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Porcupine family: Difference between revisions

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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 164.166
* [[WE]]: ~2 = 1199.5444{{c}}, ~10/9 = 163.8881{{c}}
: [[error map]]: {{val| 0.000 +5.547 -7.143 }}
: [[error map]]: {{val| -0.456 +5.469 -7.121 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 163.950
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.0621{{c}}
: error map: {{val| 0.000 +6.194 -6.065 }}
: error map: {{val| 0.000 +5.859 -6.624 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 33: Line 33:
{{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 ===
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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
* WE: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 164.078
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{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 ====
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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 -1 -2 0 5 | 0 6 10 8 -3 }}


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


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~88/65 = 518.086
* WE: ~2 = 1199.4791{{c}}, ~88/65 = 517.9845{{c}}
* POTE: ~2 = 1200.000, ~88/65 = 518.209
* CWE: ~2 = 1200.0000{{c}}, ~88/65 = 518.1740{{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 ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 163.203
* [[WE]]: ~2 = 1197.8178{{c}}, ~10/9 = 162.5839{{c}}
: [[error map]]: {{val| 0.000 +8.435 -2.330 +10.394 }}
: [[error map]]: {{val| -2.182 +5.929 -5.780 +2.313 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 162.880
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 162.9493{{c}}
: error map: {{val| 0.000 +9.405 -0.714 +8.455 }}
: error map: {{val| 0.000 +9.197 -1.060 +8.870 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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{{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 131: Line 129:


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


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


Minimax tuning:  
Minimax tuning:  
Line 168: Line 166:
* 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 182: Line 180:


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


Minimax tuning:  
Minimax tuning:  
Line 190: Line 188:


Tuning ranges:  
Tuning ranges:  
* 13-odd-limit diamond monotone: ~10/9 = [160.000, 162.162] (2\15 to 5\37)
* 13-odd-limit diamond monotone: ~11/10 = [160.000, 162.162] (2\15 to 5\37)
* 15-odd-limit diamond monotone: ~10/9 = 162.162 (5\37)
* 15-odd-limit diamond monotone: ~11/10 = 162.162 (5\37)
* 13- and 15-odd-limit diamond tradeoff: ~10/9 = [150.637, 182.404]
* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]


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


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


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


Minimax tuning:  
Minimax tuning:  
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{{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 ==
{{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
* [[WE]]: ~2 = 1195.7927{{c}}, ~10/9 = 159.1315{{c}}
: [[error map]]: {{val| 0.000 +14.126 +7.155 -20.583 }}
: [[error map]]: {{val| -4.207 +12.236 +5.407 -17.838 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 159.691
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 160.4589{{c}}
: error map: {{val| 0.000 +18.971 +15.229 -6.048 }}
: error map: {{val| 0.000 +16.668 +11.392 -12.956 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 256: Line 256:
{{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 ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 161.365
* WE: ~2 = 1196.2331{{c}}, ~11/10 = 159.3050{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 159.807
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.4644{{c}}


Minimax tuning:  
Minimax tuning:  
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{{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 284:


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


Minimax tuning:  
Minimax tuning:  
Line 292: Line 292:
{{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 304:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 164.391
* [[WE]]: ~2 = 1200.0685{{c}}, ~10/9 = 164.4215{{c}}
: [[error map]]: {{val| 0.000 +4.871 -8.270 +0.913 }}
: [[error map]]: {{val| +0.068 +4.917 -8.216 +0.772 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 164.412
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.4060{{c}}
: error map: {{val| 0.000 +4.809 -8.375 +0.580 }}
: error map: {{val| 0.000 +4.827 -8.344 +0.678 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 313: Line 313:
: [[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 325:


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


Minimax tuning:  
Minimax tuning:  
Line 334: Line 334:
{{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 344:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 164.478
* WE: ~2 = 1202.1557{{c}}, ~11/10 = 165.2494{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 164.953
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 164.8579{{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 364:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 166.094
* [[WE]]: ~2 = 1202.6772{{c}}, ~10/9 = 166.4110{{c}}
: [[error map]]: {{val| 0.000 -0.236 -16.783 -9.607 }}
: [[error map]]: {{val| +2.678 +4.166 -10.337 -2.806 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 166.041
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 166.0511{{c}}
: error map: {{val| 0.000 -0.077 -16.516 -10.299 }}
: error map: {{val| 0.000 -0.108 -16.569 -10.161 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 373: Line 373:
: [[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 385:


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


Minimax tuning:  
Minimax tuning:  
Line 394: Line 394:
{{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 404:


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


Minimax tuning:  
Minimax tuning:  
Line 413: Line 413:
{{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 425:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 165.185
* [[WE]]: ~2 = 1187.8599{{c}}, ~10/9 = 157.2605{{c}}
: [[error map]]: {{val| 0.000 +2.491 -12.236 +65.990 }}
: [[error map]]: {{val| -12.140 +1.983 -9.037 +37.493 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 158.868
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 161.2833{{c}}
: error map: {{val| 0.000 +21.442 +19.348 +72.306 }}
: error map: {{val| 0.000 +14.195 +7.270 +69.891 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 436: Line 436:
{{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 446:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/10 = 164.768
* WE: ~2 = 1189.2810{{c}}, ~11/10 = 157.3322{{c}}
* POTE: ~2 = 1200.000, ~11/10 = 158.750
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.9603{{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 ==
{{See also| Sensamagic clan | Stearnsmic clan }}
{{See also| Sensamagic clan | Stearnsmic clan }}


Hedgehog has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out [[245/243]], the sensamagic comma. It is a strong extension of [[BPS]] (as BPS has no 2 or sqrt(2)). Its ploidacot is diploid omega-tricot.  
Hedgehog has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out [[245/243]], the sensamagic comma. It is a strong extension of [[BPS]] (as BPS has no 2 or sqrt(2)). Its ploidacot is diploid alpha-tricot.  


22edo provides an obvious tuning, which happens to be the only [[patent val|patent-val]] tuning, but if you are looking for an alternative you could try the {{val| 146 232 338 411 }} (146bccdd) val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14-note mos gives scope for harmony while stopping well short of 22. A related temperament is [[echidna]], which offers much more accuracy. They merge on 22edo.  
22edo provides an obvious tuning, which happens to be the only [[patent val|patent-val]] tuning, but if you are looking for an alternative you could try the {{val| 146 232 338 411 }} (146bccdd) val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14-note mos gives scope for harmony while stopping well short of 22. A related temperament is [[echidna]], which offers much more accuracy. They merge on 22edo.  
Line 469: Line 469:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~9/7 = 435.258
* [[WE]]: ~7/5 = 599.6061{{c}}, ~9/7 = 435.3620{{c}}
: [[error map]]: {{val| 0.000 +3.819 -10.024 +7.464 }}
: [[error map]]: {{val| -0.788 +3.737 -9.897 +7.197 }}
* [[POTE]]: ~7/5 = 600.000, ~9/7 = 435.648
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4483{{c}}
: error map: {{val| 0.000 +4.989 -8.074 +9.414 }}
: error map: {{val| 0.000 +4.390 -9.072 +8.416 }}


{{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 486:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~9/7 = 435.528
* WE: ~7/5 = 600.1133{{c}}, ~9/7 = 435.4680{{c}}
* POTE: ~7/5 = 600.000, ~9/7 = 435.386
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4431{{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 501:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~9/7 = 436.309
* WE: ~7/5 = 600.3651{{c}}, ~9/7 = 436.1258{{c}}
* POTE: ~7/5 = 600.000, ~9/7 = 435.861
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 436.0483{{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 516:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~9/7 = 435.186
* WE: ~7/5 = 598.3303{{c}}, ~9/7 = 435.8617{{c}}
* POTE: ~7/5 = 600.000, ~9/7 = 437.078
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 436.3485{{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 531:


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


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


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


; 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
* [[WE]]: ~2 = 1202.1642{{c}}, ~21/20 = 82.6542{{c}}
: [[error map]]: {{val| 0.000 +6.559 -5.457 -14.569 }}
: [[error map]]: {{val| +2.164 +6.448 -6.364 -10.296 }}
* [[POTE]]: ~2 = 1200.000, ~21/20 = 82.505
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 82.2758{{c}}
: error map: {{val| 0.000 +3.012 -11.368 -16.342 }}
: error map: {{val| 0.000 +4.390 -9.072 -15.653 }}


{{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 570:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 81.802
* WE: ~2 = 1202.3781{{c}}, ~21/20 = 82.6673{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 82.504
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.2434{{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 585:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 81.912
* WE: ~2 = 1202.4145{{c}}, ~21/20 = 82.6963{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 82.530
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.3130{{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 600:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 82.034
* WE: ~2 = 1199.0072{{c}}, ~21/20 = 81.6911{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 81.759
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 81.8576{{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
* [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 ==
{{See also|Subgroup temperaments #Ammon}}
Ammonite adds 686/675 to the comma list and may be described as the {{nowrap| 8d & 29 }} temperament. Its ploidacot is epsilon-enneacot. [[37edo]] provides an obvious tuning.  
Ammonite adds 686/675 to the comma list and may be described as the {{nowrap| 8d & 29 }} temperament. Its ploidacot is epsilon-enneacot. [[37edo]] provides an obvious tuning.  


Line 617: Line 618:
[[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, ~9/7 = 454.550
* [[WE]]: ~2 = 1199.3342{{c}}, ~14/9 = 745.1379{{c}}
: [[error map]]: {{val| 0.000 +7.095 -4.564 -5.276 }}
: [[error map]]: {{val| -0.666 +6.949 -4.584 -5.213 }}
* [[POTE]]: ~2 = 1200.000, ~9/7 = 454.448
* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 745.4994{{c}}
: error map: {{val| 0.000 +8.009 -3.040 -3.346 }}
: error map: {{val| 0.000 +7.540 -3.823 -4.337 }}


{{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 637:
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, ~9/7 = 454.505
* WE: ~2 = 1200.0141{{c}}, ~14/9 = 745.4971{{c}}
* POTE: ~2 = 1200.000, ~9/7 = 454.512
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 745.4894{{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 652:
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, ~13/10 = 454.480
* WE: ~2 = 1200.2478{{c}}, ~14/9 = 745.6252{{c}}
* POTE: ~2 = 1200.000, ~13/10 = 454.529
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 745.4904{{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 674:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~36/35 = 54.804
* [[WE]]: ~2 = 1197.6274{{c}}, ~36/35 = 54.2770{{c}}
: [[error map]]: {{val| 0.000 +4.809 -8.374 +11.958 }}
: [[error map]]: {{val| -2.373 +4.807 -7.586 +6.948 }}
* [[POTE]]: ~2 = 1200.000, ~36/35 = 54.384
* [[CWE]]: ~2 = 1200.0000{{c}}, ~36/35 = 54.5489{{c}}
: error map: {{val| 0.000 +8.585 -2.081 +13.636 }}
: error map: {{val| 0.000 +7.105 -4.548 +12.978 }}


{{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 691:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~36/35 = 54.702
* WE: ~2 = 1198.2851{{c}}, ~36/35 = 54.2986{{c}}
* POTE: ~2 = 1200.000, ~36/35 = 54.376
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 54.4992{{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 706:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~36/35 = 54.575
* WE: ~2 = 1200.3864{{c}}, ~36/35 = 54.6830{{c}}
* POTE: ~2 = 1200.000, ~36/35 = 54.665
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 54.6396{{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]]
[[Category:Pages with mostly numerical content]]
[[Category:Porcupine family| ]] <!-- main article -->
[[Category:Porcupine family| ]] <!-- main article -->
[[Category:Porcupine| ]] <!-- key article -->
[[Category:Porcupine| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Porcupine_family"