Xenharmonic Wiki

Porcupine family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Rework intro
Restore the POTE tuning of opossum (with correction). +error maps. Spell out 1\1 etc. in cents. Note the badness metric being used. Misc. cleanup
Line 21: Line 21:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~10/9 = 164.1659
* [[CTE]]: ~2 = 1200.000, ~10/9 = 164.166
* [[POTE]]: ~2 = 1\1, ~10/9 = 163.950
: [[error map]]: {{val| 0.000 +5.547 -7.143 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 163.950
: error map: {{val| 0.000 +6.194 -6.065 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* 5-odd-limit [[diamond monotone]]: ~10/9 = [150.000, 171.429] (1\8 to 1\7)
* [[5-odd-limit]] [[diamond monotone]]: ~10/9 = [150.000, 171.429] (1\8 to 1\7)
* 5-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
* 5-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]


{{Optimal ET sequence|legend=1| 7, 15, 22, 95c }}
{{Optimal ET sequence|legend=1| 7, 15, 22, 95c }}


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


=== Overview to extensions ===
=== Overview to extensions ===
Line 57: Line 59:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 163.8867
* CTE: ~2 = 1200.000, ~11/10 = 163.887
* POTE: ~2 = 1\1, ~11/10 = 164.0777
* POTE: ~2 = 1200.000, ~11/10 = 164.078


Optimal ET sequence: {{Optimal ET sequence| 7, 15, 22, 73ce, 95ce }}
{{Optimal ET sequence|legend=0| 7, 15, 22, 73ce, 95ce }}


Badness: 0.0097
Badness (Smith): 0.0097


==== Undecimation ====
==== Undecimation ====
Line 74: Line 76:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~88/65 = 518.0865
* CTE: ~2 = 1200.000, ~88/65 = 518.086
* POTE: ~2 = 1\1, ~88/65 = 518.2094
* POTE: ~2 = 1200.000, ~88/65 = 518.209


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


Badness: 0.0305
Badness (Smith): 0.0305


== Septimal porcupine ==
== Septimal porcupine ==
Line 95: Line 97:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~10/9 = 163.2032
* [[CTE]]: ~2 = 1200.000, ~10/9 = 163.203
* [[POTE]]: ~2 = 1\1, ~10/9 = 162.880
: [[error map]]: {{val| 0.000 +8.435 -2.330 +10.394 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 162.880
: error map: {{val| 0.000 +9.405 -0.714 +8.455 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
* [[7-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5
* [[9-odd-limit]]: ~10/9 = {{monzo| 1/6 -1/6 0 1/12 }}
* [[9-odd-limit]]: ~10/9 = {{monzo| 1/6 -1/6 0 1/12 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 111: Line 115:
{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59, 81bd }}
{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59, 81bd }}


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


=== 11-limit ===
=== 11-limit ===
Line 121: Line 125:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 163.1055
* CTE: ~2 = 1200.000, ~11/10 = 163.105
* POTE: ~2 = 1\1, ~11/10 = 162.747
* POTE: ~2 = 1200.000, ~11/10 = 162.747


Minimax tuning:  
Minimax tuning:  
Line 132: Line 136:
* 11-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]
* 11-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]


Optimal ET sequence: {{Optimal ET sequence| 7, 15, 22, 37, 59 }}
{{Optimal ET sequence|legend=0| 7, 15, 22, 37, 59 }}


Badness: 0.021562
Badness (Smith): 0.021562


==== 13-limit ====
==== 13-limit ====
Line 144: Line 148:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 163.4425
* CTE: ~2 = 1200.000, ~11/10 = 163.442
* POTE: ~2 = 1\1, ~11/10 = 162.708
* POTE: ~2 = 1200.000, ~11/10 = 162.708


Minimax tuning:  
Minimax tuning:  
Line 156: Line 160:
* 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: {{Optimal ET sequence| 7, 15, 22f, 37f }}
{{Optimal ET sequence|legend=0| 7, 15, 22f, 37f }}


Badness: 0.021276
Badness (Smith): 0.021276


==== Porcupinefish ====
==== Porcupinefish ====
Line 170: Line 174:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 162.6361
* CTE: ~2 = 1200.000, ~11/10 = 162.636
* POTE: ~2 = 1\1, ~11/10 = 162.277
* POTE: ~2 = 1200.000, ~11/10 = 162.277


Minimax tuning:  
Minimax tuning:  
Line 182: Line 186:
* 13- and 15-odd-limit diamond tradeoff: ~10/9 = [150.637, 182.404]
* 13- and 15-odd-limit diamond tradeoff: ~10/9 = [150.637, 182.404]


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


Badness: 0.025314
Badness (Smith): 0.025314


==== Pourcup ====
==== Pourcup ====
Line 194: Line 198:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 163.3781
* CTE: ~2 = 1200.000, ~11/10 = 163.378
* POTE: ~2 = 1\1, ~11/10 = 162.482
* POTE: ~2 = 1200.000, ~11/10 = 162.482


Minimax tuning:  
Minimax tuning:  
Line 201: Line 205:
: eigenmonzo (unchanged-interval) basis: 2.13/7
: eigenmonzo (unchanged-interval) basis: 2.13/7


Optimal ET sequence: {{Optimal ET sequence| 15f, 22f, 37, 59f }}
{{Optimal ET sequence|legend=0| 15f, 22f, 37, 59f }}


Badness: 0.035130
Badness (Smith): 0.035130


==== Porkpie ====
==== Porkpie ====
Line 213: Line 217:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 163.6778
* CTE: ~2 = 1200.000, ~11/10 = 163.678
* POTE: ~2 = 1\1, ~11/10 = 163.688
* POTE: ~2 = 1200.000, ~11/10 = 163.688


Minimax tuning:  
Minimax tuning:  
Line 220: Line 224:
: eigenmonzo (unchanged-interval) basis: 2.9/7
: eigenmonzo (unchanged-interval) basis: 2.9/7


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


Badness: 0.026043
Badness (Smith): 0.026043


== Opossum ==
== Opossum ==
Line 235: Line 239:
{{Multival|legend=1| 3 5 9 1 6 7 }}
{{Multival|legend=1| 3 5 9 1 6 7 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 161.3063
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~10/9 = 161.306
: [[error map]]: {{val| 0.000 +14.126 +7.155 -20.583 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 159.691
: error map: {{val| 0.000 +18.971 +15.229 -6.048 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7


{{Optimal ET sequence|legend=1| 7d, 8d, 15 }}
{{Optimal ET sequence|legend=1| 7d, 8d, 15 }}


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


=== 11-limit ===
=== 11-limit ===
Line 253: Line 261:
{{Multival|legend=1| 3 5 9 4 1 6 -4 7 -8 -20 }}
{{Multival|legend=1| 3 5 9 4 1 6 -4 7 -8 -20 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 161.3646
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/10 = 161.365
* POTE: ~2 = 1200.000, ~11/10 = 159.807


Minimax tuning:  
Minimax tuning:  
* 11-odd-limit eigenmonzo (unchanged-interval) basis: 2.7
* 11-odd-limit eigenmonzo (unchanged-interval) basis: 2.7


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


Badness: 0.022325
Badness (Smith): 0.022325


=== 13-limit ===
=== 13-limit ===
Line 269: Line 279:
Mapping: {{mapping| 1 2 3 4 4 4 | 0 -3 -5 -9 -4 -2 }}
Mapping: {{mapping| 1 2 3 4 4 4 | 0 -3 -5 -9 -4 -2 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 161.6312
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/10 = 161.631
* POTE: ~2 = 1200.000, ~11/10 = 158.805


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7
* 13- and 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7


Optimal ET sequence: {{Optimal ET sequence| 7d, 8d, 15, 38bceff }}
{{Optimal ET sequence|legend=0| 7d, 8d, 15, 38bceff }}


Badness: 0.019389
Badness (Smith): 0.019389


== Porky ==
== Porky ==
Line 290: Line 302:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~10/9 = 164.3913
* [[CTE]]: ~2 = 1200.000, ~10/9 = 164.391
* [[POTE]]: ~2 = 1\1, ~10/9 = 164.412
: [[error map]]: {{val| 0.000 +4.871 -8.270 +0.913 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 164.412
: error map: {{val| 0.000 +4.809 -8.375 +0.580 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/11 0 1/11 -1/11 }}
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/11 0 1/11 -1/11 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5


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


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


=== 11-limit ===
=== 11-limit ===
Line 308: Line 322:
Mapping: {{mapping| 1 2 3 5 4 | 0 -3 -5 -16 -4 }}
Mapping: {{mapping| 1 2 3 5 4 | 0 -3 -5 -16 -4 }}


{{Multival|legend=1| 3 5 16 4 1 17 -4 23 -8 -44 }}
Wedgie: {{multival| 3 5 16 4 1 17 -4 23 -8 -44 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 164.3207
* CTE: ~2 = 1200.000, ~11/10 = 164.321
* POTE: ~2 = 1\1, ~11/10 = 164.552
* POTE: ~2 = 1200.000, ~11/10 = 164.552


Minimax tuning:  
Minimax tuning:  
Line 318: Line 332:
: eigenmonzo (unchanged-interval) basis: 2.7/5
: eigenmonzo (unchanged-interval) basis: 2.7/5


Optimal ET sequence: {{Optimal ET sequence| 7d, 15d, 22, 51 }}
{{Optimal ET sequence|legend=0| 7d, 15d, 22, 51 }}


Badness: 0.027268
Badness (Smith): 0.027268


=== 13-limit ===
=== 13-limit ===
Line 330: Line 344:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 164.4782
* CTE: ~2 = 1200.000, ~11/10 = 164.478
* POTE: ~2 = 1\1, ~11/10 = 164.953
* POTE: ~2 = 1200.000, ~11/10 = 164.953


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


Badness: 0.026543
Badness (Smith): 0.026543


; Music
; Music
* [https://www.youtube.com/watch?v=CN4cLOyaVGE ''Improvisation in 29edo''] (2024) by [[Budjarn Lambeth]] – Palace scale in 29edo tuning
* [https://www.youtube.com/watch?v=CN4cLOyaVGE ''Improvisation in 29edo''] (2024) by [[Budjarn Lambeth]] – in Palace scale, 29edo tuning


== Coendou ==
== Coendou ==
Line 352: Line 366:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~10/9 = 166.0938
* [[CTE]]: ~2 = 1200.000, ~10/9 = 166.094
* [[POTE]]: ~2 = 1\1, ~10/9 = 166.041
: [[error map]]: {{val| 0.000 -0.236 -16.783 -9.607 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 166.041
: error map: {{val| 0.000 -0.077 -16.516 -10.299 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/3 -1/3 }}
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/3 -1/3 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3


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


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


=== 11-limit ===
=== 11-limit ===
Line 371: Line 387:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 165.9246
* CTE: ~2 = 1200.000, ~11/10 = 165.925
* POTE: ~2 = 1\1, ~11/10 = 165.981
* POTE: ~2 = 1200.000, ~11/10 = 165.981


Minimax tuning:  
Minimax tuning:  
Line 378: Line 394:
: eigenmonzo (unchanged-interval) basis: 2.3
: eigenmonzo (unchanged-interval) basis: 2.3


Optimal ET sequence: {{Optimal ET sequence| 7, 22d, 29, 65ce }}
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65ce }}


Badness: 0.049669
Badness (Smith): 0.049669


=== 13-limit ===
=== 13-limit ===
Line 390: Line 406:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 166.0459
* CTE: ~2 = 1200.000, ~11/10 = 166.046
* POTE: ~2 = 1\1, ~11/10 = 165.974
* POTE: ~2 = 1200.000, ~11/10 = 165.974


Minimax tuning:  
Minimax tuning:  
Line 397: Line 413:
: eigenmonzo (unchanged-interval) basis: 2.3
: eigenmonzo (unchanged-interval) basis: 2.3


Optimal ET sequence: {{Optimal ET sequence| 7, 22d, 29, 65cef }}
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65cef }}


Badness: 0.030233
Badness (Smith): 0.030233


== Hystrix ==
== Hystrix ==
Line 413: Line 429:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~10/9 = 165.1845
* [[CTE]]: ~2 = 1200.000, ~10/9 = 165.185
* [[POTE]]: ~2 = 1\1, ~10/9 = 158.868
: [[error map]]: {{val| 0.000 +2.491 -12.236 +65.990 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 158.868
: error map: {{val| 0.000 +21.442 +19.348 +72.306 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 422: Line 440:
{{Optimal ET sequence|legend=1| 7, 8d, 15d }}
{{Optimal ET sequence|legend=1| 7, 8d, 15d }}


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


=== 11-limit ===
=== 11-limit ===
Line 432: Line 450:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 164.7684
* CTE: ~2 = 1200.000, ~11/10 = 164.768
* POTE: ~2 = 1\1, ~11/10 = 158.750
* POTE: ~2 = 1200.000, ~11/10 = 158.750


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


Badness: 0.026790
Badness (Smith): 0.026790


== Oxygen ==
== Oxygen ==
Line 451: Line 469:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~10/9 = 161.3408
* [[CTE]]: ~2 = 1200.000, ~10/9 = 161.341
* [[POTE]]: ~2 = 1\1, ~10/9 = 169.112
: [[error map]]: {{val| 0.000 +14.023 +6.982 -91.507 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 169.112
: error map: {{val| 0.000 -9.291 -31.873 -107.050 }}


{{Optimal ET sequence|legend=1| 7d }}
{{Optimal ET sequence|legend=1| 1c, …, 6bcd, 7d }}


[[Badness]]: 0.059866
[[Badness]] (Smith): 0.059866


== Hedgehog ==
== Hedgehog ==
{{See also| Sensamagic clan }}
{{See also| Sensamagic clan | Stearnsmic clan }}
{{See also| 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)). 22edo provides the obvious (i.e the only [[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.  
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)). 22edo provides the obvious (i.e the only [[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 475: Line 494:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~9/7 = 435.2580
* [[CTE]]: ~7/5 = 600.000, ~9/7 = 435.258
* [[POTE]]: ~7/5 = 1\2, ~9/7 = 435.648
: [[error map]]: {{val| 0.000 +3.819 -10.024 +7.464 }}
* [[POTE]]: ~7/5 = 600.000, ~9/7 = 435.648
: 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]]: 0.043983
[[Badness]] (Smith): 0.043983


=== 11-limit ===
=== 11-limit ===
Line 492: Line 513:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~9/7 = 435.5281
* CTE: ~7/5 = 600.000, ~9/7 = 435.528
* POTE: ~7/5 = 1\2, ~9/7 = 435.386
* POTE: ~7/5 = 600.000, ~9/7 = 435.386


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


Badness: 0.023095
Badness (Smith): 0.023095


==== 13-limit ====
==== 13-limit ====
Line 507: Line 528:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~9/7 = 436.3087
* CTE: ~7/5 = 600.000, ~9/7 = 436.309
* POTE: ~7/5 = 1\2, ~9/7 = 435.861
* POTE: ~7/5 = 600.000, ~9/7 = 435.861


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


Badness: 0.021516
Badness (Smith): 0.021516


==== Urchin ====
==== Urchin ====
Line 522: Line 543:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~9/7 = 435.1856
* CTE: ~7/5 = 600.000, ~9/7 = 435.186
* POTE: ~7/5 = 1\2, ~9/7 = 437.078
* POTE: ~7/5 = 600.000, ~9/7 = 437.078


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


Badness: 0.025233
Badness (Smith): 0.025233


=== Hedgepig ===
=== Hedgepig ===
Line 539: Line 560:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~9/7 = 435.3289
* CTE: ~7/5 = 600.000, ~9/7 = 435.329
* POTE: ~7/5 = 1\2, ~9/7 = 435.425
* POTE: ~7/5 = 600.000, ~9/7 = 435.425


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


Badness: 0.068406
Badness (Smith): 0.068406


; Music
; Music
* [http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 ''Phobos Light''] by [[Chris Vaisvil]] in [[hedgehog14|hedgehog[14]]] to 22edo.
* [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 561: Line 582:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~21/20 = 81.9143
* [[CTE]]: ~2 = 1200.000, ~21/20 = 81.914
* [[POTE]]: ~2 = 1\1, ~21/20 = 82.505
: [[error map]]: {{val| 0.000 +6.559 -5.457 -14.569 }}
* [[POTE]]: ~2 = 1200.000, ~21/20 = 82.505
: 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, 44d }}


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


=== 11-limit ===
=== 11-limit ===
Line 578: Line 601:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~21/20 = 81.8017
* CTE: ~2 = 1200.000, ~21/20 = 81.802
* POTE: ~2 = 1\1, ~21/20 = 82.504
* POTE: ~2 = 1200.000, ~21/20 = 82.504


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


Badness: 0.026023
Badness (Smith): 0.026023


==== 13-limit ====
==== 13-limit ====
Line 593: Line 616:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~21/20 = 81.9123
* CTE: ~2 = 1200.000, ~21/20 = 81.912
* POTE: ~2 = 1\1, ~21/20 = 82.530
* POTE: ~2 = 1200.000, ~21/20 = 82.530


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


Badness: 0.022285
Badness (Smith): 0.022285


==== Belauensis ====
==== Belauensis ====
Line 608: Line 631:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~21/20 = 82.0342
* CTE: ~2 = 1200.000, ~21/20 = 82.034
* POTE: ~2 = 1\1, ~21/20 = 81.759
* POTE: ~2 = 1200.000, ~21/20 = 81.759


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


Badness: 0.029816
Badness (Smith): 0.029816


; Music
; Music
Line 630: Line 653:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~9/7 = 454.5500
* [[CTE]]: ~2 = 1200.000, ~9/7 = 454.550
* [[POTE]]: ~2 = 1\1, ~9/7 = 454.448
: [[error map]]: {{val| 0.000 +7.095 -4.564 -5.276 }}
* [[POTE]]: ~2 = 1200.000, ~9/7 = 454.448
: 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]]: 0.107686
[[Badness]] (Smith): 0.107686


=== 11-limit ===
=== 11-limit ===
Line 644: Line 669:
Mapping: {{mapping| 1 5 8 10 8 | 0 -9 -15 -19 -12 }}
Mapping: {{mapping| 1 5 8 10 8 | 0 -9 -15 -19 -12 }}


{{Multival|legend=1| 9 15 19 12 3 5 -12 2 -24 -32 }}
Wedgie: {{multival| 9 15 19 12 3 5 -12 2 -24 -32 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~9/7 = 454.5050
* CTE: ~2 = 1200.000, ~9/7 = 454.505
* POTE: ~2 = 1\1, ~9/7 = 454.512
* POTE: ~2 = 1200.000, ~9/7 = 454.512


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


Badness: 0.045694
Badness (Smith): 0.045694


=== 13-limit ===
=== 13-limit ===
Line 662: Line 687:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~13/10 = 454.4798
* CTE: ~2 = 1200.000, ~13/10 = 454.480
* POTE: ~2 = 1\1, ~13/10 = 454.529
* POTE: ~2 = 1200.000, ~13/10 = 454.529


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


Badness: 0.027168
Badness (Smith): 0.027168


== Ceratitid ==
== Ceratitid ==
Line 681: Line 706:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~36/35 = 54.8040
* [[CTE]]: ~2 = 1200.000, ~36/35 = 54.804
* [[POTE]]: ~2 = 1\1, ~36/35 = 54.384
: [[error map]]: {{val| 0.000 +4.809 -8.374 +11.958 }}
* [[POTE]]: ~2 = 1200.000, ~36/35 = 54.384
: 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]]: 0.115304
[[Badness]] (Smith): 0.115304


=== 11-limit ===
=== 11-limit ===
Line 696: Line 723:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~36/35 = 54.7019
* CTE: ~2 = 1200.000, ~36/35 = 54.702
* POTE: ~2 = 1\1, ~36/35 = 54.376
* POTE: ~2 = 1200.000, ~36/35 = 54.376


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


Badness: 0.051319
Badness (Smith): 0.051319


=== 13-limit ===
=== 13-limit ===
Line 711: Line 738:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~36/35 = 54.5751
* CTE: ~2 = 1200.000, ~36/35 = 54.575
* POTE: ~2 = 1\1, ~36/35 = 54.665
* POTE: ~2 = 1200.000, ~36/35 = 54.665


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


Badness: 0.044739
Badness (Smith): 0.044739


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