Porcupine family: Difference between revisions

Porcupine: base the sharpness on 4/3 rather than 3/2 (see talk). Hystrix isn't actually flat of 8d
m Units. + missing links. Fix dead links.
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 164.166
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 164.166{{c}}
: [[error map]]: {{val| 0.000 +5.547 -7.143 }}
: [[error map]]: {{val| 0.000 +5.547 -7.143 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 163.950
* [[POTE]]: ~2 = 1200.000{{c}}, ~10/9 = 163.950{{c}}
: error map: {{val| 0.000 +6.194 -6.065 }}
: error map: {{val| 0.000 +6.194 -6.065 }}


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Comma list: 55/54, 100/99
Comma list: 55/54, 100/99


Sval mapping: {{mapping| 1 2 3 4 | 0 -3 -5 -4 }}
Subgroup-val mapping: {{mapping| 1 2 3 4 | 0 -3 -5 -4 }}


Gencom mapping: {{mapping| 1 2 3 0 4 | 0 -3 -5 0 -4 }}
Gencom mapping: {{mapping| 1 2 3 0 4 | 0 -3 -5 0 -4 }}
: gencom: [2 10/9; 55/54, 100/99]


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 163.887
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.887{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 164.078
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 164.078{{c}}


{{Optimal ET sequence|legend=0| 7, 15, 22, 73ce, 95ce }}
{{Optimal ET sequence|legend=0| 7, 15, 22, 73ce, 95ce }}
Line 79: Line 77:
Comma list: 55/54, 100/99, 512/507
Comma list: 55/54, 100/99, 512/507


Sval mapping: {{mapping| 1 5 8 8 2 | 0 -6 -10 -8 3 }}
Subgroup-val mapping: {{mapping| 1 5 8 8 2 | 0 -6 -10 -8 3 }}


: sval mapping generators: ~2, ~65/44
: mapping generators: ~2, ~65/44


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~88/65 = 518.086
* CTE: ~2 = 1200.000{{c}}, ~88/65 = 518.086{{c}}
* POTE: ~2 = 1200.000, ~88/65 = 518.209
* POTE: ~2 = 1200.000{{c}}, ~88/65 = 518.209{{c}}


{{Optimal ET sequence|legend=0| 7, 23bc, 30, 37, 44 }}
{{Optimal ET sequence|legend=0| 7, 23bc, 30, 37, 44 }}
Line 103: Line 101:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 163.203
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 163.203{{c}}
: [[error map]]: {{val| 0.000 +8.435 -2.330 +10.394 }}
: [[error map]]: {{val| 0.000 +8.435 -2.330 +10.394 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 162.880
* [[POTE]]: ~2 = 1200.000{{c}}, ~10/9 = 162.880{{c}}
: error map: {{val| 0.000 +9.405 -0.714 +8.455 }}
: error map: {{val| 0.000 +9.405 -0.714 +8.455 }}


Line 131: Line 129:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 163.105
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.105{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 162.747
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.747{{c}}


Minimax tuning:  
Minimax tuning:  
Line 156: Line 154:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 163.442
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.442{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 162.708
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.708{{c}}


Minimax tuning:  
Minimax tuning:  
Line 182: Line 180:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 162.636
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 162.636{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 162.277
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.277{{c}}


Minimax tuning:  
Minimax tuning:  
Line 206: Line 204:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 163.378
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.378{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 162.482
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.482{{c}}


Minimax tuning:  
Minimax tuning:  
Line 225: Line 223:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 163.678
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.678{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 163.688
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 163.688{{c}}


Minimax tuning:  
Minimax tuning:  
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== Opossum ==
== Opossum ==
{{Main| Opossum }}
Opossum can be described as {{nowrap| 8d & 15 }}. Tempering out [[28/27]], the perfect fifth of three generator steps is conflated with not [[32/21]] as in porcupine but [[14/9]]. Three such fifths or nine generator steps octave reduced give a flat 7/4. 2\15 is a good generator.  
Opossum can be described as {{nowrap| 8d & 15 }}. Tempering out [[28/27]], the perfect fifth of three generator steps is conflated with not [[32/21]] as in porcupine but [[14/9]]. Three such fifths or nine generator steps octave reduced give a flat 7/4. 2\15 is a good generator.  


Line 246: Line 246:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 161.306
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 161.306{{c}}
: [[error map]]: {{val| 0.000 +14.126 +7.155 -20.583 }}
: [[error map]]: {{val| 0.000 +14.126 +7.155 -20.583 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 159.691
* [[POTE]]: ~2 = 1200.000{{c}}, ~10/9 = 159.691{{c}}
: error map: {{val| 0.000 +18.971 +15.229 -6.048 }}
: error map: {{val| 0.000 +18.971 +15.229 -6.048 }}


Line 266: Line 266:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 161.365
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 161.365{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 159.807
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 159.807{{c}}


Minimax tuning:  
Minimax tuning:  
Line 284: Line 284:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 161.631
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 161.631{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 158.805
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 158.805{{c}}


Minimax tuning:  
Minimax tuning:  
Line 304: Line 304:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 164.391
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 164.391{{c}}
: [[error map]]: {{val| 0.000 +4.871 -8.270 +0.913 }}
: [[error map]]: {{val| 0.000 +4.871 -8.270 +0.913 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 164.412
* [[POTE]]: ~2 = 1200.000{{c}}, ~10/9 = 164.412{{c}}
: error map: {{val| 0.000 +4.809 -8.375 +0.580 }}
: error map: {{val| 0.000 +4.809 -8.375 +0.580 }}


Line 325: Line 325:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 164.321
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 164.321{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 164.552
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 164.552{{c}}


Minimax tuning:  
Minimax tuning:  
Line 344: Line 344:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 164.478
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 164.478{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 164.953
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 164.953{{c}}


{{Optimal ET sequence|legend=0| 7d, 22, 29, 51f, 80cdeff }}
{{Optimal ET sequence|legend=0| 7d, 22, 29, 51f, 80cdeff }}
Line 364: Line 364:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 166.094
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 166.094{{c}}
: [[error map]]: {{val| 0.000 -0.236 -16.783 -9.607 }}
: [[error map]]: {{val| 0.000 -0.236 -16.783 -9.607 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 166.041
* [[POTE]]: ~2 = 1200.000{{c}}, ~10/9 = 166.041{{c}}
: error map: {{val| 0.000 -0.077 -16.516 -10.299 }}
: error map: {{val| 0.000 -0.077 -16.516 -10.299 }}


Line 385: Line 385:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 165.925
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 165.925{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 165.981
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 165.981{{c}}


Minimax tuning:  
Minimax tuning:  
Line 404: Line 404:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 166.046
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 166.046{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 165.974
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 165.974{{c}}


Minimax tuning:  
Minimax tuning:  
Line 425: Line 425:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 165.185
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 165.185{{c}}
: [[error map]]: {{val| 0.000 +2.491 -12.236 +65.990 }}
: [[error map]]: {{val| 0.000 +2.491 -12.236 +65.990 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 158.868
* [[POTE]]: ~2 = 1200.000{{c}}, ~10/9 = 158.868{{c}}
: error map: {{val| 0.000 +21.442 +19.348 +72.306 }}
: error map: {{val| 0.000 +21.442 +19.348 +72.306 }}


Line 446: Line 446:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 164.768
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 164.768{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 158.750
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 158.750{{c}}


{{Optimal ET sequence|legend=0| 7, 8d, 15d }}
{{Optimal ET sequence|legend=0| 7, 8d, 15d }}
Line 469: Line 469:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~9/7 = 435.258
* [[CTE]]: ~7/5 = 600.000{{c}}, ~9/7 = 435.258{{c}}
: [[error map]]: {{val| 0.000 +3.819 -10.024 +7.464 }}
: [[error map]]: {{val| 0.000 +3.819 -10.024 +7.464 }}
* [[POTE]]: ~7/5 = 600.000, ~9/7 = 435.648
* [[POTE]]: ~7/5 = 600.000{{c}}, ~9/7 = 435.648{{c}}
: error map: {{val| 0.000 +4.989 -8.074 +9.414 }}
: error map: {{val| 0.000 +4.989 -8.074 +9.414 }}


Line 486: Line 486:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~9/7 = 435.528
* CTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.528{{c}}
* POTE: ~7/5 = 600.000, ~9/7 = 435.386
* POTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.386{{c}}


{{Optimal ET sequence|legend=0| 8d, 14c, 22, 58ce }}
{{Optimal ET sequence|legend=0| 8d, 14c, 22, 58ce }}
Line 501: Line 501:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~9/7 = 436.309
* CTE: ~7/5 = 600.000{{c}}, ~9/7 = 436.309{{c}}
* POTE: ~7/5 = 600.000, ~9/7 = 435.861
* POTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.861{{c}}


{{Optimal ET sequence|legend=0| 8d, 14cf, 22 }}
{{Optimal ET sequence|legend=0| 8d, 14cf, 22 }}
Line 516: Line 516:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~9/7 = 435.186
* CTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.186{{c}}
* POTE: ~7/5 = 600.000, ~9/7 = 437.078
* POTE: ~7/5 = 600.000{{c}}, ~9/7 = 437.078{{c}}


{{Optimal ET sequence|legend=0| 14c, 22f }}
{{Optimal ET sequence|legend=0| 14c, 22f }}
Line 531: Line 531:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~9/7 = 435.329
* CTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.329{{c}}
* POTE: ~7/5 = 600.000, ~9/7 = 435.425
* POTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.425{{c}}


{{Optimal ET sequence|legend=0| 22 }}
{{Optimal ET sequence|legend=0| 22 }}
Line 539: Line 539:


; Music
; Music
* [http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 ''Phobos Light''] by [[Chris Vaisvil]] – in [[hedgehog14|hedgehog[14]]], 22edo tuning.
* [https://web.archive.org/web/20240624173512/http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 ''Phobos Light''] by [[Chris Vaisvil]] – in [[hedgehog14|Hedgehog[14]]], 22edo tuning.


== Nautilus ==
== Nautilus ==
Line 553: Line 553:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~21/20 = 81.914
* [[CTE]]: ~2 = 1200.000{{c}}, ~21/20 = 81.914{{c}}
: [[error map]]: {{val| 0.000 +6.559 -5.457 -14.569 }}
: [[error map]]: {{val| 0.000 +6.559 -5.457 -14.569 }}
* [[POTE]]: ~2 = 1200.000, ~21/20 = 82.505
* [[POTE]]: ~2 = 1200.000{{c}}, ~21/20 = 82.505{{c}}
: error map: {{val| 0.000 +3.012 -11.368 -16.342 }}
: error map: {{val| 0.000 +3.012 -11.368 -16.342 }}


Line 570: Line 570:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 81.802
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 81.802{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 82.504
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 82.504{{c}}


{{Optimal ET sequence|legend=0| 14c, 15, 29, 44d }}
{{Optimal ET sequence|legend=0| 14c, 15, 29, 44d }}
Line 585: Line 585:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 81.912
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 81.912{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 82.530
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 82.530{{c}}


{{Optimal ET sequence|legend=0| 14cf, 15, 29, 44d }}
{{Optimal ET sequence|legend=0| 14cf, 15, 29, 44d }}
Line 600: Line 600:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 82.034
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 82.034{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 81.759
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 81.759{{c}}


{{Optimal ET sequence|legend=0| 14c, 15, 29f, 44dff }}
{{Optimal ET sequence|legend=0| 14c, 15, 29f, 44dff }}
Line 608: Line 608:


; Music
; Music
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 ''Nautilus Reverie''] by [[Igliashon Jones|Igliashon Calvin Jones-Coolidge]]
* [https://web.archive.org/web/20201127013840/http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 ''Nautilus Reverie''] by [[Igliashon Jones]]


== Ammonite ==
== Ammonite ==
Line 622: Line 622:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~9/7 = 454.550
* [[CTE]]: ~2 = 1200.000{{c}}, ~9/7 = 454.550{{c}}
: [[error map]]: {{val| 0.000 +7.095 -4.564 -5.276 }}
: [[error map]]: {{val| 0.000 +7.095 -4.564 -5.276 }}
* [[POTE]]: ~2 = 1200.000, ~9/7 = 454.448
* [[POTE]]: ~2 = 1200.000{{c}}, ~9/7 = 454.448{{c}}
: error map: {{val| 0.000 +8.009 -3.040 -3.346 }}
: error map: {{val| 0.000 +8.009 -3.040 -3.346 }}


Line 639: Line 639:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~9/7 = 454.505
* CTE: ~2 = 1200.000{{c}}, ~9/7 = 454.505{{c}}
* POTE: ~2 = 1200.000, ~9/7 = 454.512
* POTE: ~2 = 1200.000{{c}}, ~9/7 = 454.512{{c}}


{{Optimal ET sequence|legend=0| 8d, 21cde, 29, 37, 66 }}
{{Optimal ET sequence|legend=0| 8d, 21cde, 29, 37, 66 }}
Line 654: Line 654:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/10 = 454.480
* CTE: ~2 = 1200.000{{c}}, ~13/10 = 454.480{{c}}
* POTE: ~2 = 1200.000, ~13/10 = 454.529
* POTE: ~2 = 1200.000{{c}}, ~13/10 = 454.529{{c}}


{{Optimal ET sequence|legend=0| 8d, 21cdef, 29, 37, 66 }}
{{Optimal ET sequence|legend=0| 8d, 21cdef, 29, 37, 66 }}
Line 673: Line 673:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~36/35 = 54.804
* [[CTE]]: ~2 = 1200.000{{c}}, ~36/35 = 54.804{{c}}
: [[error map]]: {{val| 0.000 +4.809 -8.374 +11.958 }}
: [[error map]]: {{val| 0.000 +4.809 -8.374 +11.958 }}
* [[POTE]]: ~2 = 1200.000, ~36/35 = 54.384
* [[POTE]]: ~2 = 1200.000{{c}}, ~36/35 = 54.384{{c}}
: error map: {{val| 0.000 +8.585 -2.081 +13.636 }}
: error map: {{val| 0.000 +8.585 -2.081 +13.636 }}


Line 690: Line 690:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~36/35 = 54.702
* CTE: ~2 = 1200.000{{c}}, ~36/35 = 54.702{{c}}
* POTE: ~2 = 1200.000, ~36/35 = 54.376
* POTE: ~2 = 1200.000{{c}}, ~36/35 = 54.376{{c}}


{{Optimal ET sequence|legend=0| 1ce, 21ce, 22 }}
{{Optimal ET sequence|legend=0| 1ce, 21ce, 22 }}
Line 705: Line 705:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~36/35 = 54.575
* CTE: ~2 = 1200.000{{c}}, ~36/35 = 54.575{{c}}
* POTE: ~2 = 1200.000, ~36/35 = 54.665
* POTE: ~2 = 1200.000{{c}}, ~36/35 = 54.665{{c}}


{{Optimal ET sequence|legend=0| 1ce, 21cef, 22 }}
{{Optimal ET sequence|legend=0| 1ce, 21cef, 22 }}