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. 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 one which is joined by the three quartertone-size equal temperaments: 22, 24, and 26. 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

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