' tempers out the stearnsma, the no-fives comma {{monzo| 1 10 0 -6 }} = 118098/117649. Stearnsmic temperaments not listed include [[Gravity family #Harry|harry]], [[Marvel temperaments #Wizard|wizard]], [[Schismatic family #Pogo|pogo]], [[Porcupine family #Hedgehog|hedgehog]], [[Porwell temperaments #Septisuperfourth|septisuperfourth]], and [[Ragismic microtemperaments #Octoid|octoid]].


== No-five stearnsmic ==
== No-five stearnsmic ==
Comma: 118098/117649
Subgroup: 2.3.7


No-five map: [{{val|2 1 0 2}}, {{val|0 3 0 5}}]
[[Comma list]]: 118098/117649


No-five POTE generator: ~9/7 = 433.888
[[Sval]] [[mapping]]: [{{val| 2 1 2 }}, {{val| 0 3 5 }}]


No-five vals: {{Val list| 14, 22, 36, 94, 130, 224, 354, 484, 838 }}
[[Gencom]] [[mapping]]: [{{val| 2 1 0 2 }}, {{val| 0 3 0 5 }}]
 
[[POTE generator]]: ~9/7 = 433.888
 
{{Val list|legend=1| 14, 22, 36, 94, 130, 224, 354, 484, 838 }}
 
== Supers ==
Subgroup: 2.3.5.7
 
[[Comma list]]: 5120/5103, 118098/117649
 
[[Mapping]]: [{{val| 2 1 -12 2 }}, {{val| 0 3 23 5 }}]
 
{{Multival|legend=1| 6 46 10 59 -1 -106 }}
 
[[POTE generator]]: ~9/7 = 434.218
 
{{Val list|legend=1| 58, 94, 152 }}
 
[[Badness]]: 0.092748
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 4000/3993, 5120/5103
 
Mapping: [{{val| 2 1 -12 2 -9 }}, {{val| 0 3 23 5 22 }}]
 
POTE generator: ~9/7 = 434.217
 
Vals: {{Val list| 58, 94, 152 }}
 
Badness: 0.028240
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 540/539, 729/728, 1575/1573
 
Mapping: [{{val| 2 1 -12 2 -9 -2 }}, {{val| 0 3 23 5 22 13 }}]
 
POTE generator: ~9/7 = 434.221
 
Vals: {{Val list| 58, 94, 152f }}
 
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: [{{val| 2 1 -12 2 -9 -2 6 }}, {{val| 0 3 23 5 22 13 3 }}]
 
POTE generator: ~9/7 = 434.181
 
Vals: {{Val list| 58, 94, 152f }}
 
Badness: 0.021316


== Stearnscape ==
== Stearnscape ==
Line 163: Line 221:
Badness: 0.018232
Badness: 0.018232


[[Category:Theory]]
[[Category:Regular temeprament theory]]
[[Category:Temperament clan]]
[[Category:Temperament clan]]
[[Category:Stearnsmic clan| ]] <!-- main article -->
[[Category:Rank 2]]

Revision as of 12:59, 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 harry, wizard, pogo, hedgehog, septisuperfourth, and octoid.

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

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

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: ~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

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

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

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

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

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