Septiennealimmal clan: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 16: Line 16:
[[POTE generator]]: ~3/2 = 701.965
[[POTE generator]]: ~3/2 = 701.965


{{Val list|legend=1| 27, 36, 99, 135, 171, 306, 4419d, 4725d, ... , 8397dd, 8703dd }}
{{Optimal ET sequence|legend=1| 27, 36, 99, 135, 171, 306, 4419d, 4725d, ... , 8397dd, 8703dd }}


=== Ennea ===
=== Ennea ===
Line 29: Line 29:
[[POTE generator]]: ~99/98 = 17.626
[[POTE generator]]: ~99/98 = 17.626


{{Val list|legend=1| 54, 63, 72, 135, 342, 477, 1089, 1566 }}
{{Optimal ET sequence|legend=1| 54, 63, 72, 135, 342, 477, 1089, 1566 }}


== Undecentic ==
== Undecentic ==
Line 42: Line 42:
[[POTE generator]]: ~11/8 = 552.756
[[POTE generator]]: ~11/8 = 552.756


{{Val list|legend=1| 99e, 198, 297e, 495ce }}
{{Optimal ET sequence|legend=1| 99e, 198, 297e, 495ce }}


[[Badness]]: 0.058801
[[Badness]]: 0.058801
Line 55: Line 55:
POTE generator: ~11/8 = 552.024
POTE generator: ~11/8 = 552.024


Optimal GPV sequence: {{Val list| 99ef, 198 }}
{{Optimal ET sequence|legend=1| 99ef, 198 }}


Badness: 0.042547
Badness: 0.042547
Line 70: Line 70:
[[POTE generator]]: ~11/8 = 550.954
[[POTE generator]]: ~11/8 = 550.954


{{Val list|legend=1| 171, 342 }}
{{Optimal ET sequence|legend=1| 171, 342 }}


[[Badness]]: 0.031739
[[Badness]]: 0.031739
Line 83: Line 83:
POTE generator: ~11/8 = 551.322
POTE generator: ~11/8 = 551.322


Optimal GPV sequence: {{Val list| 171, 342, 855ff, 1197fff }}
{{Optimal ET sequence|legend=1| 171, 342, 855ff, 1197fff }}


Badness: 0.054029
Badness: 0.054029
Line 96: Line 96:
POTE generator: ~11/8 = 551.365
POTE generator: ~11/8 = 551.365


Optimal GPV sequence: {{Val list| 171, 342, 855ff, 1197fff }}
{{Optimal ET sequence|legend=1| 171, 342, 855ff, 1197fff }}


Badness: 0.031323
Badness: 0.031323
Line 109: Line 109:
POTE generator: ~11/8 = 551.625
POTE generator: ~11/8 = 551.625


Optimal GPV sequence: {{Val list| 171, 342f, 513, 855f }}
{{Optimal ET sequence|legend=1| 171, 342f, 513, 855f }}


Badness: 0.046843
Badness: 0.046843
Line 122: Line 122:
POTE generator: ~11/8 = 551.756
POTE generator: ~11/8 = 551.756


Optimal GPV sequence: {{Val list| 171, 342f, 513, 855f }}
{{Optimal ET sequence|legend=1| 171, 342f, 513, 855f }}


Badness: 0.030622
Badness: 0.030622
Line 137: Line 137:
[[POTE generator]]: ~11/8 = 551.3584
[[POTE generator]]: ~11/8 = 551.3584


{{Val list|legend=1| 441, 882, 1323, 2205, 3528 }}
{{Optimal ET sequence|legend=1| 441, 882, 1323, 2205, 3528 }}


[[Badness]]: 0.091939
[[Badness]]: 0.091939
Line 150: Line 150:
POTE generator: ~11/8 = 551.4043
POTE generator: ~11/8 = 551.4043


Optimal GPV sequence: {{Val list| 441, 882, 1323, 3528f, 4851ff, 6174dff }}
{{Optimal ET sequence|legend=1| 441, 882, 1323, 3528f, 4851ff, 6174dff }}


Badness: 0.042975
Badness: 0.042975
Line 163: Line 163:
POTE generator: ~11/8 = 551.3688
POTE generator: ~11/8 = 551.3688


Optimal GPV sequence: {{Val list| 441, 882, 1323, 2205f, 3528f }}
{{Optimal ET sequence|legend=1| 441, 882, 1323, 2205f, 3528f }}


Badness: 0.029334
Badness: 0.029334


[[Category:Temperament clans]]
[[Category:Temperament clans]]

Revision as of 16:23, 7 May 2023

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

Optimal ET sequence: 27, 36, 99, 135, 171, 306, 4419d, 4725d, ... , 8397dd, 8703dd

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

Optimal ET sequence: 54, 63, 72, 135, 342, 477, 1089, 1566

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

Optimal ET sequence: 99e, 198, 297e, 495ce

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 ET sequence: 99ef, 198

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

Optimal ET sequence: 171, 342

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 ET sequence: 171, 342, 855ff, 1197fff

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 ET sequence: 171, 342, 855ff, 1197fff

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 ET sequence: 171, 342f, 513, 855f

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 ET sequence: 171, 342f, 513, 855f

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

Optimal ET sequence: 441, 882, 1323, 2205, 3528

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 ET sequence: 441, 882, 1323, 3528f, 4851ff, 6174dff

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 ET sequence: 441, 882, 1323, 2205f, 3528f

Badness: 0.029334

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