Keenanismic 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-3 temperaments tempering out the keenanisma, 385/384. For the rank-4 keenanismic temperament, see Keenanismic family.
Temperaments discussed elsewhere include:
- Selenium (+49/48 or 56/55) → Semaphoresmic family
- Polyhymnia (+81/80) → Didymus rank-3 family
- Orwellian (+99/98) → Orwellismic family
- Keemic (+100/99) → Keemic family
- Zeus (+121/120 or 176/175) → Porwell family and Biyatismic clan
- Starling (+126/125) → Starling family
- Marvel (+225/224) → Marvel family
- Mirwomo (+243/242) → Rastmic rank-3 clan
- Sensamagic (+245/243) → Sensamagic family
- Portent (+441/440) → Gamelismic family
- Augustus (+1232/1215) → Diaschismic rank-3 family
- Agni (+1375/1372) → Breed family
- Akea (+2200/2187) → Hemifamity family
- Zelda (+3388/3375) → Horwell family
- Beyla (+4375/4374) → Ragismic family
- Enlil (+6250/6237) → Kleismic rank-3 family
Considered below are uniwiz and tritiwiz.
Uniwiz
- For the 7-limit version, see Miscellaneous 7-limit temperaments #Uniwiz.
Uniwiz tempers out the keenanisma, 385/384, the kalisma, 9801/9800, as well as the Alpharabian comma, 131769/131072 ([-17 2 0 0 4⟩), in the 11-limit. The extension to the 2.3.5.7.11.17 subgroup tempers out two no-13's 17-limit PIFE commas, 561/560 and 595/594, along with their product, 289/288, thus also equating the half-octave with 17/12~24/17. The S-expression-based comma list of this extension is {(S17), S33, S34, S35 = S49 × S50, (S99 = S33/S35)}.
It features the split of the whole tone into four equal parts, each representing 36/35~35/34~34/33~33/32. Therefore, it is most interesting to those who would like to make extensive use of quartertones. It can be viewed as the temperament described by the three quartertone-size equal temperaments: 22, 24 and 26. In the 11-limit it shares the optimal patent val, 284, with keenanismic.
Subgroup: 2.3.5.7.11
Comma list: 385/384, 9801/9800
Mapping: [⟨2 1 0 7 8], ⟨0 2 0 3 -1], ⟨0 0 1 -1 0]]
- mapping generators: ~99/70, ~16/11, ~5
- WE: ~99/70 = 600.2029 ¢, ~16/11 = 650.9604 ¢, ~5/4 = 385.1616 ¢
- error map: ⟨+0.406 +0.169 -0.341 -0.498 -0.655]
- CWE: ~99/70 = 600.0000 ¢, ~16/11 = 650.8311 ¢, ~5/4 = 385.1658 ¢
- error map: ⟨0.000 -0.293 -1.148 -1.499 -2.149]
Optimal ET sequence: 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de
Badness (Sintel): 0.636
2.3.5.7.11.17 subgroup
Subgroup: 2.3.5.7.11.17
Comma list: 289/288, 385/384, 561/560
Subgroup-val mapping: [⟨2 1 0 7 8 6], ⟨0 2 0 3 -1 2], ⟨0 0 1 -1 0 0]]
Gencom mapping: [⟨2 1 0 7 8 0 6], ⟨0 2 0 3 -1 0 2], ⟨0 0 1 -1 0 0 0]]
Optimal tunings:
- WE: ~99/70 = 600.2365 ¢, ~16/11 = 651.0126 ¢, ~5/4 = 385.1864 ¢
- CWE: ~99/70 = 600.0000 ¢, ~16/11 = 650.8664 ¢, ~5/4 = 385.1951 ¢
Optimal ET sequence: 22, 46, 68, 72, 118, 190g, 212g, 284g, 330eg, 402degg
Badness (Sintel): 0.351
Tritiwiz
Subgroup: 2.3.5.7.11
Comma list: 385/384, 4000/3993
Mapping: [⟨1 2 0 8 1], ⟨0 -3 0 -4 1], ⟨0 0 1 -2 1]]
- mapping generators: ~2, ~11/10, ~5
- WE: ~2 = 1200.0000 ¢, ~11/10 = 166.1752 ¢, ~5/4 = 384.3796 ¢
- error map: ⟨+0.400 +0.320 -1.133 -0.684 +0.438]
- CWE: ~2 = 1200.0000 ¢, ~11/10 = 166.0419 ¢, ~5/4 = 384.3625 ¢
- error map: ⟨0.000 -0.081 -1.951 -1.718 -0.914]
Optimal ET sequence: 15, 22, 37, 50, 65, 72, 159, 231, 253, 325c, 412cd, 484cd
Badness (Sintel): 0.879