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 (''quindromeda'' temperament). 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.

Equating 225/224 with 256/255 leads ''quintakwai'' (12&193), which tempers out 400/399 in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads ''~~quintoneum~~'' (12&217), which tempers out 476/475 in the 2.3.5.7.17.19 subgroup.

Equating 225/224 with 256/255 leads ''quintakwai'' (12&193), which tempers out 400/399 in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads ''quintagar'' (12&217), which tempers out 476/475 in the 2.3.5.7.17.19 subgroup.

'''Quindromeda (12&193)'''

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Vals: 12, 181, 193, 374, 567ce, 941bcegh, 1508bccdeegghh

Badness: 0.025861

'''[[Hemimean clan #~~Quintoneum~~|~~Quintoneum~~]] (12&217)'''

'''[[Hemimean clan #Quintagar|Quintagar]] (12&217)'''

'''7-limit'''

Comma list: 3136/3125, 33554432/33480783

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Vals: 12, 217, 229, 446, 675c

Badness: 0.142897

'''[[Hemimean clan #Quintagar|Quintoneum]] (12&217)'''

'''11-limit'''

Comma list: 441/440, 3136/3125, 7168000/7144929

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Vals: 12f, 205df, 217

Badness: 0.025782

'''[[Hemimean clan #~~Quintoneum~~|Quintoneoid]] (12&217)'''

'''[[Hemimean clan #Quintagar|Quintoneoid]] (12&217)'''

'''13-limit'''

Comma list: 441/440, 1001/1000, 3136/3125, 59150/59049

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Vals: 12, 205d, 217

Badness: 0.028983

'''[[Hemimean clan #~~Quintoneum~~|Quintasandra]] (217&229)'''

'''[[Hemimean clan #Quintagar|Quintasandra]] (217&229)'''

'''11-limit'''

Comma list: 3136/3125, 19712/19683, 41503/41472

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Vals: 12e, 217, 446, 663ch

Badness: 0.026654

'''[[Hemimean clan #~~Quintoneum~~|Quintasandroid]] (229&241)'''

'''[[Hemimean clan #Quintagar|Quintasandroid]] (229&241)'''

'''11-limit'''

Comma list: 3136/3125, 8019/8000, 15488/15435

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Vals: 12f, 217ef, 229, 241, 470cd

Badness: 0.033145

'''[[Hemimean clan #~~Quintoneum~~|Quintasand]] (12&229)'''

'''[[Hemimean clan #Quintagar|Quintasand]] (12&229)'''

'''13-limit'''

Comma list: 1573/1568, 3136/3125, 4096/4095, 4459/4455

@@ 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 (''quindromeda'' temperament). 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.
-Equating 225/224 with 256/255 leads ''quintakwai'' (12&amp;193), which tempers out 400/399 in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads ''quintoneum'' (12&amp;217), which tempers out 476/475 in the 2.3.5.7.17.19 subgroup.
+Equating 225/224 with 256/255 leads ''quintakwai'' (12&amp;193), which tempers out 400/399 in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads ''quintagar'' (12&amp;217), which tempers out 476/475 in the 2.3.5.7.17.19 subgroup.
 '''<font style="font-size: 1.35em">Quindromeda (12&amp;193)</font>'''<br>
@@ Line 204: / Line 204: @@
 Vals: 12, 181, 193, 374, 567ce, 941bcegh, 1508bccdeegghh<br>
 Badness: 0.025861<br><br>
-'''<font style="font-size: 1.35em">[[Hemimean clan #Quintoneum|Quintoneum]] (12&amp;217)</font>'''<br>
+'''<font style="font-size: 1.35em">[[Hemimean clan #Quintagar|Quintagar]] (12&amp;217)</font>'''<br>
 '''<font style="font-size: 1.2em">7-limit</font>'''<br>
 Comma list: 3136/3125, 33554432/33480783<br>
@@ Line 211: / Line 211: @@
 Vals: 12, 217, 229, 446, 675c<br>
 Badness: 0.142897<br><br>
+'''<font style="font-size: 1.35em">[[Hemimean clan #Quintagar|Quintoneum]] (12&amp;217)</font>'''<br>
 '''<font style="font-size: 1.2em">11-limit</font>'''<br>
 Comma list: 441/440, 3136/3125, 7168000/7144929<br>
@@ Line 235: / Line 236: @@
 Vals: 12f, 205df, 217<br>
 Badness: 0.025782<br><br>
-'''<font style="font-size: 1.35em">[[Hemimean clan #Quintoneum|Quintoneoid]] (12&amp;217)</font>'''<br>
+'''<font style="font-size: 1.35em">[[Hemimean clan #Quintagar|Quintoneoid]] (12&amp;217)</font>'''<br>
 '''<font style="font-size: 1.2em">13-limit</font>'''<br>
 Comma list: 441/440, 1001/1000, 3136/3125, 59150/59049<br>
@@ Line 254: / Line 255: @@
 Vals: 12, 205d, 217<br>
 Badness: 0.028983<br><br>
-'''<font style="font-size: 1.35em">[[Hemimean clan #Quintoneum|Quintasandra]] (217&amp;229)</font>'''<br>
+'''<font style="font-size: 1.35em">[[Hemimean clan #Quintagar|Quintasandra]] (217&amp;229)</font>'''<br>
 '''<font style="font-size: 1.2em">11-limit</font>'''<br>
 Comma list: 3136/3125, 19712/19683, 41503/41472<br>
@@ Line 279: / Line 280: @@
 Vals: 12e, 217, 446, 663ch<br>
 Badness: 0.026654<br><br>
-'''<font style="font-size: 1.35em">[[Hemimean clan #Quintoneum|Quintasandroid]] (229&amp;241)</font>'''<br>
+'''<font style="font-size: 1.35em">[[Hemimean clan #Quintagar|Quintasandroid]] (229&amp;241)</font>'''<br>
 '''<font style="font-size: 1.2em">11-limit</font>'''<br>
 Comma list: 3136/3125, 8019/8000, 15488/15435<br>
@@ Line 304: / Line 305: @@
 Vals: 12f, 217ef, 229, 241, 470cd<br>
 Badness: 0.033145<br><br>
-'''<font style="font-size: 1.35em">[[Hemimean clan #Quintoneum|Quintasand]] (12&amp;229)</font>'''<br>
+'''<font style="font-size: 1.35em">[[Hemimean clan #Quintagar|Quintasand]] (12&amp;229)</font>'''<br>
 '''<font style="font-size: 1.2em">13-limit</font>'''<br>
 Comma list: 1573/1568, 3136/3125, 4096/4095, 4459/4455<br>