Keenanismic temperaments: Difference between revisions
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: mapping generators: ~99/70, ~16/11, ~5 | : mapping generators: ~99/70, ~16/11, ~5 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~99/70 = 600.2029{{c}}, ~16/11 = 650.9604{{c}}, ~5/4 = 385.1616{{c}} | |||
: [[error map]]: {{val| +0.406 +0.169 -0.341 -0.498 -0.655 }} | |||
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~16/11 = 650.8311{{c}}, ~5/4 = 385.1658{{c}} | |||
: error map: {{val| 0.000 -0.293 -1.148 -1.499 -2.149 }} | |||
<!-- * [[CTE]]: ~99/70 = 600.0000{{c}}, ~16/11 = 651.1082{{c}}, ~5/4 = 385.5778{{c}} --> | |||
{{Optimal ET sequence|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de }} | {{Optimal ET sequence|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 0.636 | ||
=== 2.3.5.7.11.17 subgroup === | === 2.3.5.7.11.17 subgroup === | ||
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Gencom mapping: {{mapping| 2 1 0 7 8 0 6 | 0 2 0 3 -1 0 2 | 0 0 1 -1 0 0 0 }} | Gencom mapping: {{mapping| 2 1 0 7 8 0 6 | 0 2 0 3 -1 0 2 | 0 0 1 -1 0 0 0 }} | ||
Optimal | Optimal tunings: | ||
* WE: ~99/70 = 600.2365{{c}}, ~16/11 = 651.0126{{c}}, ~5/4 = 385.1864{{c}} | |||
* CWE: ~99/70 = 600.0000{{c}}, ~16/11 = 650.8664{{c}}, ~5/4 = 385.1951{{c}} | |||
<!-- * CTE: ~17/12 = 600.0000{{c}}, ~16/11 = 651.2344{{c}}, ~5/4 = 385.7289{{c}} --> | |||
{{Optimal ET sequence|legend=0| 22, 46, 68, 72, 118, 190g, 212g, 284g, 330eg, 402degg }} | {{Optimal ET sequence|legend=0| 22, 46, 68, 72, 118, 190g, 212g, 284g, 330eg, 402degg }} | ||
Badness ( | Badness (Sintel): 0.351 | ||
== Tritiwiz == | == Tritiwiz == | ||
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: mapping generators: ~2, ~11/10, ~5 | : mapping generators: ~2, ~11/10, ~5 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.0000{{c}}, ~11/10 = 166.1752{{c}}, ~5/4 = 384.3796{{c}} | |||
: [[error map]]: {{val| +0.400 +0.320 -1.133 -0.684 +0.438 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 166.0419{{c}}, ~5/4 = 384.3625{{c}} | |||
: error map: {{val| 0.000 -0.081 -1.951 -1.718 -0.914 }} | |||
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~11/10 = 165.8258{{c}}, ~5/4 = 384.6711{{c}} --> | |||
{{Optimal ET sequence|legend=1| 15, 22, 37, 50, 65, 72, 159, 231, 253, 325c, 412cd, 484cd }} | {{Optimal ET sequence|legend=1| 15, 22, 37, 50, 65, 72, 159, 231, 253, 325c, 412cd, 484cd }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 0.879 | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
Revision as of 15:27, 27 November 2025
- 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