Swetismic temperaments: Difference between revisions
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This is a collection of rank-3 temperaments tempering out [[540/539]] | This is a collection of rank-3 temperaments tempering out [[540/539]]. Temperaments discussed elsewhere are: | ||
Temperaments discussed elsewhere are: | |||
* ''[[Terpsichore]]'', {81/80, 540/539} → [[Didymus rank three family #Terpsichore]] | * ''[[Terpsichore]]'', {81/80, 540/539} → [[Didymus rank three family #Terpsichore]] | ||
* ''[[Big Brother]]'', {99/98, 121/120} → [[Nuwell family #Big Brother]] | * ''[[Big Brother]]'', {99/98, 121/120} → [[Nuwell family #Big Brother]] | ||
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* ''[[Albus]]'', {540/539, 8019/8000} → [[Cataharry family #Albus]] | * ''[[Albus]]'', {540/539, 8019/8000} → [[Cataharry family #Albus]] | ||
Considered below are hades, minos, persephone and hypnos | Considered below are hades, minos, persephone and hypnos, but we can begin by looking at the rank-4 temperament | ||
== Swetismic == | == Swetismic == | ||
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== Hades == | == Hades == | ||
=== 7-limit (stearnsmic) === | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 118098/117649 | |||
[[Mapping]]: [{{val| 2 1 0 2 }}, {{val| 0 3 0 5 }}, {{val| 0 0 1 0 }}] | |||
Mapping generators: ~343/243, ~9/7, ~5 | |||
{{Val list|legend=1| 22, 50, 58, 72, 130, 152, 202, 224, 354 }} | |||
[[Badness]]: 0.748 × 10<sup>-3</sup> | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Mapping]]: [{{val| 2 1 0 2 3 }}, {{val| 0 3 0 5 -1 }}, {{val| 0 0 1 0 1 }}] | [[Mapping]]: [{{val| 2 1 0 2 3 }}, {{val| 0 3 0 5 -1 }}, {{val| 0 0 1 0 1 }}] | ||
{{Val list|legend=1| 22, 50, 58, 72, 130, 152, 224, 354, 506e, 578, 730e, 1084de, 1308dee }} | |||
{{Val list|legend=1| 22, 50, 58, 72, 130, 152, 224, 354, 578 }} | |||
[[Badness]]: 0.361 × 10<sup>-3</sup> | [[Badness]]: 0.361 × 10<sup>-3</sup> | ||
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Mapping: [{{val| 2 1 0 2 3 -2 }}, {{val| 0 3 0 5 -1 13 }}, {{val| 0 0 1 0 1 0 }}] | Mapping: [{{val| 2 1 0 2 3 -2 }}, {{val| 0 3 0 5 -1 13 }}, {{val| 0 0 1 0 1 0 }}] | ||
Vals: {{val list| 36, 58, 72, 130, 224, 354, 578 }} | Vals: {{val list| 22f, 36, 58, 72, 130, 224, 354, 578 }} | ||
Badness: 0.535 × 10<sup>-3</sup> | Badness: 0.535 × 10<sup>-3</sup> | ||
Revision as of 21:46, 28 October 2021
This is a collection of rank-3 temperaments tempering out 540/539. Temperaments discussed elsewhere are:
- Terpsichore, {81/80, 540/539} → Didymus rank three family #Terpsichore
- Big Brother, {99/98, 121/120} → Nuwell family #Big Brother
- Octarod, {100/99, 245/243} → Sensamagic family #Octarod
- Aplonis, {126/125, 540/539} → Starling family #Aplonis
- Guanyin, {176/175, 540/539} → Orwellismic family #Guanyin
- Marvel, {225/224, 385/384} → Marvel family #Undecimal marvel
- Jove, {243/242, 441/440} → Breed family #Jove
- Uni, {540/539, 896/891} → Hemimage family #Uni
- Indra, {540/539, 1375/1372} → Mirkwai family #Indra
- Claudius, {540/539, 2048/2025} → Diaschismic rank three family #Claudius
- Laka, {540/539, 5120/5103} → Hemifamity family #Laka
- Jupiter, {540/539, 5632/5625} → Porwell family #Jupiter
- Albus, {540/539, 8019/8000} → Cataharry family #Albus
Considered below are hades, minos, persephone and hypnos, but we can begin by looking at the rank-4 temperament
Swetismic
Subgroup: 2.3.5.7.11
Comma list: 540/539
Mapping: [⟨1 0 0 0 2], ⟨0 1 0 0 3], ⟨0 0 0 1 -2]]
Mapping generators: ~2, ~3, ~5, ~7
Hades
7-limit (stearnsmic)
Subgroup: 2.3.5.7
Comma list: 118098/117649
Mapping: [⟨2 1 0 2], ⟨0 3 0 5], ⟨0 0 1 0]]
Mapping generators: ~343/243, ~9/7, ~5
Badness: 0.748 × 10-3
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993
Mapping: [⟨2 1 0 2 3], ⟨0 3 0 5 -1], ⟨0 0 1 0 1]]
Badness: 0.361 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1575/1573
Mapping: [⟨2 1 0 2 3 -2], ⟨0 3 0 5 -1 13], ⟨0 0 1 0 1 0]]
Vals: Template:Val list
Badness: 0.535 × 10-3
Cerberus
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 540/539
Mapping: [⟨2 1 0 2 3 1], ⟨0 3 0 5 -1 -4], ⟨0 0 1 0 1 2]]
Vals: Template:Val list
Badness: 0.766 × 10-3
Minos
Subgroup: 2.3.5.7.11
Comma list: 540/539, 12005/11979
Mapping: [⟨1 0 2 1 2], ⟨0 2 4 3 4], ⟨0 0 -5 -1 -3]]
Mapping generators: ~2, ~121/70, ~49/33
Badness: 0.886 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 540/539, 676/675
Mapping: [⟨1 0 2 1 2 1], ⟨0 2 4 3 4 7], ⟨0 0 -5 -1 -3 -5]]
Vals: Template:Val list
Badness: 0.724 × 10-3
Persephone
Subgroup: 2.3.5.7.11
Comma list: 540/539, 88209/87500
Mapping: [⟨1 0 4 -2 10], ⟨0 1 4 0 7], ⟨0 0 -5 3 -11]]
Mapping generators: ~2, ~3, ~100/33
Badness: 2.015 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 847/845
Mapping: [⟨1 0 4 -2 10 7], ⟨0 1 4 0 7 5], ⟨0 0 -5 3 -11 -7]]
Vals: Template:Val list
Badness: 0.997 × 10-3
Hypnos
Subgroup: 2.3.5.7.11
Comma list: 540/539, 72171/71680
Mapping: [⟨1 0 0 -3 8], ⟨0 3 0 11 -13], ⟨0 0 1 0 1]]
Mapping generators: ~2, ~81/56, ~5
Badness: 1.629 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 540/539, 729/728
Mapping: [⟨1 0 0 -3 8 0], ⟨0 3 0 11 -13 7], ⟨0 0 1 0 1 0]]
Vals: Template:Val list
Badness: 1.439 × 10-3