28ed5: Difference between revisions

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28ed5 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[Subgroup temperaments|subgroup temperament]] which tempers out 1216/1215, 1445/1444, and 6144/6137, which is a [[cluster temperament]] with 12 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 1088/1083 ~ 256/255 ~ 289/288 ~ 324/323 ~ 361/360 all tempered together. This temperament is supported by [[12edo]], [[205edo]], and [[217edo]] among others.

'''5-limit 12&193'''

'''5-limit 12&193 (quinsa-quingu)'''

Comma: |56 -28 -5>

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Badness: 0.093971

'''2.3.5.17.19 subgroup 12&193'''~~ ~~

'''7-limit 12&422'''

Commas: 1216/1215, 1445/1444, 6144/6137~~ ~~

POTE generator: ~18/17 = 99.524~~ ~~

Commas: 102760448/102515625, 1220703125/1219784832

Map: [<1 2 0 5 4|, <0 -5 28 -11 3|]~~ ~~

EDOs: 12, 169, 181, 193, 205, 217, 229, 241, 374, 398, 422, 446, 591, 603~~ ~~

POTE generator: ~1323/1250 = 99.521

Map: [<2 4 0 -5|, <0 -5 28 64|]

EDOs: 12, 398, 410, 422, 808, 832, 1242

Badness: 0.233140

'''11-limit 12&422'''

Commas: 5632/5625, 9801/9800, 85937500/85766121

POTE generator: ~1323/1250 = 99.525

Map: [<2 4 0 -5 -10|, <0 -5 28 64 102|]

EDOs: 12, 410, 422, 832

Badness: 0.093926

'''2.3.5.17.19 subgroup 12&193'''

Commas: 1216/1215, 1445/1444, 6144/6137

POTE generator: ~18/17 = 99.524

Map: [<1 2 0 5 4|, <0 -5 28 -11 3|]

EDOs: 12, 169, 181, 193, 205, 217, 229, 241, 374, 398, 422, 446, 591, 603

==See also==

@@ Line 157: / Line 157: @@
 ed5 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[Subgroup temperaments|subgroup temperament]] which tempers out 1216/1215, 1445/1444, and 6144/6137, which is a [[cluster temperament]] with 12 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 1088/1083 ~ 256/255 ~ 289/288 ~ 324/323 ~ 361/360 all tempered together. This temperament is supported by [[12edo]], [[205edo]], and [[217edo]] among others.
-'''<font style="font-size: 1.2em">5-limit 12&amp;193</font>'''
+'''<font style="font-size: 1.2em">5-limit 12&amp;193 (quinsa-quingu)</font>'''
 Comma: |56 -28 -5&gt;
@@ Line 217: / Line 217: @@
 Badness: 0.093971<br>
-'''<font style="font-size: 1.2em">2.3.5.17.19 subgroup 12&amp;193</font>'''<br><br>
+'''<font style="font-size: 1.2em">7-limit 12&amp;422</font>'''
-Commas: 1216/1215, 1445/1444, 6144/6137<br><br>
-POTE generator: ~18/17 = 99.524<br><br>
+Commas: 102760448/102515625, 1220703125/1219784832
-Map: [&lt;1 2 0 5 4|, &lt;0 -5 28 -11 3|]<br><br>
-EDOs: 12, 169, 181, 193, 205, 217, 229, 241, 374, 398, 422, 446, 591, 603<br><br>
+POTE generator: ~1323/1250 = 99.521
+Map: [&lt;2 4 0 -5|, &lt;0 -5 28 64|]
+EDOs: 12, 398, 410, 422, 808, 832, 1242
+Badness: 0.233140<br>
+'''<font style="font-size: 1.2em">11-limit 12&amp;422</font>'''
+Commas: 5632/5625, 9801/9800, 85937500/85766121
+POTE generator: ~1323/1250 = 99.525
+Map: [&lt;2 4 0 -5 -10|, &lt;0 -5 28 64 102|]
+EDOs: 12, 410, 422, 832
+Badness: 0.093926<br>
+'''<font style="font-size: 1.2em">2.3.5.17.19 subgroup 12&amp;193</font>'''
+Commas: 1216/1215, 1445/1444, 6144/6137
+POTE generator: ~18/17 = 99.524
+Map: [&lt;1 2 0 5 4|, &lt;0 -5 28 -11 3|]
+EDOs: 12, 169, 181, 193, 205, 217, 229, 241, 374, 398, 422, 446, 591, 603<br>
 ==See also==