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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.
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.


'''<font style="font-size: 1.2em">5-limit 12&amp;193 (quinsa-quingu)</font>'''
'''<font style="font-size: 1.25em">5-limit 12&amp;193 (quinsa-quingu)</font>'''


Comma: |56 -28 -5&gt;
Comma: |56 -28 -5&gt;
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Badness: 0.399849<br>
Badness: 0.399849<br>


'''<font style="font-size: 1.2em">7-limit 12&amp;193</font>'''
'''<font style="font-size: 1.25em">7-limit 12&amp;193</font>'''


Commas: 5120/5103, 9765625/9680832
Commas: 5120/5103, 9765625/9680832
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Badness: 0.155536<br>
Badness: 0.155536<br>


'''<font style="font-size: 1.2em">11-limit 12&amp;193</font>'''
'''<font style="font-size: 1.15em">11-limit 12&amp;193</font>'''


Commas: 1375/1372, 4375/4356, 5120/5103
Commas: 1375/1372, 4375/4356, 5120/5103
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Badness: 0.073158<br>
Badness: 0.073158<br>


'''<font style="font-size: 1.2em">7-limit 12&amp;229</font>'''
'''<font style="font-size: 1.15em">13-limit 12&amp;193</font>'''
 
Commas: 325/324, 1375/1372, 1575/1573, 4096/4095
 
POTE generator: ~35/33 = 99.468
 
Map: [&lt;1 2 0 -2 -4 10|, &lt;0 -5 28 58 90 -76|]
 
EDOs: 12, 181, 193, 374
 
Badness: 0.062737<br>
 
'''<font style="font-size: 1.15em">17-limit 12&amp;193</font>'''
 
Commas: 325/324, 375/374, 595/594, 1275/1274, 4096/4095
 
POTE generator: ~18/17 = 99.469
 
Map: [&lt;1 2 0 -2 -4 10 5|, &lt;0 -5 28 58 90 -76 -11|]
 
EDOs: 12, 181, 193, 374
 
Badness: 0.037855<br>
 
'''<font style="font-size: 1.15em">19-limit 12&amp;193</font>'''
 
Commas: 325/324, 375/374, 400/399, 595/594, 1216/1215, 1275/1274
 
POTE generator: ~18/17 = 99.469
 
Map: [&lt;1 2 0 -2 -4 10 5 4|, &lt;0 -5 28 58 90 -76 -11 3|]
 
EDOs: 12, 181, 193, 374
 
Badness: 0.025861<br>
 
'''<font style="font-size: 1.25em">7-limit 12&amp;229</font>'''


Commas: 3136/3125, 33554432/33480783
Commas: 3136/3125, 33554432/33480783
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Badness: 0.142897<br>
Badness: 0.142897<br>


'''<font style="font-size: 1.2em">11-limit 12&amp;229</font>'''
'''<font style="font-size: 1.15em">11-limit 12&amp;229</font>'''


Commas: 3136/3125, 8019/8000, 15488/15435
Commas: 3136/3125, 8019/8000, 15488/15435
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Map: [&lt;1 2 0 -3 -6|, &lt;0 -5 28 70 114|]
Map: [&lt;1 2 0 -3 -6|, &lt;0 -5 28 70 114|]


EDOs: 12, 217e, 229, 241
EDOs: 12, 217e, 229, 241, 446e


Badness: 0.093971<br>
Badness: 0.093971<br>


'''<font style="font-size: 1.2em">7-limit 12&amp;422</font>'''
'''<font style="font-size: 1.15em">13-limit 12&amp;229</font>'''
 
Commas: 1573/1568, 3136/3125, 4096/4095, 4459/4455
 
POTE generator: ~200/189 = 99.556
 
Map: [&lt;1 2 0 -3 -6 11|, &lt;0 -5 28 70 114 -88|]
 
EDOs: 12, 217e, 229, 241f, 446e
 
Badness: 0.100195<br>
 
'''<font style="font-size: 1.15em">17-limit 12&amp;229</font>'''
 
Commas: 561/560, 715/714, 1701/1700, 3136/3125, 4096/4095
 
POTE generator: ~18/17 = 99.556
 
Map: [&lt;1 2 0 -3 -6 11 5|, &lt;0 -5 28 70 114 -88 -11|]
 
EDOs: 12, 217e, 229, 241f, 446e
 
Badness: 0.057851<br>
 
'''<font style="font-size: 1.15em">19-limit 12&amp;229</font>'''
 
Commas: 286/285, 476/475, 561/560, 627/625, 1216/1215, 1729/1728
 
POTE generator: ~18/17 = 99.557
 
Map: [&lt;1 2 0 -3 -6 11 5 4|, &lt;0 -5 28 70 114 -88 -11 3|]
 
EDOs: 12, 217e, 229, 241f, 446e
 
Badness: 0.040410<br>
 
'''<font style="font-size: 1.25em">7-limit 12&amp;422</font>'''


Commas: 102760448/102515625, 1220703125/1219784832
Commas: 102760448/102515625, 1220703125/1219784832
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Badness: 0.233140<br>
Badness: 0.233140<br>


'''<font style="font-size: 1.2em">11-limit 12&amp;422</font>'''
'''<font style="font-size: 1.15em">11-limit 12&amp;422</font>'''


Commas: 5632/5625, 9801/9800, 85937500/85766121
Commas: 5632/5625, 9801/9800, 85937500/85766121
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Badness: 0.093926<br>
Badness: 0.093926<br>


'''<font style="font-size: 1.2em">2.3.5.17.19 subgroup 12&amp;193</font>'''
'''<font style="font-size: 1.15em">13-limit 12f&amp;422</font>'''
 
Commas: 1716/1715, 2080/2079, 5632/5625, 831875/830466
 
POTE generator: ~1323/1250 = 99.523
 
Map: [&lt;2 4 0 -5 -10 -13|, &lt;0 -5 28 64 102 123|]
 
EDOs: 12f, 410, 422, 832
 
Badness: 0.053361<br>
 
'''<font style="font-size: 1.15em">17-limit 12f&amp;422</font>'''
 
Commas: 1716/1715, 2080/2079, 2500/2499, 5632/5625, 15895/15876
 
POTE generator: ~18/17 = 99.522
 
Map: [&lt;2 4 0 -5 -10 -13 10|, &lt;0 -5 28 64 102 123 -11|]
 
EDOs: 12f, 410, 422, 832
 
Badness: 0.034659<br>
 
'''<font style="font-size: 1.15em">19-limit 12f&amp;422</font>'''
 
Commas: 1216/1215, 1445/1444, 1716/1715, 2080/2079, 2376/2375, 2500/2499
 
POTE generator: ~18/17 = 99.523
 
Map: [&lt;2 4 0 -5 -10 -13 10 8|, &lt;0 -5 28 64 102 123 -11 3|]
 
EDOs: 12f, 410, 422, 832h
 
Badness: 0.025439<br>
 
'''<font style="font-size: 1.25em">2.3.5.17.19 subgroup 12&amp;193</font>'''


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