Keenanismic temperaments: Difference between revisions

This is a collection of rank-3 temperaments tempering out the keenanisma, [[385/384]]. For the rank-4 keenanismic temperament, see [[Keenanismic family]].  

* ''[[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 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 ===

Subgroup: 2.3.5.7

[[Comma list]]: 1500625/1492992

 

 

 

 

 

 

 

Subgroup: 2.3.5.7.11

[[Mapping]]: [{{val| 2 1 0 7 8 }}, {{val| 0 2 0 3 -1 }}, {{val| 0 0 1 -1 0 }}]

{{Multival|legend=1|rank=3| 4 -4 0 -6 2 -2 11 17 -17 -31 }}

[[POTE generator]]s: ~33/32 = 50.7404 or ~11/8 = 549.2596, ~5/4 = 385.0315

[[Badness]]: 0.529 × 10^-3

[[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

 

Other EDOs (from previous lists) supporting the temperament: {{ val list|284g, 330eg, 402degg }}

 

[[Badness]]: ?

Subgroup: 2.3.5.7.11

[[Mapping]]: [{{val| 1 2 0 8 1 }}, {{val| 0 -3 0 -4 1 }}, {{val| 0 0 1 -2 1 }}]

 

Mapping generators: ~2, ~11/10, ~5

 

[[POTE generator]]s: ~11/10 = 166.198, ~5/4 = 384.3513

{{Val list|legend=1| 15, 22, 37, 50, 65, 72, 159, 231, 253, 325c, 412cd, 484cd }}

[[Badness]]: 0.732 × 10^-3