Fractional-octave temperaments: Difference between revisions
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Temperaments discussed elsewhere include: | Temperaments discussed elsewhere include: | ||
* [[ | * [[Cloudy clan|Cloudy temperaments]] (1\5 period) | ||
** [[Limmic temperaments #Blacksmith|Blacksmith]] | |||
** [[Meantone family #Cloudtone|Cloudtone]] | |||
** [[Cloudy clan #Coblack|Coblack]] | |||
** [[Pental family|Pental]] | |||
** [[Qintosec family #Sengasec|Sengasec]] | |||
** [[Cloudy clan #Quinkee|Quinkee]] | |||
* [[Landscape microtemperaments #Sextile|Sextile]], [[Stearnsmic clan #Stearnscape|Stearnscape]] (1\6 period) | |||
* [[Akjaysma|Akjaysmic temperaments]] (1\7 period) | |||
** [[Ragismic microtemperaments #Brahmagupta|Brahmagupta]] | ** [[Ragismic microtemperaments #Brahmagupta|Brahmagupta]] | ||
** [[Schismatic family #Septant|Septant]] | ** [[Schismatic family #Septant|Septant]] | ||
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** [[Keemic temperaments #Sevond|Sevond]] | ** [[Keemic temperaments #Sevond|Sevond]] | ||
** [[Mistismic temperaments #Neutron|Neutron]] | ** [[Mistismic temperaments #Neutron|Neutron]] | ||
* [[Ragismic microtemperaments #Octoid|Octoid]] (1\8 period) | * [[Ragismic microtemperaments #Octoid|Octoid]], [[Schismatic family #Octant|Octant]] (1\8 period) | ||
* [[Tritrizo clan|Tritrizo temperaments]] (1\9 period) | * [[Tritrizo clan|Tritrizo temperaments]] (1\9 period) | ||
** [[Ragismic microtemperaments #Ennealimmal|Ennealimmal]] | ** [[Ragismic microtemperaments #Ennealimmal|Ennealimmal]] | ||
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* [[Ragismic microtemperaments #Chlorine|Chlorine]] (1\17 period) | * [[Ragismic microtemperaments #Chlorine|Chlorine]] (1\17 period) | ||
* [[Ragismic microtemperaments #Ennealimmal|Hemiennealimmal]] (1\18 period) | * [[Ragismic microtemperaments #Ennealimmal|Hemiennealimmal]] (1\18 period) | ||
* [[Ragismic microtemperaments #Enneadecal|Enneadecal]] (1\19 period) | * [[Ragismic microtemperaments #Enneadecal|Enneadecal]], [[Meantone family #Meanmag|Meanmag]] (1\19 period) | ||
* [[Hemimage temperaments #Degrees|Degrees]] (1\20 period) | * [[Hemimage temperaments #Degrees|Degrees]] (1\20 period) | ||
* [[Porwell temperaments #Hendecatonic|Icosidillic]] (1\22 period) | * [[Porwell temperaments #Hendecatonic|Icosidillic]] (1\22 period) | ||
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Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: 176/175, 640/637, 847/845, 1375/1372 | |||
Mapping: [{{val|37 0 86 104 128 137}}, {{val|0 1 0 0 0 0}}] | |||
POTE generator: ~3/2 = 703.0520 | |||
{{Val list | Vals: {{Val list| 37, 74, 111 }} | ||
Badness: 0.048732 | |||
== 65th-octave temperaments == | == 65th-octave temperaments == | ||
Revision as of 12:54, 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:
- Cloudy temperaments (1\5 period)
- Sextile, Stearnscape (1\6 period)
- Akjaysmic temperaments (1\7 period)
- Octoid, Octant (1\8 period)
- Tritrizo temperaments (1\9 period)
- Linus temperaments (1\10 period)
- Hendecatonic, Undeka (1\11 period)
- Compton, Atomic (1\12 period)
- Triskaidekic (1\13 period)
- Pentadecal, Quindecic (1\15 period)
- Hexadecoid (1\16 period)
- Chlorine (1\17 period)
- Hemiennealimmal (1\18 period)
- Enneadecal, Meanmag (1\19 period)
- Degrees (1\20 period)
- Icosidillic (1\22 period)
- Icositritonic (1\23 period)
- Hours (1\24 period)
- Bosonic (1\26 period)
- Trinealimmal (1\27 period)
- Oquatonic (1\28 period)
- Mystery (1\29 period)
- Birds (1\31 period)
- Decades (1\36 period)
- Hemienneadecal (1\38 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)
- Schisennealimmal (1\171 period)
- Lunennealimmal (1\441 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
Vals: Template:Val list
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
118th-octave temperaments
118EDO is accurate for harmonics 3 and 5, so various 118th-octave temperaments actually make sense.
Parakleischis
118EDO and its multiples are members of both parakleismic and schismic, and from this it derives its name.
Subgroup: 2.3.5.7
Comma list: 32805/32768, 1224440064/1220703125
Mapping: [⟨118 187 274 0], ⟨0 0 0 1]]
POTE generator: ~8/7 = 231.2765
Badness: 0.145166
11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 32805/32768, 137781/137500
Mapping: [⟨118 187 274 0 77], ⟨0 0 0 1 1]]
POTE generator: ~8/7 = 231.4883
Vals: Template:Val list
Badness: 0.049316