Fractional-octave temperaments: Difference between revisions
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* [[Ragismic microtemperaments #Chlorine|Chlorine]] (1\17 period) | * [[Ragismic microtemperaments #Chlorine|Chlorine]] (1\17 period) | ||
* [[Ragismic microtemperaments #Enneadecal|Enneadecal]] (1\19 period) | * [[Ragismic microtemperaments #Enneadecal|Enneadecal]] (1\19 period) | ||
* [[Hemimage temperaments #Degrees|Degrees]] (1\20 period) | |||
* [[Porwell temperaments #Icositritonic|Icositritonic]] (1\23 period) | * [[Porwell temperaments #Icositritonic|Icositritonic]] (1\23 period) | ||
* [[Compton family #Hours|Hours]] (1\24 period) | * [[Compton family #Hours|Hours]] (1\24 period) | ||
* [[26th-octave temperaments|Bosonic]] (1\26 period) | * [[26th-octave temperaments|Bosonic]] (1\26 period) | ||
* [[Horwell temperaments #Oquatonic|Oquatonic]] (1\28 period) | |||
* [[Hemifamity temperaments #Mystery|Mystery]] (1\29 period) | |||
* [[31st-octave temperaments|Birds]] (1\31 period) | * [[31st-octave temperaments|Birds]] (1\31 period) | ||
* [[Compton family #Decades|Decades]] (1\36 period) | * [[Compton family #Decades|Decades]] (1\36 period) | ||
* [[Counterpyth family|Counterpyth]] (1\41 period) | * [[Counterpyth family|Counterpyth]] (1\41 period) | ||
* [[Mitonismic temperaments #Meridic|Meridic]] (1\43 period) | * [[Mitonismic temperaments #Meridic|Meridic]] (1\43 period) | ||
* [[Ragismic microtemperaments #Palladium|Palladium]] (1\46 period) | |||
* [[Mercator family|Mercator]] (1\53 period) | * [[Mercator family|Mercator]] (1\53 period) | ||
* [[Compton family #Omicronbeta|Omicronbeta]] (1\72 period) | * [[Compton family #Omicronbeta|Omicronbeta]] (1\72 period) | ||
Revision as of 03:52, 12 October 2021
All temperaments on this page have a fractional-octave period, such as 1\26, 1\31, or 1\41.
Temperaments discussed elsewhere include:
- Chlorine (1\17 period)
- Enneadecal (1\19 period)
- Degrees (1\20 period)
- Icositritonic (1\23 period)
- Hours (1\24 period)
- Bosonic (1\26 period)
- Oquatonic (1\28 period)
- Mystery (1\29 period)
- Birds (1\31 period)
- Decades (1\36 period)
- Counterpyth (1\41 period)
- Meridic (1\43 period)
- Palladium (1\46 period)
- Mercator (1\53 period)
- Omicronbeta (1\72 period)
- Garistearn (1\94 period)
- Undecentic (1\99 period)
37th-octave temperaments
37EDO is accurate for harmonics 5, 7, 11, and 13, so various 37th-octave temperaments actually make sense.
Rubidium
The name of rubidium temperament comes from Rubidium, the 37th element.
Subgroup: 2.3.5.7
Comma list: 3136/3125, 4194304/4117715
Mapping: [⟨37 0 86 104], ⟨0 1 0 0]]
POTE generator: ~3/2 = 703.3903
Badness: 0.312105
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1375/1372, 65536/65219
Mapping: [⟨37 0 86 104 128], ⟨0 1 0 0 0]]
POTE generator: ~3/2 = 703.0355
Vals: Template:Val list
Badness: 0.101001
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 640/637, 847/845, 1375/1372
Mapping: [⟨37 0 86 104 128 137], ⟨0 1 0 0 0 0]]
POTE generator: ~3/2 = 703.0520
Badness: 0.048732
65th-octave temperaments
65EDO is accurate for harmonics 3. 5, and 11, so various 65th-octave temperaments actually make sense.
Terbium
The name of terbium temperament comes from Terbium, the 65th element.
Subgroup: 2.3.5.7
Comma list: 32805/32768, 78732/78125
Mapping: [⟨65 103 151 0], ⟨0 0 0 1]]
POTE generator: ~8/7 = 230.8641
Badness: 0.169778
11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 4000/3993, 5632/5625
Mapping: [⟨65 103 151 0 225], ⟨0 0 0 1 0]]
POTE generator: ~8/7 = 230.4285
Vals: Template:Val list
Badness: 0.059966
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 351/350, 2080/2079, 3584/3575
Mapping: [⟨65 103 151 0 225 58], ⟨0 0 0 1 0 1]]
POTE generator: ~8/7 = 230.0388
Vals: Template:Val list
Badness: 0.036267