Keenanismic temperaments: Difference between revisions
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== Uniwiz == | == Uniwiz == | ||
Uniwiz tempers out 1500625/1492992 = {{monzo| -11 -6 4 4 }} in the 7-limit, and the keenanisma, 385/384, the kalisma, [[9801/9800]], as well as the [[Alpharabian comma]], 131769/131072 = {{monzo| -17 2 0 0 4 }}, in the 11-limit. It features the split of the whole tone into four equal parts, each representing 36/35~33/32. Therefore, it is most interesting to those who would like to make extensive use of quartertones. It can be viewed as | Uniwiz tempers out 1500625/1492992 = {{monzo| -11 -6 4 4 }} in the 7-limit, and the keenanisma, 385/384, the kalisma, [[9801/9800]], as well as the [[Alpharabian comma]], 131769/131072 = {{monzo| -17 2 0 0 4 }}, in the 11-limit. In the 17-limit it tempers 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. | ||
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: [[22edo|22]], [[24edo|24]] and [[26edo|26]]. In the 11-limit it shares the [[optimal patent val]], [[284edo|284]], with [[keenanismic]]. | |||
=== 7-limit === | === 7-limit === | ||
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[[Badness]]: 0.529 × 10<sup>-3</sup> | [[Badness]]: 0.529 × 10<sup>-3</sup> | ||
=== No-13's 17-limit === | |||
Subgroup 2.3.5.7.11.17 | |||
[[Comma list]]: 385/384, 9801/9800, 256/255 | |||
[[Mapping]]: [{{val| 2 1 0 7 8 6 }}, {{val| 0 2 0 3 -1 2 }}, {{val| 0 0 1 -1 0 0 }}] | |||
[[Wedgie]]: ? | |||
[[CTE tuning]]: 17/12~99/70 = 600.000, 33/32~34/33~35/34~36/35 = 51.234 or 16/11~35/24 = 651.234, 5/4 = 385.730 | |||
All EDOs supporting the temperament by patent val: {{ val list|22, 24, 26, 46, 48, 50, 68, 72, 90, 92, 94, 114, 116, 118, 136, 140, 162, 164, 186 }} | |||
Other EDOs (from previous lists) supporting the temperament: {{ val list|284g, 330eg, 402degg }} | |||
[[Badness]]: ? | |||
== Tritiwiz == | == Tritiwiz == | ||
Revision as of 23:52, 25 July 2022
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, 56/55} → Semiphore family #Selenium
- Polyhymnia, {81/80, 385/384} → Didymus rank three family #Polyhymnia
- Orwellian, {99/98, 385/384} → Orwellismic family #Orwellian
- Supermagic, {100/99, 385/384} → Keemic family #Undecimal supermagic
- Zeus, {121/120, 176/175} → Porwell family #Zeus
- Starling, {126/125, 385/384} → Starling family #Undecimal starling
- Marvel, {225/224, 385/384} → Marvel family #Undecimal marvel (unimarv)
- Mirwomo, {243/242, 385/384} → Rastmic temperaments #Mirwomo
- Sensamagic, {245/243, 385/384} → Sensamagic family #Undecimal sensamagic
- Portent, {385/384, 441/440} → Gamelismic family #Portent
- Augustus, {385/384, 1232/1215} → Diaschismic rank three family #Augustus
- Agni, {385/384, 1375/1372} → Breed family #Agni
- Beyla, {385/384, 4375/4374} → Ragismic family #Beyla
- Enlil, {385/384, 6250/6237} → Kleismic rank three family #Enlil
Considered below are uniwiz and tritiwiz.
Uniwiz
Uniwiz tempers out 1500625/1492992 = [-11 -6 4 4⟩ in the 7-limit, and 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. In the 17-limit it tempers 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.
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.
7-limit
Subgroup: 2.3.5.7
Comma list: 1500625/1492992
Mapping: [⟨2 1 0 7], ⟨0 2 0 3], ⟨0 0 1 -1]]
Mapping generators: ~1225/864, ~35/24, ~5
Wedgie: ⟨⟨⟨ 4 -4 -6 11 ]]]
POTE generators: ~36/35 = 50.9529 or ~48/35 = 549.0471, ~5/4 = 385.3326
Badness: 0.7042 × 10-3
11-limit
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]]
Wedgie: ⟨⟨⟨ 4 -4 0 -6 2 -2 11 17 -17 -31 ]]]
POTE generators: ~33/32 = 50.7404 or ~11/8 = 549.2596, ~5/4 = 385.0315
Badness: 0.529 × 10-3
No-13's 17-limit
Subgroup 2.3.5.7.11.17
Comma list: 385/384, 9801/9800, 256/255
Mapping: [⟨2 1 0 7 8 6], ⟨0 2 0 3 -1 2], ⟨0 0 1 -1 0 0]]
Wedgie: ?
CTE tuning: 17/12~99/70 = 600.000, 33/32~34/33~35/34~36/35 = 51.234 or 16/11~35/24 = 651.234, 5/4 = 385.730
All EDOs supporting the temperament by patent val: Template:Val list
Other EDOs (from previous lists) supporting the temperament: Template:Val list
Badness: ?
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
Wedgie: ⟨⟨⟨ 3 -6 3 -4 1 2 16 5 -26 -12 ]]]
POTE generators: ~11/10 = 166.198, ~5/4 = 384.3513
Badness: 0.732 × 10-3