34ed7: Difference between revisions

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-'''[[Ed7|Division of the 7th harmonic]] into 34 equal parts''' (34ed7) is related to [[12edo|12 edo]], but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 99.0831 cents. It is consistent to the [[11-odd-limit|11-integer-limit]], but not to the 12-integer-limit. In comparison, 12edo is only consistent up to the [[9-odd-limit|10-integer-limit]].
+'''[[Ed7|Division of the 7th harmonic]] into 34 equal parts''' (34ED7) is related to [[12edo|12 EDO]], but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 99.0831 cents. It is consistent to the [[11-odd-limit|11-integer-limit]], but not to the 12-integer-limit. In comparison, 12EDO is only consistent up to the [[9-odd-limit|10-integer-limit]].
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-==34ed7 as a generator==
+== 34ed7 as a generator ==
-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. This temperament is supported by [[12edo]], [[109edo]], and [[121edo]] among others.
+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. This temperament is supported by [[12edo|12EDO]], [[109edo|109EDO]], and [[121edo|121EDO]] among others.
-'''<font style="font-size: 1.2em">5-limit 12&amp;121 (trisa-quingu)</font>'''
+'''<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>
+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: 1.2em">7-limit</font>'''<br>
+Comma list: 4000/3969, 458752/455625<br>
+Mapping: [{{val|1 2 1 0}}, {{val|0 -5 16 34}}]<br>
+POTE generator: ~135/128 = 99.175<br>
+Vals: 12, 97, 109, 121<br>
+Badness: 0.111620<br><br>
+'''<font style="font-size: 1.2em">11-limit</font>'''<br>
+Comma list: 896/891, 1375/1372, 4375/4356<br>
+Mapping: [{{val|1 2 1 0 -1}}, {{val|0 -5 16 34 54}}]<br>
+POTE generator: ~132/125 = 99.156<br>
+Vals: 12, 109, 121, 351bde, 472bdee<br>
+Badness: 0.056501<br><br>
+'''<font style="font-size: 1.2em">13-limit</font>'''<br>
+Comma list: 352/351, 364/363, 625/624, 2704/2695<br>
+Mapping: [{{va|1 2 1 0 -1 -2}}, {{val|0 -5 16 34 54 69|]<br>
+POTE generator: ~55/52 = 99.165<br>
+Vals: 12f, 109, 121<br>
+Badness: 0.038431<br><br>
+'''<font style="font-size: 1.2em">17-limit</font>'''<br>
+Comma list: 256/255, 352/351, 364/363, 375/374, 442/441<br>
+Mapping: [{{va|1 2 1 0 -1 -2 5}}, {{val|0 -5 16 34 54 69 -11|]<br>
+POTE generator: ~18/17 = 99.172<br>
+Vals: 12f, 109, 121<br>
+Badness: 0.028721<br><br>
-Comma: |37 -16 -5&gt;
+== See also ==
-POTE generator: ~135/128 = 99.267
-Map: [&lt;1 2 1|, &lt;0 -5 16|]
-EDOs: 12, 85, 97, 109, 121, 133, 145, 157, 206, 230, 254
-Badness: 0.444506<br>
-'''<font style="font-size: 1.2em">7-limit 12&amp;121</font>'''
-Commas: 4000/3969, 458752/455625
-POTE generator: ~135/128 = 99.175
-Map: [&lt;1 2 1 0|, &lt;0 -5 16 34|]
-EDOs: 12, 97, 109, 121, 206, 230
-Badness: 0.111620<br>
-'''<font style="font-size: 1.2em">11-limit 12&amp;121</font>'''
-Commas: 896/891, 1375/1372, 4375/4356
-POTE generator: ~132/125 = 99.156
-Map: [&lt;1 2 1 0 -1|, &lt;0 -5 16 34 54|]
-EDOs: 12, 109, 121, 230
-Badness: 0.056501<br>
-'''<font style="font-size: 1.2em">13-limit 12f&amp;121</font>'''
-Commas: 352/351, 364/363, 625/624, 2704/2695
-POTE generator: ~55/52 = 99.165
-Map: [&lt;1 2 1 0 -1 -2|, &lt;0 -5 16 34 54 69|]
-EDOs: 12f, 109, 121, 230
-Badness: 0.038431<br>
-==See also==
 *[[12edo]]: relative EDO
 *[[19ED3|19ed3]]: relative ED3