Keenanismic 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, 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

Template:Val list

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

Template:Val list

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

Template:Val list

Badness: 0.732 × 10^-3