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|12EDO]], [[205edo|205EDO]], and [[217edo|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|12EDO]], [[205edo|205EDO]], and [[217edo|217EDO]] among others. | ||
'''<font style="font-size: 1.35em"> | '''<font style="font-size: 1.35em">Quindromeda (12&193)</font>'''<br> | ||
'''<font style="font-size: 1.2em">5-limit</font>'''<br> | '''<font style="font-size: 1.2em">5-limit</font>'''<br> | ||
Comma: {{monzo|56 -28 -5}}<br> | Comma: {{monzo|56 -28 -5}}<br> | ||
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Vals: 12, 169, 181, 193, 205, 217, 422<br> | Vals: 12, 169, 181, 193, 205, 217, 422<br> | ||
Badness: 0.399849<br><br> | Badness: 0.399849<br><br> | ||
'''<font style="font-size: 1.35em">Quintakwai (12&193)</font>'''<br> | '''<font style="font-size: 1.2em">2.3.5.17.19 subgroup</font>'''<br> | ||
Comma list: 1216/1215, 1445/1444, 6144/6137<br> | |||
Gencom: [2 18/17; 1216/1215 1445/1444 6144/6137]<br> | |||
Gencom mapping: [{{val|1 2 0 5 4}}, {{val|0 -5 28 -11 3}}]<br> | |||
POTE generator: ~18/17 = 99.524<br> | |||
Vals: 12, 169, 181, 193, 205, 422<br> | |||
RMS error: 0.0813 cents<br><br> | |||
'''<font style="font-size: 1.35em">[[Hemifamity temperaments #Quintakwai|Quintakwai]] (12&193)</font>'''<br> | |||
'''<font style="font-size: 1.2em">7-limit</font>'''<br> | '''<font style="font-size: 1.2em">7-limit</font>'''<br> | ||
Comma list: 5120/5103, 9765625/9680832<br> | Comma list: 5120/5103, 9765625/9680832<br> | ||
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Vals: 12, 181, 193, 374, 567ce, 941bcegh, 1508bccdeegghh<br> | Vals: 12, 181, 193, 374, 567ce, 941bcegh, 1508bccdeegghh<br> | ||
Badness: 0.025861<br><br> | Badness: 0.025861<br><br> | ||
'''<font style="font-size: 1.35em">Quintoneum (12&217)</font>'''<br> | '''<font style="font-size: 1.35em">[[Hemimean clan #Quintoneum|Quintoneum]] (12&217)</font>'''<br> | ||
'''<font style="font-size: 1.2em">7-limit</font>'''<br> | '''<font style="font-size: 1.2em">7-limit</font>'''<br> | ||
Comma list: 3136/3125, 33554432/33480783<br> | Comma list: 3136/3125, 33554432/33480783<br> | ||
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Vals: 12, 217e, 229, 446e, 675ceefh<br> | Vals: 12, 217e, 229, 446e, 675ceefh<br> | ||
Badness: 0.040410<br><br> | Badness: 0.040410<br><br> | ||
'''<font style="font-size: 1.35em">Semiquindromeda (12&422)</font>''' | '''<font style="font-size: 1.35em">Semiquindromeda (12&422)</font>'''<br> | ||
'''<font style="font-size: 1.2em">7-limit</font>'''<br> | '''<font style="font-size: 1.2em">7-limit</font>'''<br> | ||
Comma list: 102760448/102515625, 1220703125/1219784832<br> | Comma list: 102760448/102515625, 1220703125/1219784832<br> | ||
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Vals: 12f, 410, 422, 1254dfhh, 1676bdffhh<br> | Vals: 12f, 410, 422, 1254dfhh, 1676bdffhh<br> | ||
Badness: 0.025439<br><br> | Badness: 0.025439<br><br> | ||
== See also == | == See also == | ||