Xenharmonic Wiki

Porcupine family: Difference between revisions

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m Units. + missing links. Fix dead links.
Switch to Sintel's badness, WE & CWE tunings, per community consensus
Line 22: Line 22:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 164.166{{c}}
* [[WE]]: ~2 = 1199.5444{{c}}, ~10/9 = 163.8881{{c}}
: [[error map]]: {{val| -0.456 +5.469 -7.121 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.0621{{c}}
: error map: {{val| 0.000 +5.859 -6.624 }}
<!-- * [[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{{c}}, ~10/9 = 163.950{{c}}
* [[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 }} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 33: Line 37:
{{Optimal ET sequence|legend=1| 7, 15, 22, 95c }}
{{Optimal ET sequence|legend=1| 7, 15, 22, 95c }}


[[Badness]] (Smith): 0.030778
[[Badness]] (Sintel): 0.722


=== Overview to extensions ===
=== Overview to extensions ===
Line 65: Line 69:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.887{{c}}
* WE: ~2 = 1200.3290{{c}}, ~10/9 = 164.1227{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 164.078{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/9 = 163.9951{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.887{{c}}
* 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 }}


Badness (Smith): 0.0097
Badness (Sintel): 0.303


==== Undecimation ====
==== Undecimation ====
Line 77: Line 83:
Comma list: 55/54, 100/99, 512/507
Comma list: 55/54, 100/99, 512/507


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


: mapping generators: ~2, ~65/44
: mapping generators: ~2, ~88/65


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~88/65 = 518.086{{c}}
* WE: ~2 = 1199.4791{{c}}, ~88/65 = 517.9845{{c}}
* POTE: ~2 = 1200.000{{c}}, ~88/65 = 518.209{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~88/65 = 518.1740{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~88/65 = 518.086{{c}}
* 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 }}


Badness (Smith): 0.0305
Badness (Sintel): 1.21


== Septimal porcupine ==
== Septimal porcupine ==
Line 101: Line 109:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 163.203{{c}}
* [[WE]]: ~2 = 1197.8178{{c}}, ~10/9 = 162.5839{{c}}
: [[error map]]: {{val| -2.182 +5.929 -5.780 +2.313 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 162.9493{{c}}
: error map: {{val| 0.000 +9.197 -1.060 +8.870 }}
<!-- * [[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{{c}}, ~10/9 = 162.880{{c}}
* [[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 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 119: Line 131:
{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59, 81bd }}
{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59, 81bd }}


[[Badness]] (Smith): 0.041057
[[Badness]] (Sintel): 1.04


=== 11-limit ===
=== 11-limit ===
Line 129: Line 141:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.105{{c}}
* WE: ~2 = 1198.3250{{c}}, ~11/10 = 162.5202{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.747{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.8156{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.105{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.747{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 142: Line 156:
{{Optimal ET sequence|legend=0| 7, 15, 22, 37, 59 }}
{{Optimal ET sequence|legend=0| 7, 15, 22, 37, 59 }}


Badness (Smith): 0.021562
Badness (Sintel): 0.713


==== Porcupinefowl ====
==== Porcupinefowl ====
Line 154: Line 168:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.442{{c}}
* WE: ~2 = 1197.0054{{c}}, ~11/10 = 162.3022{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.708{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.8314{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.442{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.708{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 166: Line 182:
* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [138.573, 182.404]
* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [138.573, 182.404]


{{Optimal ET sequence|legend=0| 7, 15, 22f, 37f }}
{{Optimal ET sequence|legend=0| 7, 15, 22f }}


Badness (Smith): 0.021276
Badness (Sintel): 0.879


==== Porcupinefish ====
==== Porcupinefish ====
Line 180: Line 196:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 162.636{{c}}
* WE: ~2 = 1198.3206{{c}}, ~11/10 = 162.0502{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.277{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.3458{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 162.636{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.277{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 194: Line 212:
{{Optimal ET sequence|legend=0| 15, 22, 37 }}
{{Optimal ET sequence|legend=0| 15, 22, 37 }}


Badness (Smith): 0.025314
Badness (Sintel): 1.05


==== Pourcup ====
==== Pourcup ====
Line 204: Line 222:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.378{{c}}
* WE: ~2 = 1198.0537{{c}}, ~11/10 = 162.2183{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.482{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.4665{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.378{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 162.482{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 213: Line 233:
{{Optimal ET sequence|legend=0| 15f, 22f, 37, 59f }}
{{Optimal ET sequence|legend=0| 15f, 22f, 37, 59f }}


Badness (Smith): 0.035130
Badness (Sintel): 1.45


==== Porkpie ====
==== Porkpie ====
Line 223: Line 243:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.678{{c}}
* WE: ~2 = 1200.0223{{c}}, ~11/10 = 163.6908{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 163.688{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.6874{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 163.678{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 163.688{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 232: Line 254:
{{Optimal ET sequence|legend=0| 7, 15f, 22 }}
{{Optimal ET sequence|legend=0| 7, 15f, 22 }}


Badness (Smith): 0.026043
Badness (Sintel): 1.08


== Opossum ==
== Opossum ==
Line 246: Line 268:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 161.306{{c}}
* [[WE]]: ~2 = 1195.7927{{c}}, ~10/9 = 159.1315{{c}}
: [[error map]]: {{val| -4.207 +12.236 +5.407 -17.838 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 160.4589{{c}}
: error map: {{val| 0.000 +16.668 +11.392 -12.956 }}
<!-- * [[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{{c}}, ~10/9 = 159.691{{c}}
* [[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 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 256: Line 282:
{{Optimal ET sequence|legend=1| 7d, 8d, 15 }}
{{Optimal ET sequence|legend=1| 7d, 8d, 15 }}


[[Badness]] (Smith): 0.040650
[[Badness]] (Sintel): 1.03


=== 11-limit ===
=== 11-limit ===
Line 266: Line 292:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 161.365{{c}}
* WE: ~2 = 1196.2331{{c}}, ~11/10 = 159.3050{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 159.807{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.4644{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 161.365{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 159.807{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 274: Line 302:
{{Optimal ET sequence|legend=0| 7d, 8d, 15 }}
{{Optimal ET sequence|legend=0| 7d, 8d, 15 }}


Badness (Smith): 0.022325
Badness (Sintel): 0.738


=== 13-limit ===
=== 13-limit ===
Line 284: Line 312:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 161.631{{c}}
* WE: ~2 = 1193.5447{{c}}, ~11/10 = 157.9505{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 158.805{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 159.7600{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 161.631{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 158.805{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 292: Line 322:
{{Optimal ET sequence|legend=0| 7d, 8d, 15, 38bceff }}
{{Optimal ET sequence|legend=0| 7d, 8d, 15, 38bceff }}


Badness (Smith): 0.019389
Badness (Sintel): 0.801


== Porky ==
== Porky ==
Line 304: Line 334:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 164.391{{c}}
* [[WE]]: ~2 = 1200.0685{{c}}, ~10/9 = 164.4215{{c}}
: [[error map]]: {{val| +0.068 +4.917 -8.216 +0.772 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.4060{{c}}
: error map: {{val| 0.000 +4.827 -8.344 +0.678 }}
<!-- * [[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{{c}}, ~10/9 = 164.412{{c}}
* [[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 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 313: Line 347:
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5


{{Optimal ET sequence|legend=1| 7d, 15d, 22, 29, 51, 73c }}
{{Optimal ET sequence|legend=1| 7d, 15d, 22, 51, 73c }}


[[Badness]] (Smith): 0.054389
[[Badness]] (Sintel): 1.38


=== 11-limit ===
=== 11-limit ===
Line 325: Line 359:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 164.321{{c}}
* WE: ~2 = 1200.8706{{c}}, ~11/10 = 164.6715{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 164.552{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 164.4810{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 164.321{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 164.552{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 334: Line 370:
{{Optimal ET sequence|legend=0| 7d, 15d, 22, 51 }}
{{Optimal ET sequence|legend=0| 7d, 15d, 22, 51 }}


Badness (Smith): 0.027268
Badness (Sintel): 0.901


=== 13-limit ===
=== 13-limit ===
Line 344: Line 380:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 164.478{{c}}
* WE: ~2 = 1202.1557{{c}}, ~11/10 = 165.2494{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 164.953{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 164.8579{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 164.478{{c}}
* 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 }}


Badness (Smith): 0.026543
Badness (Sintel): 1.10


; Music
; Music
Line 364: Line 402:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 166.094{{c}}
* [[WE]]: ~2 = 1202.6772{{c}}, ~10/9 = 166.4110{{c}}
: [[error map]]: {{val| +2.678 +4.166 -10.337 -2.806 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 166.0511{{c}}
: error map: {{val| 0.000 -0.108 -16.569 -10.161 }}
<!-- * [[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{{c}}, ~10/9 = 166.041{{c}}
* [[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 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 373: Line 415:
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3


{{Optimal ET sequence|legend=1| 7, 22d, 29, 65c, 94cd }}
{{Optimal ET sequence|legend=1| 7, 22d, 29, 65c }}


[[Badness]] (Smith): 0.118344
[[Badness]] (Sintel): 2.99


=== 11-limit ===
=== 11-limit ===
Line 385: Line 427:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 165.925{{c}}
* WE: ~2 = 1203.0245{{c}}, ~11/10 = 166.3991{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 165.981{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9714{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 165.925{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 165.981{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 394: Line 438:
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65ce }}
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65ce }}


Badness (Smith): 0.049669
Badness (Sintel): 1.64


=== 13-limit ===
=== 13-limit ===
Line 404: Line 448:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 166.046{{c}}
* WE: ~2 = 1202.9957{{c}}, ~11/10 = 166.3885{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 165.974{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9843{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 166.046{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 165.974{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 413: Line 459:
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65cef }}
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65cef }}


Badness (Smith): 0.030233
Badness (Sintel): 1.25


== Hystrix ==
== Hystrix ==
Line 425: Line 471:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 165.185{{c}}
* [[WE]]: ~2 = 1187.8599{{c}}, ~10/9 = 157.2605{{c}}
: [[error map]]: {{val| -12.140 +1.983 -9.037 +37.493 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 161.2833{{c}}
: error map: {{val| 0.000 +14.195 +7.270 +69.891 }}
<!-- * [[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{{c}}, ~10/9 = 158.868{{c}}
* [[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 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 436: Line 486:
{{Optimal ET sequence|legend=1| 7, 8d, 15d }}
{{Optimal ET sequence|legend=1| 7, 8d, 15d }}


[[Badness]] (Smith): 0.044944
[[Badness]] (Sintel): 1.14


=== 11-limit ===
=== 11-limit ===
Line 446: Line 496:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/10 = 164.768{{c}}
* WE: ~2 = 1189.2810{{c}}, ~11/10 = 157.3322{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/10 = 158.750{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.9603{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/10 = 164.768{{c}}
* 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 }}


Badness (Smith): 0.026790
Badness (Sintel): 0.886


== Hedgehog ==
== Hedgehog ==
Line 469: Line 521:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000{{c}}, ~9/7 = 435.258{{c}}
* [[WE]]: ~7/5 = 599.6061{{c}}, ~9/7 = 435.3620{{c}}
: [[error map]]: {{val| -0.788 +3.737 -9.897 +7.197 }}
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4483{{c}}
: error map: {{val| 0.000 +4.390 -9.072 +8.416 }}
<!-- * [[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{{c}}, ~9/7 = 435.648{{c}}
* [[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 }} -->


{{Optimal ET sequence|legend=1| 8d, 14c, 22 }}
{{Optimal ET sequence|legend=1| 8d, 14c, 22 }}


[[Badness]] (Smith): 0.043983
[[Badness]] (Sintel): 1.11


=== 11-limit ===
=== 11-limit ===
Line 486: Line 542:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.528{{c}}
* WE: ~7/5 = 600.1133{{c}}, ~9/7 = 435.4680{{c}}
* POTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.386{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4431{{c}}
<!-- * CTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.528{{c}}
* 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 }}


Badness (Smith): 0.023095
Badness (Sintel): 0.764


==== 13-limit ====
==== 13-limit ====
Line 501: Line 559:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000{{c}}, ~9/7 = 436.309{{c}}
* WE: ~7/5 = 600.3651{{c}}, ~9/7 = 436.1258{{c}}
* POTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.861{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 436.0483{{c}}
<!-- * CTE: ~7/5 = 600.000{{c}}, ~9/7 = 436.309{{c}}
* 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 }}


Badness (Smith): 0.021516
Badness (Sintel): 0.889


==== Urchin ====
==== Urchin ====
Line 516: Line 576:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.186{{c}}
* WE: ~7/5 = 598.3303{{c}}, ~9/7 = 435.8617{{c}}
* POTE: ~7/5 = 600.000{{c}}, ~9/7 = 437.078{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 436.3485{{c}}
<!-- * CTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.186{{c}}
* 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 }}


Badness (Smith): 0.025233
Badness (Sintel): 1.04


=== Hedgepig ===
=== Hedgepig ===
Line 531: Line 593:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.329{{c}}
* WE: ~7/5 = 599.7917{{c}}, ~9/7 = 435.2737{{c}}
* POTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.425{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4047{{c}}
<!-- * CTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.329{{c}}
* POTE: ~7/5 = 600.000{{c}}, ~9/7 = 435.425{{c}} -->


{{Optimal ET sequence|legend=0| 22 }}
{{Optimal ET sequence|legend=0| 22 }}


Badness (Smith): 0.068406
Badness (Sintel): 2.26


; Music
; Music
Line 553: Line 617:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~21/20 = 81.914{{c}}
* [[WE]]: ~2 = 1202.1642{{c}}, ~21/20 = 82.6542{{c}}
: [[error map]]: {{val| +2.164 +6.448 -6.364 -10.296 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 82.2758{{c}}
: error map: {{val| 0.000 +4.390 -9.072 -15.653 }}
<!-- * [[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{{c}}, ~21/20 = 82.505{{c}}
* [[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 }} -->


{{Optimal ET sequence|legend=1| 14c, 15, 29, 44d }}
{{Optimal ET sequence|legend=1| 14c, 15, 29 }}


[[Badness]] (Smith): 0.057420
[[Badness]] (Sintel): 1.45


=== 11-limit ===
=== 11-limit ===
Line 570: Line 638:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 81.802{{c}}
* WE: ~2 = 1202.3781{{c}}, ~21/20 = 82.6673{{c}}
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 82.504{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.2434{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~21/20 = 81.802{{c}}
* 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 }}


Badness (Smith): 0.026023
Badness (Sintel): 0.860


==== 13-limit ====
==== 13-limit ====
Line 585: Line 655:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 81.912{{c}}
* WE: ~2 = 1202.4145{{c}}, ~21/20 = 82.6963{{c}}
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 82.530{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.3130{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~21/20 = 81.912{{c}}
* 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 }}


Badness (Smith): 0.022285
Badness (Sintel): 0.921


==== Belauensis ====
==== Belauensis ====
Line 600: Line 672:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 82.034{{c}}
* WE: ~2 = 1199.0072{{c}}, ~21/20 = 81.6911{{c}}
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 81.759{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 81.8576{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~21/20 = 82.034{{c}}
* 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 }}


Badness (Smith): 0.029816
Badness (Sintel): 1.23


; Music
; Music
Line 617: Line 691:
[[Comma list]]: 250/243, 686/675
[[Comma list]]: 250/243, 686/675


{{Mapping|legend=1| 1 5 8 10 | 0 -9 -15 -19 }}
{{Mapping|legend=1| 1 -4 -7 -9 | 0 9 15 19 }}


: mapping generators: ~2, ~9/7
: mapping generators: ~2, ~14/9


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~9/7 = 454.550{{c}}
* [[WE]]: ~2 = 1199.3342{{c}}, ~14/9 = 745.1379{{c}}
: [[error map]]: {{val| -0.666 +6.949 -4.584 -5.213 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 745.4994{{c}}
: error map: {{val| 0.000 +7.540 -3.823 -4.337 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~14/9 = 745.450{{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{{c}}, ~9/7 = 454.448{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~14/9 = 745.552{{c}}
: error map: {{val| 0.000 +8.009 -3.040 -3.346 }}
: error map: {{val| 0.000 +8.009 -3.040 -3.346 }} -->


{{Optimal ET sequence|legend=1| 8d, 21cd, 29, 37, 66 }}
{{Optimal ET sequence|legend=1| 8d, 21cd, 29, 37, 66 }}


[[Badness]] (Smith): 0.107686
[[Badness]] (Sintel): 2.73


=== 11-limit ===
=== 11-limit ===
Line 636: Line 714:
Comma list: 55/54, 100/99, 686/675
Comma list: 55/54, 100/99, 686/675


Mapping: {{mapping| 1 5 8 10 8 | 0 -9 -15 -19 -12 }}
Mapping: {{mapping| 1 -4 -7 -9 -4 | 0 9 15 19 12 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~9/7 = 454.505{{c}}
* WE: ~2 = 1200.0141{{c}}, ~14/9 = 745.4971{{c}}
* POTE: ~2 = 1200.000{{c}}, ~9/7 = 454.512{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 745.4894{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~14/9 = 745.495{{c}}
* POTE: ~2 = 1200.000{{c}}, ~14/9 = 745.488{{c}} -->


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


Badness (Smith): 0.045694
Badness (Sintel): 1.51


=== 13-limit ===
=== 13-limit ===
Line 651: Line 731:
Comma list: 55/54, 91/90, 100/99, 169/168
Comma list: 55/54, 91/90, 100/99, 169/168


Mapping: {{mapping| 1 5 8 10 8 9 | 0 -9 -15 -19 -12 -14 }}
Mapping: {{mapping| 1 -4 -7 -9 -4 -5 | 0 9 15 19 12 14 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~13/10 = 454.480{{c}}
* WE: ~2 = 1200.2478{{c}}, ~14/9 = 745.6252{{c}}
* POTE: ~2 = 1200.000{{c}}, ~13/10 = 454.529{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 745.4904{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~14/9 = 745.520{{c}}
* POTE: ~2 = 1200.000{{c}}, ~14/9 = 745.471{{c}} -->


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


Badness (Smith): 0.027168
Badness (Sintel): 1.12


== Ceratitid ==
== Ceratitid ==
Line 673: Line 755:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~36/35 = 54.804{{c}}
* [[WE]]: ~2 = 1197.6274{{c}}, ~36/35 = 54.2770{{c}}
: [[error map]]: {{val| -2.373 +4.807 -7.586 +6.948 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~36/35 = 54.5489{{c}}
: error map: {{val| 0.000 +7.105 -4.548 +12.978 }}
<!-- * [[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{{c}}, ~36/35 = 54.384{{c}}
* [[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 }} -->


{{Optimal ET sequence|legend=1| 1c, 21c, 22 }}
{{Optimal ET sequence|legend=1| 1c, 21c, 22 }}


[[Badness]] (Smith): 0.115304
[[Badness]] (Sintel): 2.92


=== 11-limit ===
=== 11-limit ===
Line 690: Line 776:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~36/35 = 54.702{{c}}
* WE: ~2 = 1198.2851{{c}}, ~36/35 = 54.2986{{c}}
* POTE: ~2 = 1200.000{{c}}, ~36/35 = 54.376{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 54.4992{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~36/35 = 54.702{{c}}
* 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 }}


Badness (Smith): 0.051319
Badness (Sintel): 1.70


=== 13-limit ===
=== 13-limit ===
Line 705: Line 793:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~36/35 = 54.575{{c}}
* WE: ~2 = 1200.3864{{c}}, ~36/35 = 54.6830{{c}}
* POTE: ~2 = 1200.000{{c}}, ~36/35 = 54.665{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 54.6396{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~36/35 = 54.575{{c}}
* 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 }}


Badness (Smith): 0.044739
Badness (Sintel): 1.85


[[Category:Temperament families]]
[[Category:Temperament families]]
Retrieved from "https://en.xen.wiki/w/Porcupine_family"