16ed5/2: Difference between revisions

Line 171:

== 16ed5/2 as a generator ==

16ED5/2 can also be thought as a [[generator]] of a [[cluster temperament]] which tempers out {{monzo|37 -16 -5}} (trisa-quingu comma). It has twelve clusters of notes in an octave. There are some extensions for 7 and higher limit including ''quintupole'' (12&121), ''quinticosiennic'' (12&145), and ''quintapole'' (12&85).

'''Trisa-quingu (12&121)'''

'''5-limit'''

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

Comma: {{monzo|37 -16 -5}} = 137438953472/1345210003125

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

POTE generator: ~135/128 = 99.267

Line 192:

Line 194:

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

Badness: 0.056501

'''[[Marvel temperaments|12&85 ~~temperament]]~~'''

'''[[Hemifamity temperaments #Quinticosiennic|Quinticosiennic]] (12&145)'''

'''7-limit'''

Comma list: 5120/5103, 395136/390625

Mapping: [{{val|1 2 1 -1}}, {{val|0 -5 16 46}}]

POTE generator: ~135/128 = 99.345

Vals: 12, 133, 145, 157, 302c, 459bcc

Badness: 0.158041

'''11-limit'''

Comma list: 441/440, 896/891, 78408/78125

Mapping: [{{val|1 2 1 -1 -2}}, {{val|0 -5 16 46 66}}]

POTE generator: ~35/33 = 99.318

Vals: 12, 133, 145

Badness: 0.080674

'''[[Marvel temperaments #Quintapole|Quintapole]] (12&85)'''

'''7-limit'''

Comma list: 225/224, 7812500/7411887

@@ Line 171: / Line 171: @@
 == 16ed5/2 as a generator ==
+ED5/2 can also be thought as a [[generator]] of a [[cluster temperament]] which tempers out {{monzo|37 -16 -5}} (trisa-quingu comma). It has twelve clusters of notes in an octave. There are some extensions for 7 and higher limit including ''quintupole'' (12&amp;121), ''quinticosiennic'' (12&amp;145), and ''quintapole'' (12&amp;85).
 '''<font style="font-size: 1.35em">Trisa-quingu (12&amp;121)</font>'''<br>
 '''<font style="font-size: 1.2em">5-limit</font>'''<br>
-Comma: {{monzo|37 -16 -5}}<br>
+Comma: {{monzo|37 -16 -5}} = 137438953472/1345210003125<br>
 Mapping: [{{val|1 2 1}}, {{val|0 -5 16}}]<br>
 POTE generator: ~135/128 = 99.267<br>
@@ Line 192: / Line 194: @@
 Vals: 12, 109, 121, 351bde, 472bdee<br>
 Badness: 0.056501<br><br>
-'''<font style="font-size: 1.35em">[[Marvel temperaments|12&amp;85 temperament]]</font>'''<br>
+'''<font style="font-size: 1.35em">[[Hemifamity temperaments #Quinticosiennic|Quinticosiennic]] (12&amp;145)</font>'''<br>
+'''<font style="font-size: 1.2em">7-limit</font>'''<br>
+Comma list: 5120/5103, 395136/390625<br>
+Mapping: [{{val|1 2 1 -1}}, {{val|0 -5 16 46}}]<br>
+POTE generator: ~135/128 = 99.345<br>
+Vals: 12, 133, 145, 157, 302c, 459bcc<br>
+Badness: 0.158041<br><br>
+'''<font style="font-size: 1.2em">11-limit</font>'''<br>
+Comma list: 441/440, 896/891, 78408/78125<br>
+Mapping: [{{val|1 2 1 -1 -2}}, {{val|0 -5 16 46 66}}]<br>
+POTE generator: ~35/33 = 99.318<br>
+Vals: 12, 133, 145<br>
+Badness: 0.080674<br><br>
+'''<font style="font-size: 1.35em">[[Marvel temperaments #Quintapole|Quintapole]] (12&amp;85)</font>'''<br>
+{{See also|42ed11 #42ed11 as a generator}}
 '''<font style="font-size: 1.2em">7-limit</font>'''<br>
 Comma list: 225/224, 7812500/7411887<br>