Septiennealimmal clan: Difference between revisions
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The '''tritrizo clan''' of temperaments tempers out the tritrizo comma, {{monzo| -11 -9 0 9 }} = 40353607/40310784, and includes these: | The '''tritrizo clan''' of temperaments tempers out the tritrizo comma (no-five ennealimma), {{monzo| -11 -9 0 9 }} = 40353607/40310784, and includes these: | ||
* ''[[Niner]]'' → [[Augmented family #Niner]] | * ''[[Niner]]'' → [[Augmented family #Niner]] | ||
* ''[[Enneaportent]]'' → [[Marvel temperaments #Enneaportent]] | * ''[[Enneaportent]]'' → [[Marvel temperaments #Enneaportent]] | ||
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* [[Ennealimmal]], also in: [[Ragismic microtemperaments #Ennealimmal]] | * [[Ennealimmal]], also in: [[Ragismic microtemperaments #Ennealimmal]] | ||
= No-five tritrizo = | |||
Subgroup: 2.3.7 | Subgroup: 2.3.7 | ||
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{{Val list|legend=1| 27, 36, 99, 135, 171, 306, 4419d, 4725d, ... , 8397dd, 8703dd }} | {{Val list|legend=1| 27, 36, 99, 135, 171, 306, 4419d, 4725d, ... , 8397dd, 8703dd }} | ||
== 171&342 | = Schisennealimmal = | ||
Schisennealimmal (171&342, named by [[User:Xenllium|Xenllium]]) has a period of 1/171 octave. [[171edo|171EDO]] and its multiple are members of both [[Schismatic family|schismic]] and [[Ragismic microtemperaments #Ennealimmal|ennealimmal]], and from this it derives its name. | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Badness]]: 0.031739 | [[Badness]]: 0.031739 | ||
== 13-limit == | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generator: ~11/8 = 551.322 | POTE generator: ~11/8 = 551.322 | ||
Vals: {{Val list| 171, 342 }} | Vals: {{Val list| 171, 342, 855ff, 1197fff }} | ||
Badness: 0.054029 | Badness: 0.054029 | ||
=== | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 625/624, 729/728, 833/832, 1225/1224, 2205/2197 | |||
Mapping: [{{val| 171 271 397 480 0 633 699 }}, {{val| 0 0 0 0 1 0 0 }}] | |||
POTE generator: ~11/8 = 551.365 | |||
Vals: {{Val list| 171, 342, 855ff, 1197fff }} | |||
Badness: 0.031323 | |||
== Schisennealimmic == | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.046843 | Badness: 0.046843 | ||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 936/935, 1225/1224, 1701/1700, 2025/2023, 11271/11264 | |||
Mapping: [{{val|171 271 397 480 0 41 699 }}, {{val|0 0 0 0 1 1 0 }}] | |||
POTE generator: ~11/8 = 551.756 | |||
Vals: {{Val list|171, 342f, 513, 855f }} | |||
Badness: 0.030622 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament clan]] | [[Category:Temperament clan]] | ||
Revision as of 22:08, 31 May 2021
The tritrizo clan of temperaments tempers out the tritrizo comma (no-five ennealimma), [-11 -9 0 9⟩ = 40353607/40310784, and includes these:
- Niner → Augmented family #Niner
- Enneaportent → Marvel temperaments #Enneaportent
- Novemkleismic → Kleismic family #Novemkleismic
- Ennealimmal, also in: Ragismic microtemperaments #Ennealimmal
No-five tritrizo
Subgroup: 2.3.7
Comma list: 40353607/40310784
Sval mapping: [⟨9 0 11], ⟨0 1 1]]
POTE generator: ~3/2 = 701.965
Schisennealimmal
Schisennealimmal (171&342, named by Xenllium) has a period of 1/171 octave. 171EDO and its multiple are members of both schismic and ennealimmal, and from this it derives its name.
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4375/4374, 32805/32768
Mapping: [⟨171 271 397 480 0], ⟨0 0 0 0 1]]
POTE generator: ~11/8 = 550.954
Badness: 0.031739
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 729/728, 2205/2197, 2401/2400
Mapping: [⟨171 271 397 480 0 633], ⟨0 0 0 0 1 0]]
POTE generator: ~11/8 = 551.322
Vals: Template:Val list
Badness: 0.054029
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 625/624, 729/728, 833/832, 1225/1224, 2205/2197
Mapping: [⟨171 271 397 480 0 633 699], ⟨0 0 0 0 1 0 0]]
POTE generator: ~11/8 = 551.365
Vals: Template:Val list
Badness: 0.031323
Schisennealimmic
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4375/4374, 32805/32768
Mapping: [⟨171 271 397 480 0 41], ⟨0 0 0 0 1 1]]
POTE generator: ~11/8 = 551.625
Vals: Template:Val list
Badness: 0.046843
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 936/935, 1225/1224, 1701/1700, 2025/2023, 11271/11264
Mapping: [⟨171 271 397 480 0 41 699], ⟨0 0 0 0 1 1 0]]
POTE generator: ~11/8 = 551.756
Vals: Template:Val list
Badness: 0.030622