Keenanismic temperaments: Difference between revisions
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This is a collection of rank-3 temperaments tempering out the keenanisma, [[385/384]]. For the rank-4 keenanismic temperament, see [[Keenanismic family]]. | 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 is ''headquarters''. | |||
== Headquarters == | == Headquarters == | ||
Revision as of 14:32, 22 August 2021
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 is headquarters.
Headquarters
Headquarters 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: 0.5292 × 10-3