Keenanismic temperaments: Difference between revisions

Line 1:

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

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

Temperaments discussed elsewhere include:

Line 23:

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. The [[extension]] to the 2.3.5.7.11.13.17 [[subgroup]] tempers out two no-13's 17-limit [[PIFE comma]]s, [[561/560]] and [[595/594]], along with their product, [[289/288]], thus also equating the half-octave with 17/12~24/17. The S-expression-based comma list of this extension is {([[289/288|S17]],) [[1089/1088|S33]], [[1156/1155|S34]], [[1225/1224|S35 = S49*S50]](, [[9801/9800|S99 = S33/S35]])}.

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]].

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 [[quartertone]]s. 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 ===

@@ Line 1: / Line 1: @@
-This is a collection of [[rank-3 temperament|rank-3]] [[temperament]]s [[tempering out]] the keenanisma, [[385/384]]. For the rank-4 keenanismic temperament, see [[Keenanismic family]].
+This is a collection of [[rank-3 temperament|rank-3]] [[temperament]]s [[tempering out]] the keenanisma, [[385/384]]. For the [[rank-4]] keenanismic temperament, see [[Keenanismic family]].
 Temperaments discussed elsewhere include:
@@ Line 23: / Line 23: @@
 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. The [[extension]] to the 2.3.5.7.11.13.17 [[subgroup]] tempers out two no-13's 17-limit [[PIFE comma]]s, [[561/560]] and [[595/594]], along with their product, [[289/288]], thus also equating the half-octave with 17/12~24/17. The S-expression-based comma list of this extension is {([[289/288|S17]],) [[1089/1088|S33]], [[1156/1155|S34]], [[1225/1224|S35 = S49*S50]](, [[9801/9800|S99 = S33/S35]])}.
-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]].
+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 [[quartertone]]s. 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 ===