Xenharmonic Wiki

Porcupine family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled
4,516 edits
No edit summary
Xenllium (talk | contribs)
autopatrolled
4,516 edits
mNo edit summary
Line 48: Line 48:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]] eigenmonzo: 9/7
* [[7-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
: Eigenmonzos: 2, 5/4
* [[9-odd-limit]]: ~10/9 = {{monzo| 1/6 -1/6 0 1/12 }}
: Eigenmonzos: 2, 9/7


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: [160.000, 163.636] (2\15 to 3\22)
* [[Diamond monotone]] range: ~10/9 = [160.000, 163.636] (2\15 to 3\22)
* [[Diamond tradeoff]] range: [157.821, 166.015]
* 7-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
* Diamond monotone and tradeoff: [160.000, 163.636]
* 9-odd-limit diamond tradeoff: ~10/9 = [157.821, 182.404]
* Diamond monotone and tradeoff: ~10/9 = [160.000, 163.636]


{{Val list|legend=1| 7, 15, 22, 59, 81bd, 140bbd }}
{{Val list|legend=1| 7, 15, 22, 59, 81bd, 140bbd }}
Line 66: Line 70:
Mapping: [{{val| 1 2 3 2 4 }}, {{val| 0 -3 -5 6 -4 }}]
Mapping: [{{val| 1 2 3 2 4 }}, {{val| 0 -3 -5 6 -4 }}]


POTE generator: ~11/10 = 162.747
POTE generator: ~10/9 = 162.747


Minimax tuning:  
Minimax tuning:  
* 11-odd-limit eigenmonzo: 9/7
* 11-odd-limit: ~10/9 = {{monzo| 1/6 -1/6 0 1/12 }}
: Eigenmonzos: 2, 9/7


Tuning ranges:  
Tuning ranges:  
* [[Diamond monotone]] range: [160.000, 163.636] (2\15 to 3\22)
* Diamond monotone range: ~10/9  = [160.000, 163.636] (2\15 to 3\22)
* [[Diamond tradeoff]] range: [150.637, 182.404]
* Diamond tradeoff range: ~10/9 = [150.637, 182.404]
* Diamond monotone and tradeoff: [160.000, 163.636]
* Diamond monotone and tradeoff: ~10/9 =  [160.000, 163.636]


Vals: {{val list| 7, 15, 22, 37, 59 }}
Vals: {{val list| 7, 15, 22, 37, 59 }}
Line 87: Line 92:
Mapping: [{{val| 1 2 3 2 4 4 }}, {{val| 0 -3 -5 6 -4 -2 }}]
Mapping: [{{val| 1 2 3 2 4 4 }}, {{val| 0 -3 -5 6 -4 -2 }}]


POTE generator: ~11/10 = 162.708
POTE generator: ~10/9 = 162.708


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit eigenmonzo: 11/8
* 13- and 15-odd-limit: ~10/9 = {{monzo| 1 0 0 0 -1/4 }}
: Eigenmonzo: 2, 11/8


Tuning ranges:  
Tuning ranges:  
* [[Diamond monotone]] range: [160.000, 163.636] (2\15 to 3\22)
* Diamond monotone range: [160.000, 163.636] (2\15 to 3\22)
* [[Diamond tradeoff]] range: [138.573, 182.404]
* Diamond tradeoff range: [138.573, 182.404]
* Diamond monotone and tradeoff: [160.000, 163.636]
* Diamond monotone and tradeoff: [160.000, 163.636]


Line 110: Line 116:
Mapping: [{{val| 1 2 3 2 4 6 }}, {{val| 0 -3 -5 6 -4 -17 }}]
Mapping: [{{val| 1 2 3 2 4 6 }}, {{val| 0 -3 -5 6 -4 -17 }}]


POTE generator: ~11/10 = 162.277
POTE generator: ~10/9 = 162.277


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit eigenmonzo: 13/11
* 13- and 15-odd-limit: ~10/9 = {{monzo| 2/13 0 0 0 1/13 -1/13 }}
: Eigenmonzos: 2, 13/11


Tuning ranges:  
Tuning ranges:  
* [[Diamond monotone]] range: [160.000, 162.162] (2\15 to 5\37)
* Diamond monotone range: [160.000, 162.162] (2\15 to 5\37)
* [[Diamond tradeoff]] range: [150.637, 182.404]
* Diamond tradeoff range: [150.637, 182.404]
* Diamond monotone and tradeoff: [160.000, 162.162]
* Diamond monotone and tradeoff: [160.000, 162.162]


Line 131: Line 138:
Mapping: [{{val| 1 2 3 2 4 1 }}, {{val| 0 -3 -5 6 -4 20 }}]
Mapping: [{{val| 1 2 3 2 4 1 }}, {{val| 0 -3 -5 6 -4 20 }}]


POTE generator: ~11/10 = 162.482
POTE generator: ~10/9 = 162.482


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit eigenmonzo: 13/7
* 13- and 15-odd-limit: ~10/9 = {{monzo| 1/14 0 0 -1/14 0 1/14 }}
: Eigenmonzos: 2, 14/13


Vals: {{val list| 15f, 22f, 37 }}
Vals: {{val list| 15f, 22f, 37 }}
Line 147: Line 155:
Mapping: [{{val| 1 2 3 2 4 3 }}, {{val| 0 -3 -5 6 -4 5 }}]
Mapping: [{{val| 1 2 3 2 4 3 }}, {{val| 0 -3 -5 6 -4 5 }}]


POTE generator: ~11/10 = 163.688
POTE generator: ~10/9 = 163.688


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit eigenmonzo: 9/7
* 13- and 15-odd-limit: ~10/9 = {{monzo| 1/6 -1/6 0 1/12 }}
: Eigenmonzos: 2, 9/7


Vals: {{val list| 7, 15f, 22 }}
Vals: {{val list| 7, 15f, 22 }}
Line 167: Line 176:
{{Multival|legend=1| 3 5 1 1 -7 -12 }}
{{Multival|legend=1| 3 5 1 1 -7 -12 }}


[[POTE generator]]: ~10/9 = 158.868
[[POTE generator]]: ~8/7 = 158.868


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]] eigenmonzo: 5/4
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 3/5 0 -1/5 }}
: Eigenmonzos: 2, 5/4


{{Val list|legend=1| 7, 8d, 15d }}
{{Val list|legend=1| 7, 8d, 15d }}
Line 183: Line 193:
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -3 -5 -1 -4 }}]
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -3 -5 -1 -4 }}]


POTE generator: ~11/10 = 158.750
POTE generator: ~8/7 = 158.750


Vals: {{val list| 7, 8d, 15d }}
Vals: {{val list| 7, 8d, 15d }}
Line 201: Line 211:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]] eigenmonzo: 7/5
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/11 0 1/11 -1/11 }}
: Eigenmonzos: 2, 7/5


{{Val list|legend=1| 7d, 15d, 22, 29, 51, 73c }}
{{Val list|legend=1| 7d, 15d, 22, 29, 51, 73c }}
Line 214: Line 225:
Mapping: [{{val| 1 2 3 5 4 }}, {{val| 0 -3 -5 -16 -4 }}]
Mapping: [{{val| 1 2 3 5 4 }}, {{val| 0 -3 -5 -16 -4 }}]


POTE generator: ~11/10 = 164.552
POTE generator: ~10/9 = 164.552


Minimax tuning:  
Minimax tuning:  
* 11-odd-limit eigenmonzo: 7/5
* 11-odd-limit: ~10/9 = {{monzo| 2/11 0 1/11 -1/11 }}
: Eigenmonzos: 2, 7/5


Vals: {{val list| 7d, 15d, 22, 29, 51, 73ce }}
Vals: {{val list| 7d, 15d, 22, 29, 51, 73ce }}
Line 230: Line 242:
Mapping: [{{val| 1 2 3 5 4 3 }}, {{val| 0 -3 -5 -16 -4 5 }}]
Mapping: [{{val| 1 2 3 5 4 3 }}, {{val| 0 -3 -5 -16 -4 5 }}]


POTE generator: ~11/10 = 164.953
POTE generator: ~10/9 = 164.953


Vals: {{val list| 7d, 22, 29, 51f, 80cdeff }}
Vals: {{val list| 7d, 22, 29, 51f, 80cdeff }}
Line 248: Line 260:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]] eigenmonzo: 3/2
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/3 -1/3 }}
: Eigenmonzos: 2, 3


{{Val list|legend=1| 7, 29, 65c, 94cd }}
{{Val list|legend=1| 7, 29, 65c, 94cd }}
Line 261: Line 274:
Mapping: [{{val| 1 2 3 1 4 }}, {{val| 0 -3 -5 13 -4 }}]
Mapping: [{{val| 1 2 3 1 4 }}, {{val| 0 -3 -5 13 -4 }}]


POTE generator: ~11/10 = 165.981
POTE generator: ~10/9 = 165.981


Minimax tuning:  
Minimax tuning:  
* 11-odd-limit eigenmonzo: 3/2
* 11-odd-limit: ~10/9 = {{monzo| 2/3 -1/3 }}
: Eigenmonzos: 2, 3


Vals: {{val list| 7, 29, 65ce, 94cde }}
Vals: {{val list| 7, 29, 65ce, 94cde }}
Line 277: Line 291:
Mapping: [{{val| 1 2 3 1 4 3 }}, {{val| 0 -3 -5 13 -4 5 }}]
Mapping: [{{val| 1 2 3 1 4 3 }}, {{val| 0 -3 -5 13 -4 5 }}]


POTE generator: ~11/10 = 165.974
POTE generator: ~10/9 = 165.974


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit eigenmonzo: 3/2
* 13- and 15-odd-limit: ~10/9 = {{monzo| 2/3 -1/3 }}
: Eigenmonzos: 2, 3


Vals: {{val list| 7, 29, 65cef, 94cdef }}
Vals: {{val list| 7, 29, 65cef, 94cdef }}
Line 356: Line 371:


; Music
; Music
[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 Phobos Light] by [[Chris Vaisvil]] in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.
[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 Phobos Light] by [[Chris Vaisvil]] in Hedgehog[14] [[hedgehog14|tuned]] to 22EDO.


== Nautilus ==
== Nautilus ==
Line 467: Line 482:
[[POTE generator]]: ~36/35 = 54.384
[[POTE generator]]: ~36/35 = 54.384


{{Val list|legend=1| 22 }}
{{Val list|legend=1| 1c, 21c, 22 }}


[[Badness]]: 0.115304
[[Badness]]: 0.115304
Line 474: Line 489:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 55/54, 100/99, 5324/5145
Comma list: 55/54, 100/99, 352/343


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -9 -15 -4 -12 }}]
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -9 -15 -4 -12 }}]
Line 480: Line 495:
POTE generator: ~36/35 = 54.376
POTE generator: ~36/35 = 54.376


Vals: {{val list| 22 }}
Vals: {{val list| 1ce, 21ce, 22 }}


Badness: 0.051319
Badness: 0.051319
Line 493: Line 508:
POTE generator: ~36/35 = 54.665
POTE generator: ~36/35 = 54.665


Vals: {{val list| 22 }}
Vals: {{val list| 1ce, 21cef, 22 }}


Badness: 0.044739
Badness: 0.044739
Retrieved from "https://en.xen.wiki/w/Porcupine_family"