Fractional-octave temperaments: Difference between revisions
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Temperaments discussed elsewhere include: | Temperaments discussed elsewhere include: | ||
* [[ | * 1\2 period temperaments | ||
** [[ | ** [[Diaschismic family|Diaschismic temperaments]] | ||
** [[ | ** [[Vishnuzmic family|Vishnuzmic temperaments]] | ||
** [[ | ** [[Jubilismic clan|Jubilismic temperaments]] | ||
** [[Pental family|Pental]] | ** [[Varunismic temperaments]] | ||
** [[Qintosec family | ** [[Lokismic temperaments]] | ||
** [[Cloudy clan | * 1\3 period temperaments | ||
* [[Augmented family #Hexe|Hexe]] | ** [[Augmented family|Augmented temperaments]] | ||
** [[Misty family|Misty temperaments]] | |||
** [[Landscape microtemperaments|Landscape temperaments]] | |||
* 1\4 period temperaments | |||
** [[Dimipent family|Diminished temperaments]] | |||
** [[Undim family|Undim temperaments]] | |||
* 1\5 period temperaments | |||
** [[Pental family|Pental temperaments]] | |||
** [[Qintosec family|Qintosec temperaments]] | |||
** [[Trisedodge family|Trisedodge temperaments]] | |||
** [[Cloudy clan|Cloudy temperaments]] | |||
** [[Limmic temperaments]] | |||
* 1\6 period temperaments | |||
** [[Augmented family #Hexe|Hexe]] | |||
** [[Landscape microtemperaments #Sextile|Sextile]] | |||
** [[Stearnsmic clan #Stearnscape|Stearnscape]] | |||
* [[Akjaysma|Akjaysmic temperaments]] (1\7 period) | * [[Akjaysma|Akjaysmic temperaments]] (1\7 period) | ||
** [[Ragismic microtemperaments #Brahmagupta|Brahmagupta]] | ** [[Ragismic microtemperaments #Brahmagupta|Brahmagupta]] | ||
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** [[Keemic temperaments #Sevond|Sevond]] | ** [[Keemic temperaments #Sevond|Sevond]] | ||
** [[Mistismic temperaments #Neutron|Neutron]] | ** [[Mistismic temperaments #Neutron|Neutron]] | ||
* [[Ragismic microtemperaments #Octoid|Octoid]], [[Schismatic family #Octant| | * [[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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** [[Marvel temperaments #Enneaportent|Enneaportent]] | ** [[Marvel temperaments #Enneaportent|Enneaportent]] | ||
** [[Kleismic family #Novemkleismic|Novemkleismic]] | ** [[Kleismic family #Novemkleismic|Novemkleismic]] | ||
* [[15/ | * [[15/14 equal-step tuning|Linus temperaments]] (1\10 period) | ||
** [[Breedsmic temperaments #Decoid|Decoid]] | ** [[Breedsmic temperaments #Decoid|Decoid]] | ||
** [[Ragismic microtemperaments #Deca|Deca]] | ** [[Ragismic microtemperaments #Deca|Deca]] | ||
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** [[Vishnuzmic family #Decavish|Decavish]] | ** [[Vishnuzmic family #Decavish|Decavish]] | ||
** [[Metric microtemperaments #Decimetra|Decimetra]] | ** [[Metric microtemperaments #Decimetra|Decimetra]] | ||
* [[Porwell temperaments #Hendecatonic|Hendecatonic]], [[Keemic temperaments #Undeka| | * [[Porwell temperaments #Hendecatonic|Hendecatonic]], [[Keemic temperaments #Undeka|undeka]] (1\11 period) | ||
* [[Compton family|Compton]], [[Very high accuracy temperaments #Atomic| | * [[Compton family|Compton]], [[Very high accuracy temperaments #Atomic|atomic]] (1\12 period) | ||
* [[Orwellismic temperaments #Triskaidekic|Triskaidekic]] (1\13 period) | * [[Orwellismic temperaments #Triskaidekic|Triskaidekic]], [[Octagar temperaments #Tridecatonic|tridecatonic]], [[Ragismic microtemperaments #Trideci|trideci]] (1\13 period) | ||
* [[Cloudy clan #Pentadecal|Pentadecal]], [[Trienstonic clan #Quindecic| | * [[Cloudy clan #Pentadecal|Pentadecal]], [[Trienstonic clan #Quindecic|quindecic]] (1\15 period) | ||
* [[Ragismic microtemperaments #Octoid|Hexadecoid]], [[Jubilismic clan #Sedecic| | * [[Ragismic microtemperaments #Octoid|Hexadecoid]], [[Jubilismic clan #Sedecic|sedecic]] (1\16 period) | ||
* [[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]], [[Meantone family #Meanmag| | * [[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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* [[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) | ||
* [[Ragismic microtemperaments #Ennealimmal|Trinealimmal]] (1\27 period) | * [[Ragismic microtemperaments #Ennealimmal|Trinealimmal]], [[Tritrizo clan #Cobalt|cobalt]] (1\27 period) | ||
* [[Horwell temperaments #Oquatonic|Oquatonic]] (1\28 period) | * [[Horwell temperaments #Oquatonic|Oquatonic]] (1\28 period) | ||
* [[Hemifamity temperaments #Mystery|Mystery]] (1\29 period) | * [[Hemifamity temperaments #Mystery|Mystery]] (1\29 period) | ||
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* [[Compton family #Decades|Decades]] (1\36 period) | * [[Compton family #Decades|Decades]] (1\36 period) | ||
* [[Ragismic microtemperaments #Enneadecal|Hemienneadecal]] (1\38 period) | * [[Ragismic microtemperaments #Enneadecal|Hemienneadecal]] (1\38 period) | ||
* [[Counterpyth family|Counterpyth]] (1\41 period) | * [[Counterpyth family|Counterpyth temperaments]] (1\41 period) | ||
* [[Mitonismic temperaments #Meridic|Meridic]] (1\43 period) | * [[Mitonismic temperaments #Meridic|Meridic]] (1\43 period) | ||
* [[Ragismic microtemperaments #Palladium|Palladium]] (1\46 period) | * [[Ragismic microtemperaments #Palladium|Palladium]] (1\46 period) | ||
* [[Mercator family|Mercator]] (1\53 period) | * [[Mercator family|Mercator temperaments]] (1\53 period) | ||
* [[Compton family #Omicronbeta|Omicronbeta]] (1\72 period) | * [[Compton family #Omicronbeta|Omicronbeta]] (1\72 period) | ||
* [[Parkleiness temperaments #Octogintic|Octogintic]] (1\80 period) | * [[Parkleiness temperaments #Octogintic|Octogintic]] (1\80 period) | ||
Revision as of 11:42, 18 January 2022
All temperaments on this page have a fractional-octave period, such as 1\26, 1\31, or 1\41.
Temperaments discussed elsewhere include:
- 1\2 period temperaments
- 1\3 period temperaments
- 1\4 period temperaments
- 1\5 period temperaments
- 1\6 period temperaments
- 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, tridecatonic, trideci (1\13 period)
- Pentadecal, quindecic (1\15 period)
- Hexadecoid, sedecic (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, cobalt (1\27 period)
- Oquatonic (1\28 period)
- Mystery (1\29 period)
- Birds (1\31 period)
- Decades (1\36 period)
- Hemienneadecal (1\38 period)
- Counterpyth temperaments (1\41 period)
- Meridic (1\43 period)
- Palladium (1\46 period)
- Mercator temperaments (1\53 period)
- Omicronbeta (1\72 period)
- Octogintic (1\80 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
Triacontaheptoid
Subgroup: 2.3.5.7
Comma list: 244140625/242121642, 283115520/282475249
Mapping: [⟨37 23 74 92], ⟨0 3 1 1]]
POTE generator: ~5/4 = 385.3041
Badness: 0.784746
11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 4000/3993, 226492416/226474325
Mapping: [⟨37 23 74 92 128], ⟨0 3 1 1 0]]
POTE generator: ~5/4 = 385.3281
Vals: Template:Val list
Badness: 0.167327
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1375/1372, 4000/3993, 15379/15360
Mapping: [⟨37 23 74 92 128 125], ⟨0 3 1 1 0 1]]
POTE generator: ~5/4 = 385.3067
Vals: Template:Val list
Badness: 0.076183
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 625/624, 715/714, 1225/1224, 4000/3993, 11271/11264
Mapping: [⟨37 23 74 92 128 125 175], ⟨0 3 1 1 0 1 -2]]
POTE generator: ~5/4 = 385.3427
Vals: Template:Val list
Badness: 0.052475
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