34ed7: Difference between revisions

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34ED7 can also be thought of as a [[generator]] of the 11-limit temperament which tempers out 896/891, 1375/1372, and 4375/4356, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintupole'' temperament). This temperament is supported by [[12edo|12EDO]], [[109edo|109EDO]], and [[121edo|121EDO]] among others.

~~'''~~~~[[16ed5/2 #16ed5/2 as a generator|Trisa-quingu]]~~ (12&121)</font~~>'''<br~~>

'''~~~~5-limit~~~~'''

; Quintaleap (12&121)

Comma: {{monzo|37 -16 -5}}

'''5-limit'''

Comma: {{monzo|37 -16 -5}} = 137438953472/134521003125

Mapping: [{{val|1 2 1}}, {{val|0 -5 16}}]

POTE generator: ~135/128 = 99.267

Vals: 12, 85, 97, 109, 121, 133, 278c, 411bc, 544bc

Badness: 0.444506

~~'''~~[[Octagar temperaments #Quintupole|Quintupole]] (12&121)</font~~>'''<br~~>

; [[Octagar temperaments #Quintupole|Quintupole]] (12&121)

'''~~~~7-limit~~~~'''

'''7-limit'''

Comma list: 4000/3969, 458752/455625

Mapping: [{{val|1 2 1 0}}, {{val|0 -5 16 34}}]

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Vals: 12, 97, 109, 121

Badness: 0.111620

'''~~~~11-limit~~~~'''

'''11-limit'''

Comma list: 896/891, 1375/1372, 4375/4356

Mapping: [{{val|1 2 1 0 -1}}, {{val|0 -5 16 34 54}}]

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Vals: 12, 109, 121, 351bde, 472bdee

Badness: 0.056501

'''~~~~13-limit~~~~'''

'''13-limit'''

Comma list: 352/351, 364/363, 625/624, 2704/2695

Mapping: [{{val|1 2 1 0 -1 -2}}, {{val|0 -5 16 34 54 69}}]

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Vals: 12f, 109, 121

Badness: 0.038431

'''~~~~17-limit~~~~'''

'''17-limit'''

Comma list: 256/255, 352/351, 364/363, 375/374, 442/441

Mapping: [{{val|1 2 1 0 -1 -2 5}}, {{val|0 -5 16 34 54 69 -11}}]

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Vals: 12f, 109, 121

Badness: 0.028721

'''~~~~19-limit~~~~'''

'''19-limit'''

Comma list: 190/189, 256/255, 352/351, 361/360, 364/363, 375/374

Mapping: [{{val|1 2 1 0 -1 -2 5 4}}, {{val|0 -5 16 34 54 69 -11 3}}]

@@ Line 189: / Line 189: @@
 ED7 can also be thought of as a [[generator]] of the 11-limit temperament which tempers out 896/891, 1375/1372, and 4375/4356, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintupole'' temperament). This temperament is supported by [[12edo|12EDO]], [[109edo|109EDO]], and [[121edo|121EDO]] among others.
-'''<font style="font-size: 1.35em">[[16ed5/2 #16ed5/2 as a generator|Trisa-quingu]] (12&amp;121)</font>'''<br>
-'''<font style="font-size: 1.2em">5-limit</font>'''<br>
+; <font style="font-size: 1.15em">Quintaleap (12&amp;121)</font>
-Comma: {{monzo|37 -16 -5}}<br>
+'''5-limit'''<br>
+Comma: {{monzo|37 -16 -5}} = 137438953472/134521003125<br>
 Mapping: [{{val|1 2 1}}, {{val|0 -5 16}}]<br>
 POTE generator: ~135/128 = 99.267<br>
 Vals: 12, 85, 97, 109, 121, 133, 278c, 411bc, 544bc<br>
 Badness: 0.444506<br><br>
-'''<font style="font-size: 1.35em">[[Octagar temperaments #Quintupole|Quintupole]] (12&amp;121)</font>'''<br>
+; <font style="font-size: 1.15em">[[Octagar temperaments #Quintupole|Quintupole]] (12&amp;121)</font>
-'''<font style="font-size: 1.2em">7-limit</font>'''<br>
+'''7-limit'''<br>
 Comma list: 4000/3969, 458752/455625<br>
 Mapping: [{{val|1 2 1 0}}, {{val|0 -5 16 34}}]<br>
@@ Line 203: / Line 204: @@
 Vals: 12, 97, 109, 121<br>
 Badness: 0.111620<br><br>
-'''<font style="font-size: 1.2em">11-limit</font>'''<br>
+'''11-limit'''<br>
 Comma list: 896/891, 1375/1372, 4375/4356<br>
 Mapping: [{{val|1 2 1 0 -1}}, {{val|0 -5 16 34 54}}]<br>
@@ Line 209: / Line 210: @@
 Vals: 12, 109, 121, 351bde, 472bdee<br>
 Badness: 0.056501<br><br>
-'''<font style="font-size: 1.2em">13-limit</font>'''<br>
+'''13-limit'''<br>
 Comma list: 352/351, 364/363, 625/624, 2704/2695<br>
 Mapping: [{{val|1 2 1 0 -1 -2}}, {{val|0 -5 16 34 54 69}}]<br>
@@ Line 215: / Line 216: @@
 Vals: 12f, 109, 121<br>
 Badness: 0.038431<br><br>
-'''<font style="font-size: 1.2em">17-limit</font>'''<br>
+'''17-limit'''<br>
 Comma list: 256/255, 352/351, 364/363, 375/374, 442/441<br>
 Mapping: [{{val|1 2 1 0 -1 -2 5}}, {{val|0 -5 16 34 54 69 -11}}]<br>
@@ Line 221: / Line 222: @@
 Vals: 12f, 109, 121<br>
 Badness: 0.028721<br><br>
-'''<font style="font-size: 1.2em">19-limit</font>'''<br>
+'''19-limit'''<br>
 Comma list: 190/189, 256/255, 352/351, 361/360, 364/363, 375/374<br>
 Mapping: [{{val|1 2 1 0 -1 -2 5 4}}, {{val|0 -5 16 34 54 69 -11 3}}]<br>