Tritrizo clan
The tritrizo clan of temperaments tempers out the tritrizo comma (no-five ennealimma), [-11 -9 0 9⟩ = 40353607/40310784, and includes these:
- Cobalt → Starling temperaments #Cobalt
- Niner → Augmented family #Niner
- Enneaportent → Marvel temperaments #Enneaportent
- Novemkleismic → Kleismic family #Novemkleismic
- Decades → Compton family #Decades
- Nonant → Schismatic family #Nonant
- 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
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
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