Canousmic temperaments: Difference between revisions
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Temperaments not dicussed here include: | Temperaments not dicussed here include: | ||
* [[ | * [[godzilla]], {49/48, 81/80} → [[Meantone family #Godzilla]] | ||
* [[ | * ''[[betic]]'', {225/224, 1071875/1062882} → [[Sycamore family #Betic]] | ||
* [[ | * ''[[pentorwell]]'', {1728/1715, 179200/177147} → [[Orwellismic temperaments #Pentorwell]] | ||
* [[ | * ''[[amicable]]'', {2401/2400, 1600000/1594323} → [[Breedsmic temperaments #Amicable]] | ||
* [[ | * [[parakleismic]], {3136/3125, 4375/4374} → [[Ragismic microtemperaments #Parakleismic]] | ||
* [[ | * ''[[septiquarter]]'', {5120/5103, 420175/419904} → [[Hemifamity temperaments #Septiquarter]] | ||
* [[ | * ''[[marthirds]]'', {15625/15552, 2460375/2458624} → [[Kleismic family #Marthirds]] | ||
* ''[[kleischismic]]'', {32805/32768, 1562500/1492992} → [[Schismatic family #Kleischismic]] | |||
Discussed below are satin and semiluna. | Discussed below are satin and semiluna. | ||
Revision as of 10:24, 27 May 2021
These are rank-2 temperaments that temper out the canousma, 4802000/4782969 = [4 -14 3 4⟩. For the rank-3 temperament, see Canou family.
Note that 4802000/4782969 = 2×(10/9)3/(9/7)4, these intervals tend to have lower complexity.
Temperaments not dicussed here include:
- godzilla, {49/48, 81/80} → Meantone family #Godzilla
- betic, {225/224, 1071875/1062882} → Sycamore family #Betic
- pentorwell, {1728/1715, 179200/177147} → Orwellismic temperaments #Pentorwell
- amicable, {2401/2400, 1600000/1594323} → Breedsmic temperaments #Amicable
- parakleismic, {3136/3125, 4375/4374} → Ragismic microtemperaments #Parakleismic
- septiquarter, {5120/5103, 420175/419904} → Hemifamity temperaments #Septiquarter
- marthirds, {15625/15552, 2460375/2458624} → Kleismic family #Marthirds
- kleischismic, {32805/32768, 1562500/1492992} → Schismatic family #Kleischismic
Discussed below are satin and semiluna.
Satin
5-limit
Subgroup: 2.3.5
Comma list: [104 -70 3⟩
Mapping: [⟨1 2 12], ⟨0 -3 -70]]
POTE generator: ~[-34 23 -1⟩ = 165.907
Badness: 2.8530
7-limit
Subgroup: 2.3.5.7
Comma list: 2100875/2097152, 4802000/4782969
Mapping: [⟨1 2 12 -3], ⟨0 -3 -70 42]]
POTE generator: ~8575/7776 = 165.913
Badness: 0.1972
11-limit
Subgroup: 2.3.5.7.11
Comma list: 4000/3993, 19712/19683, 41503/41472
Mapping: [⟨1 2 12 -3 13], ⟨0 -3 -70 42 -69]]
POTE generator: ~11/10 = 165.915
Badness: 0.0580
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1575/1573, 2080/2079, 4096/4095, 13720/13689
Mapping: [⟨1 2 12 -3 13 -1], ⟨0 -3 -70 42 -69 34]]
POTE generator: ~11/10 = 165.914
Badness: 0.0303
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 595/594, 833/832, 1156/1155, 1575/1573, 4096/4095
Mapping: [⟨1 2 12 -3 13 -1 11], ⟨0 -3 -70 42 -69 34 -50]]
POTE generator: ~11/10 = 165.913
Badness: 0.0200
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 595/594, 833/832, 969/968, 1156/1155, 1216/1215, 1575/1573
Mapping: [⟨1 2 12 -3 13 -1 11 16], ⟨0 -3 -70 42 -69 34 -50 -85]]
POTE generator: ~11/10 = 165.913
Badness: 0.0145
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 595/594, 760/759, 833/832, 875/874, 969/968, 1105/1104, 1156/1155
Mapping: [⟨1 2 12 -3 13 -1 11 16 16], ⟨0 -3 -70 42 -69 34 -50 -85 -83]]
POTE generator: ~11/10 = 165.914
Badness: 0.0122
Semiluna
Subgroup: 2.3.5.7
Comma list: 4802000/4782969, 95703125/95551488
Mapping: [⟨2 8 4 23], ⟨0 -15 2 -54]]
POTE generator: ~2187/1960 = 193.1725
Badness: 0.1922
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 14641/14580
Mapping: [⟨2 8 4 23 14], ⟨0 -15 2 -54 -22]]
POTE generator: ~121/108 = 193.1732
Badness: 0.0678