Septiennealimmal clan: Difference between revisions

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{{Val list|legend=1| 54, 63, 72, 135, 342, 477, 1089, 1566 }}
{{Val list|legend=1| 54, 63, 72, 135, 342, 477, 1089, 1566 }}
== Enneaplonic ==
Enneaplonic (27 & 81) has a period of 1/27 octave and tempers out 126/125 and 540/539, as well as the [[Starling family #Aplonis|aplonis temperament]].
Subgroup: 2.3.5.7
[[Comma list]]: 126/125, 40353607/40310784
[[Mapping]]: [{{val|27 43 63 76}}, {{val|0 -1 -1 -1}}]
[[POTE generator]]: ~3/2 = 701.244
{{Val list|legend=1| 27, 81, 108, 135c, 243c }}
[[Badness]]: 0.173308
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 126/125, 540/539, 21609/21296
Mapping: [{{val|27 43 63 76 94}}, {{val|0 -1 -1 -1 -2}}]
POTE generator: ~3/2 = 700.001
Optimal GPV sequence: {{Val list| 27e, 81, 108 }}
Badness: 0.078060
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 196/195, 21609/21296
Mapping: [{{val|27 43 63 76 94 100}}, {{val|0 -1 -1 -1 -2 0}}]
POTE generator: ~3/2 = 700.867
Optimal GPV sequence: {{Val list| 27e, 81, 108, 243ceef }}
Badness: 0.057145
==== Enneaplonoid ====
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 169/168, 540/539, 975/968
Mapping: [{{val|27 43 63 76 94 100}}, {{val|0 -1 -1 -1 -2 -1}}]
POTE generator: ~3/2 = 699.179
Optimal GPV sequence: {{Val list| 27e, 54bdef, 81f, 108f }}
Badness: 0.052732


== Undecentic ==
== Undecentic ==
Line 54: Line 108:
POTE generator: ~11/8 = 552.024
POTE generator: ~11/8 = 552.024


Vals: {{Val list| 99ef, 198 }}
Optimal GPV sequence: {{Val list| 99ef, 198 }}


Badness: 0.042547
Badness: 0.042547
Line 82: Line 136:
POTE generator: ~11/8 = 551.322
POTE generator: ~11/8 = 551.322


Vals: {{Val list| 171, 342, 855ff, 1197fff }}
Optimal GPV sequence: {{Val list| 171, 342, 855ff, 1197fff }}


Badness: 0.054029
Badness: 0.054029
Line 95: Line 149:
POTE generator: ~11/8 = 551.365
POTE generator: ~11/8 = 551.365


Vals: {{Val list| 171, 342, 855ff, 1197fff }}
Optimal GPV sequence: {{Val list| 171, 342, 855ff, 1197fff }}


Badness: 0.031323
Badness: 0.031323
Line 108: Line 162:
POTE generator: ~11/8 = 551.625
POTE generator: ~11/8 = 551.625


Vals: {{Val list| 171, 342f, 513, 855f }}
Optimal GPV sequence: {{Val list| 171, 342f, 513, 855f }}


Badness: 0.046843
Badness: 0.046843
Line 121: Line 175:
POTE generator: ~11/8 = 551.756
POTE generator: ~11/8 = 551.756


Vals: {{Val list| 171, 342f, 513, 855f }}
Optimal GPV sequence: {{Val list| 171, 342f, 513, 855f }}


Badness: 0.030622
Badness: 0.030622
Line 149: Line 203:
POTE generator: ~11/8 = 551.4043
POTE generator: ~11/8 = 551.4043


Vals: {{Val list| 441, 882, 1323, 3528f, 4851ff, 6174dff }}
Optimal GPV sequence: {{Val list| 441, 882, 1323, 3528f, 4851ff, 6174dff }}


Badness: 0.042975
Badness: 0.042975
Line 162: Line 216:
POTE generator: ~11/8 = 551.3688
POTE generator: ~11/8 = 551.3688


Vals: {{Val list| 441, 882, 1323, 2205f, 3528f }}
Optimal GPV sequence: {{Val list| 441, 882, 1323, 2205f, 3528f }}


Badness: 0.029334
Badness: 0.029334

Revision as of 10:17, 2 January 2022

The tritrizo clan of temperaments tempers out the tritrizo comma (no-five ennealimma), [-11 -9 0 9⟩ = 40353607/40310784, and includes these:

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

Template:Val list

Ennea

See also: Subgroup temperaments § No-fives subgroup

Subgroup: 2.3.7.11

Comma list: 41503/41472, 43923/43904

Sval mapping: [⟨9 0 11 24], ⟨0 2 2 1]]

POTE generator: ~99/98 = 17.626

Template:Val list

Enneaplonic

Enneaplonic (27 & 81) has a period of 1/27 octave and tempers out 126/125 and 540/539, as well as the aplonis temperament.

Subgroup: 2.3.5.7

Comma list: 126/125, 40353607/40310784

Mapping: [⟨27 43 63 76], ⟨0 -1 -1 -1]]

POTE generator: ~3/2 = 701.244

Template:Val list

Badness: 0.173308

11-limit

Subgroup: 2.3.5.7.11

Comma list: 126/125, 540/539, 21609/21296

Mapping: [⟨27 43 63 76 94], ⟨0 -1 -1 -1 -2]]

POTE generator: ~3/2 = 700.001

Optimal GPV sequence: Template:Val list

Badness: 0.078060

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 144/143, 196/195, 21609/21296

Mapping: [⟨27 43 63 76 94 100], ⟨0 -1 -1 -1 -2 0]]

POTE generator: ~3/2 = 700.867

Optimal GPV sequence: Template:Val list

Badness: 0.057145

Enneaplonoid

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 169/168, 540/539, 975/968

Mapping: [⟨27 43 63 76 94 100], ⟨0 -1 -1 -1 -2 -1]]

POTE generator: ~3/2 = 699.179

Optimal GPV sequence: Template:Val list

Badness: 0.052732

Undecentic

Undecentic (99&198) has a period of 1/99 octave.

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3136/3125, 4375/4374

Mapping: [⟨99 157 230 278 0], ⟨0 0 0 0 1]]

POTE generator: ~11/8 = 552.756

Template:Val list

Badness: 0.058801

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 847/845, 2401/2400, 3136/3125

Mapping: [⟨99 157 230 278 0 24], ⟨0 0 0 0 1 1]]

POTE generator: ~11/8 = 552.024

Optimal GPV sequence: Template:Val list

Badness: 0.042547

Schisennealimmal

Schisennealimmal (171&342) has a period of 1/171 octave. 171EDO and its multiples 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

Template:Val list

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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.030622

Lunennealimmal

Lunennealimmal (441&882) has has a period of 1/441 octave. 441EDO and its multiples are members of both luna and ennealimmal, and from this it derives its name.

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 4375/4374, 274877906944/274658203125

Mapping: [⟨441 699 1024 1238 1526], ⟨0 0 0 0 -1]]

POTE generator: ~11/8 = 551.3584

Template:Val list

Badness: 0.091939

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2401/2400, 4096/4095, 4375/4374, 85750/85683

Mapping: [⟨441 699 1024 1238 1526 1632], ⟨0 0 0 0 -1 0]]

POTE generator: ~11/8 = 551.4043

Optimal GPV sequence: Template:Val list

Badness: 0.042975

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 2401/2400, 4096/4095, 4375/4374, 8624/8619, 14161/14157

Mapping: [⟨441 699 1024 1238 1526 1632 1803], ⟨0 0 0 0 -1 0 -1]]

POTE generator: ~11/8 = 551.3688

Optimal GPV sequence: Template:Val list

Badness: 0.029334

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