28ed5: Difference between revisions

Line 157:

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.

'''5-limit 12&~~205~~'''

'''5-limit 12&193'''

Comma: |56 -28 -5>

POTE generator: ~4428675/4194304 = 99.526

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Badness: 0.399849

'''2.3.5.17.19 12&~~205~~'''

'''7-limit 12&193'''

Commas: 5120/5103, 9765625/9680832

POTE generator: ~625/588 = 99.483

Map: [<1 2 0 -2|, <0 -5 28 58|]

EDOs: 12, 169, 181, 193, 205, 374

Badness: 0.155536

'''11-limit 12&193'''

Commas: 1375/1372, 4375/4356, 5120/5103

POTE generator: ~35/33 = 99.472

Map: [<1 2 0 -2 -4|, <0 -5 28 58 90|]

EDOs: 12, 169e, 181, 193, 205e, 374

Badness: 0.073158

'''7-limit 12&229'''

Commas: 3136/3125, 33554432/33480783

POTE generator: ~200/189 = 99.555

Map: [<1 2 0 -3|, <0 -5 28 70|]

EDOs: 12, 217, 229, 241, 446

Badness: 0.142897

'''11-limit 12&229'''

Commas: 3136/3125, 8019/8000, 15488/15435

POTE generator: ~200/189 = 99.570

Map: [<1 2 0 -3 -6|, <0 -5 28 70 114|]

EDOs: 12, 217e, 229, 241

Badness: 0.093971

'''2.3.5.17.19 subgroup 12&193'''

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

POTE generator: ~18/17 = 99.524

@@ Line 157: / Line 157: @@
 ed5 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;205</font>'''<br>
+'''<font style="font-size: 1.2em">5-limit 12&amp;193</font>'''<br><br>
 Comma: |56 -28 -5&gt;<br><br>
 POTE generator: ~4428675/4194304 = 99.526<br><br>
@@ Line 164: / Line 164: @@
 Badness: 0.399849<br><br>
-'''<font style="font-size: 1.2em">2.3.5.17.19 12&amp;205</font>'''<br>
+'''<font style="font-size: 1.2em">7-limit 12&amp;193</font>'''<br><br>
+Commas: 5120/5103, 9765625/9680832<br><br>
+POTE generator: ~625/588 = 99.483<br><br>
+Map: [&lt;1 2 0 -2|, &lt;0 -5 28 58|]<br><br>
+EDOs: 12, 169, 181, 193, 205, 374<br><br>
+Badness: 0.155536<br><br>
+'''<font style="font-size: 1.2em">11-limit 12&amp;193</font>'''<br><br>
+Commas: 1375/1372, 4375/4356, 5120/5103<br><br>
+POTE generator: ~35/33 = 99.472<br><br>
+Map: [&lt;1 2 0 -2 -4|, &lt;0 -5 28 58 90|]<br><br>
+EDOs: 12, 169e, 181, 193, 205e, 374<br><br>
+Badness: 0.073158<br><br>
+'''<font style="font-size: 1.2em">7-limit 12&amp;229</font>'''<br><br>
+Commas: 3136/3125, 33554432/33480783<br><br>
+POTE generator: ~200/189 = 99.555<br><br>
+Map: [&lt;1 2 0 -3|, &lt;0 -5 28 70|]<br><br>
+EDOs: 12, 217, 229, 241, 446<br><br>
+Badness: 0.142897<br><br>
+'''<font style="font-size: 1.2em">11-limit 12&amp;229</font>'''<br><br>
+Commas: 3136/3125, 8019/8000, 15488/15435<br><br>
+POTE generator: ~200/189 = 99.570<br><br>
+Map: [&lt;1 2 0 -3 -6|, &lt;0 -5 28 70 114|]<br><br>
+EDOs: 12, 217e, 229, 241<br><br>
+Badness: 0.093971<br><br>
+'''<font style="font-size: 1.2em">2.3.5.17.19 subgroup 12&amp;193</font>'''<br><br>
 Commas: 1216/1215, 1445/1444, 6144/6137<br><br>
 POTE generator: ~18/17 = 99.524<br><br>