Orwellismic temperaments
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
This is a collection of rank-2 temperaments that temper out the orwellisma (monzo: [6 3 -1 -3⟩, ratio: 1728/1715).
Temperaments considered below are secant, infraorwell, quartonic, sentinel, diesic, philips, triskaidekic, and pentaorwell. Discussed elsewhere are:
- Beep (+21/20 or 27/25) → Bug family
- Doublewide (+50/49) → Jubilismic clan
- Superpyth (+64/63) → Archytas clan
- Mothra (+81/80) → Meantone family
- Myna (+126/125) → Starling temperaments
- Orwell (+225/224) → Semicomma family
- Secund (+405/392 or 525/512) → Greenwoodmic temperaments
- Quartonic (+4000/3969) → Quartonic family
- Buzzard (+5120/5103) → Vulture family
- Trisensory (+78732/78125) → Sensipent family
- Trimabila (+268435456/263671875) → Mabila family
Secant
Subgroup: 2.3.5.7
Comma list: 1728/1715, 177147/175000
Mapping: [⟨2 1 0 5], ⟨0 7 15 2]]
- mapping generators: ~567/400, ~10/9
Optimal tuning (POTE): ~567/400 = 600.000 ¢, ~10/9 = 185.885 ¢
Optimal ET sequence: 26, 58, 84, 142, 368cd
Badness (Smith): 0.095278
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 1344/1331, 1728/1715
Mapping: [⟨2 1 0 5 6], ⟨0 7 15 2 3]]
Optimal tuning (POTE): ~99/70 = 600.000 ¢, ~10/9 = 185.962 ¢
Optimal ET sequence: 26, 58, 142e, 200cdee
Badness (Smith): 0.046373
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 351/350, 364/363, 441/440
Mapping: [⟨2 1 0 5 6 4], ⟨0 7 15 2 3 11]]
Optimal tuning (POTE): ~99/70 = 600.000 ¢, ~10/9 = 185.955 ¢
Optimal ET sequence: 26, 58, 84, 142ef
Badness (Smith): 0.025035
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 144/143, 170/169, 221/220, 351/350, 441/440
Mapping: [⟨2 1 0 5 6 4 6], ⟨0 7 15 2 3 11 7]]
Optimal tuning (POTE): ~17/12 = 600.000 ¢, ~10/9 = 185.916 ¢
Optimal ET sequence: 26, 58, 84, 142ef
Badness (Smith): 0.021642
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 144/143, 153/152, 170/169, 210/209, 221/220, 400/399
Mapping: [⟨2 1 0 5 6 4 6 2], ⟨0 7 15 2 3 11 7 21]]
Optimal tuning (POTE): ~17/12 = 600.000 ¢, ~10/9 = 185.858 ¢
Optimal ET sequence: 26, 58h, 84, 142efh, 226deefgh
Badness (Smith): 0.018565
Infraorwell
Subgroup: 2.3.5.7
Comma list: 1728/1715, 28672/28125
Mapping: [⟨1 14 0 16], ⟨0 -16 3 -17]]
- mapping generators: ~2, ~12/7
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/6 = 269.032 ¢
Optimal ET sequence: 9, 49, 58, 165cd, 223bcd
Badness (Smith): 0.117073
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 1344/1331
Mapping: [⟨1 14 0 16 12], ⟨0 -16 3 -17 -11]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/6 = 269.036 ¢
Optimal ET sequence: 9, 49, 58, 165cdee
Badness (Smith): 0.040721
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 176/175, 196/195, 364/363
Mapping: [⟨1 14 0 16 12 20], ⟨0 -16 3 -17 -11 -21]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/6 = 269.021 ¢
Optimal ET sequence: 9, 49f, 58
Badness (Smith): 0.023683
Sentinel
- For the 5-limit version, see Miscellaneous 5-limit temperaments #Sentinel.
Subgroup: 2.3.5.7
Comma list: 1728/1715, 3645/3584
Mapping: [⟨1 3 -3 6], ⟨0 -4 15 -9]]
- mapping generators: ~2, ~9/7
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~9/7 = 425.596 ¢
Optimal ET sequence: 14, 17, 31, 110, 141, 172b, 375bc
Badness (Smith): 0.093805
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 243/242, 385/384
Mapping: [⟨1 3 -3 6 7], ⟨0 -4 15 -9 -10]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~9/7 = 425.550 ¢
Optimal ET sequence: 14, 17, 31, 79, 110e, 141e
Badness (Smith): 0.039595
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 105/104, 144/143, 243/242
Mapping: [⟨1 3 -3 6 7 3], ⟨0 -4 15 -9 -10 2]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~9/7 = 425.501 ¢
Optimal ET sequence: 14, 17, 31, 79f, 110ef, 141ef
Badness (Smith): 0.037408
Diesic
- For the 5-limit version, see Miscellaneous 5-limit temperaments #Diesic.
Subgroup: 2.3.5.7
Comma list: 1728/1715, 5103/5000
Mapping: [⟨1 2 3 3], ⟨0 -13 -21 -6]]
- mapping generators: ~2, ~36/35
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~36/35 = 38.567 ¢
Optimal ET sequence: 31, 156c, 187c, 218bc, 249bc, 280bc
Badness (Smith): 0.107348
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 441/440, 891/875
Mapping: [⟨1 2 3 3 4], ⟨0 -13 -21 -6 -17]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~36/35 = 38.565 ¢
Optimal ET sequence: 31, 156ce, 187ce, 218bcee, 249bcee
Badness (Smith): 0.044186
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 121/120, 343/338, 441/440
Mapping: [⟨1 2 3 3 4 4], ⟨0 -13 -21 -6 -17 -9]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~36/35 = 38.444 ¢
Optimal ET sequence: 31, 94cff, 125cff
Badness (Smith): 0.038116
Phillips
- For the 5-limit version, see Miscellaneous 5-limit temperaments #Phillips.
Subgroup: 2.3.5.7
Comma list: 1728/1715, 6561/6272
Mapping: [⟨2 0 33 -7], ⟨0 1 -9 4]]
- mapping generators: ~81/56, ~3
Optimal tuning (POTE): ~81/56 = 600.000 ¢, ~3/2 = 691.174 ¢
Optimal ET sequence: 14, 26, 66b, 92bc
Badness (Smith): 0.228602
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 385/384, 729/704
Mapping: [⟨2 0 33 -7 -12], ⟨0 1 -9 4 6]]
Optimal tuning (POTE): ~63/44 = 600.000 ¢, ~3/2 = 691.040 ¢
Optimal ET sequence: 14, 26, 40, 66b
Badness (Smith): 0.095777
Triskaidekic
- For the 5-limit version, see Miscellaneous 5-limit temperaments #Triskaidekic.
Subgroup: 2.3.5.7
Comma list: 1728/1715, 1875/1792
Mapping: [⟨13 0 30 16], ⟨0 1 0 1]]
- mapping generators: ~15/14, ~3
Optimal tuning (POTE): ~15/14 = 92.308 ¢, ~3/2 = 694.143 ¢
Badness (Smith): 0.219050
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 125/121, 385/384
Mapping: [⟨13 0 30 16 45], ⟨0 1 0 1 0]]
Optimal tuning (POTE): ~15/14 = 92.308 ¢, ~3/2 = 696.296 ¢
Optimal ET sequence: 13d, 26, 91cd
Badness (Smith): 0.098847
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 99/98, 125/121, 1200/1183
Mapping: [⟨13 0 30 16 45 48], ⟨0 1 0 1 0 0]]
Optimal tuning (POTE): ~15/14 = 92.308 ¢, ~3/2 = 695.879 ¢
Optimal ET sequence: 13d, 26, 91cdf
Badness (Smith): 0.059216
Pentaorwell
- For the 5-limit version, see Syntonic–diatonic equivalence continuum #Counterpental.
Named by +merlan #flirora in 2021, pentaorwell tempers out 179200/177147 and is the 75 & 80 temperament.
Subgroup: 2.3.5.7
Comma list: 1728/1715, 179200/177147
Mapping: [⟨5 0 -36 22], ⟨0 1 6 -1]]
- CTE: ~280/243 = 240.000 ¢, ~3/2 = 704.3709 ¢ (~64/63 = 15.6291 ¢)
- POTE: ~280/243 = 240.000 ¢, ~3/2 = 704.9128 ¢ (~64/63 = 15.0872 ¢)
Optimal ET sequence: 5, 75, 80
Badness (Smith): 0.148665
11-limit
Subgroup: 2.3.5.7.11
Comma list: 896/891, 1728/1715, 2200/2187
Mapping: [⟨5 0 -36 22 57], ⟨0 1 6 -1 -5]]
Optimal tunings:
- CTE: ~55/48 = 240.000 ¢, ~3/2 = 704.8440 ¢ (~99/98 = 15.1560 ¢)
- POTE: ~55/48 = 240.000 ¢, ~3/2 = 704.8788 ¢ (~99/98 = 15.1212 ¢)
Optimal ET sequence: 75e, 80, 315bcdddee
Badness (Smith): 0.071702
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 364/363, 1728/1715
Mapping: [⟨5 0 -36 22 57 82], ⟨0 1 6 -1 -5 -8]]
Optimal tunings:
- CTE: ~55/48 = 240.000 ¢, ~3/2 = 704.7636 ¢ (~99/98 = 15.2364 ¢)
- CWE: ~55/48 = 240.000 ¢, ~3/2 = 704.7112 ¢ (~99/98 = 15.2882 ¢)
Optimal ET sequence: 75e, 80, 155de
Badness (Smith): 0.0557