Keenanismic temperaments: Difference between revisions

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== Uniwiz ==

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. 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: [[22edo|22]], [[24edo|24]], and [[26edo|26]]. It shares the [[optimal patent val]], [[284edo|284]], with [[keenanismic]].

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 ===

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[[Badness]]: 0.529 × 10<sup>-3</sup>

=== No-13's 17-limit ===

Subgroup 2.3.5.7.11.17

[[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

All EDOs supporting the temperament by patent val: {{ val list|22, 24, 26, 46, 48, 50, 68, 72, 90, 92, 94, 114, 116, 118, 136, 140, 162, 164, 186 }}

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

[[Badness]]: ?

== Tritiwiz ==

@@ Line 20: / Line 20: @@
 == Uniwiz ==
-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. 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: [[22edo|22]], [[24edo|24]], and [[26edo|26]]. It shares the [[optimal patent val]], [[284edo|284]], with [[keenanismic]].
+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 ===
@@ Line 53: / Line 55: @@
 [[Badness]]: 0.529 × 10<sup>-3</sup>
+=== No-13's 17-limit ===
+Subgroup 2.3.5.7.11.17
+[[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
+All EDOs supporting the temperament by patent val: {{ val list|22, 24, 26, 46, 48, 50, 68, 72, 90, 92, 94, 114, 116, 118, 136, 140, 162, 164, 186 }}
+Other EDOs (from previous lists) supporting the temperament: {{ val list|284g, 330eg, 402degg }}
+[[Badness]]: ?
 == Tritiwiz ==