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-{{interwiki
-| de = Porcupine
-| en = Porcupine family
-| es =
-| ja =
-}}
 {{Technical data page}}
 The '''porcupine family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis.
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 {{Mapping|legend=1| 1 2 3 | 0 -3 -5 }}
 : mapping generators: ~2, ~10/9
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 Those all share the same generator with porcupine.
-[[#Nautilus|nautilus]] tempers out [[49/48]] and splits the generator in two. [[#Hedgehog|hedgehog]] tempers out [[50/49]] with a semi-octave period. Finally, [[#Ammonite|ammonite]] tempers out [[686/675]] and [[#Ceratitid|ceratitid]] tempers out [[1728/1715]]. Those split the generator in three.
+[[#Nautilus|Nautilus]] tempers out [[49/48]] and splits the generator in two. Hedgehog tempers out [[50/49]] with a semi-octave period. Finally, [[#Ammonite|ammonite]] tempers out [[686/675]] and [[#Ceratitid|ceratitid]] tempers out [[1728/1715]]. Those split the generator in three.
 Temperaments discussed elsewhere include:
-* [[Oxygen]] → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]].
+* ''[[Oxygen]]'' (+21/20) → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]]
-* [[Jamesbond]] → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]].
+* ''[[Hedgehog]]'' (+50/49 or 245/243) → [[Stearnsmic clan #Hedgehog|Stearnsmic clan]]
+* ''[[Jamesbond]]'' (+25/24) → [[Whitewood family #Jamesbond|Whitewood family]]
+The rest are considered in this page.
 ==== Subgroup extensions ====
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 Comma list: 55/54, 100/99
-Subgroup-val mapping: {{mapping| 1 2 3 4 | 0 -3 -5 -4 }}
+{{Mapping|legend=2| 1 2 3 4 | 0 -3 -5 -4 }}
-Gencom mapping: {{mapping| 1 2 3 0 4 | 0 -3 -5 0 -4 }}
+{{Mapping|legend=4| 1 2 3 0 4 | 0 -3 -5 0 -4 }}
 Optimal tunings:
-* WE: ~2 = 1200.3290{{c}}, ~10/9 = 164.1227{{c}}
+* WE: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~10/9 = 163.9951{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}
 {{Optimal ET sequence|legend=0| 7, 15, 22, 73ce, 95ce }}
 Badness (Sintel): 0.303
-==== Undecimation ====
-Subgroup: 2.3.5.11.13
-Comma list: 55/54, 100/99, 512/507
-Subgroup-val mapping: {{mapping| 1 -1 -2 0 5 | 0 6 10 8 -3 }}
-: mapping generators: ~2, ~88/65
-Optimal tunings:
-* WE: ~2 = 1199.4791{{c}}, ~88/65 = 517.9845{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~88/65 = 518.1740{{c}}
-{{Optimal ET sequence|legend=0| 7, 23bc, 30, 37, 44 }}
-Badness (Sintel): 1.21
 == Septimal porcupine ==
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 Comma list: 55/54, 64/63, 100/99
-Mapping: {{mapping| 1 2 3 2 4 | 0 -3 -5 6 -4 }}
+{{Mapping|legend=0| 1 2 3 2 4 | 0 -3 -5 6 -4 }}
 Optimal tunings:
@@ Line 151: / Line 130: @@
 Comma list: 40/39, 55/54, 64/63, 66/65
-Mapping: {{mapping| 1 2 3 2 4 4 | 0 -3 -5 6 -4 -2 }}
+{{Mapping|legend=0| 1 2 3 2 4 4 | 0 -3 -5 6 -4 -2 }}
 Optimal tunings:
@@ Line 177: / Line 156: @@
 Comma list: 55/54, 64/63, 91/90, 100/99
-Mapping: {{mapping| 1 2 3 2 4 6 | 0 -3 -5 6 -4 -17 }}
+{{Mapping|legend=0| 1 2 3 2 4 6 | 0 -3 -5 6 -4 -17 }}
 Optimal tunings:
@@ Line 188: / Line 167: @@
 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 }}
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 Comma list: 55/54, 64/63, 100/99, 196/195
-Mapping: {{mapping| 1 2 3 2 4 1 | 0 -3 -5 6 -4 20 }}
+{{Mapping|legend=0| 1 2 3 2 4 1 | 0 -3 -5 6 -4 20 }}
 Optimal tunings:
@@ Line 220: / Line 199: @@
 Comma list: 55/54, 64/63, 65/63, 100/99
-Mapping: {{mapping| 1 2 3 2 4 3 | 0 -3 -5 6 -4 5 }}
+{{Mapping|legend=0| 1 2 3 2 4 3 | 0 -3 -5 6 -4 5 }}
 Optimal tunings:
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 Badness (Sintel): 1.08
+==== Undecimation ====
+This weak extension is used by most patent vals that support porcupine and tune 13 well.
+Subgroup: 2.3.5.7.11.13
+Comma list: 55/54, 64/63, 100/99, 169/168
+{{Mapping|legend=0| 1 -1 -2 8 0 5 | 0 6 10 -12 8 -3 }}
+: mapping generators: ~2, ~35/26
+Optimal tunings:
+* WE: ~2 = 1198.4569{{c}}, ~35/26 = 517.9375{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~35/26 = 518.5822{{c}}
+{{Optimal ET sequence|legend=0| 7, 30, 37, 81bd }}
+Badness (Sintel): 1.68
 == Opossum ==
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 Comma list: 28/27, 55/54, 77/75
-Mapping: {{mapping| 1 2 3 4 4 | 0 -3 -5 -9 -4 }}
+{{Mapping|legend=0| 1 2 3 4 4 | 0 -3 -5 -9 -4 }}
 Optimal tunings:
@@ Line 281: / Line 278: @@
 Comma list: 28/27, 40/39, 55/54, 66/65
-Mapping: {{mapping| 1 2 3 4 4 4 | 0 -3 -5 -9 -4 -2 }}
+{{Mapping|legend=0| 1 2 3 4 4 4 | 0 -3 -5 -9 -4 -2 }}
 Optimal tunings:
@@ Line 322: / Line 319: @@
 Comma list: 55/54, 100/99, 225/224
-Mapping: {{mapping| 1 2 3 5 4 | 0 -3 -5 -16 -4 }}
+{{Mapping|legend=0| 1 2 3 5 4 | 0 -3 -5 -16 -4 }}
 Optimal tunings:
@@ Line 341: / Line 338: @@
 Comma list: 55/54, 65/64, 91/90, 100/99
-Mapping: {{mapping| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }}
+{{Mapping|legend=0| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }}
 Optimal tunings:
@@ Line 382: / Line 379: @@
 Comma list: 55/54, 100/99, 525/512
-Mapping: {{mapping| 1 2 3 1 4 | 0 -3 -5 13 -4 }}
+{{Mapping|legend=0| 1 2 3 1 4 | 0 -3 -5 13 -4 }}
 Optimal tunings:
@@ Line 401: / Line 398: @@
 Comma list: 55/54, 65/64, 100/99, 105/104
-Mapping: {{mapping| 1 2 3 1 4 3 | 0 -3 -5 13 -4 5 }}
+{{Mapping|legend=0| 1 2 3 1 4 3 | 0 -3 -5 13 -4 5 }}
 Optimal tunings:
@@ Line 443: / Line 440: @@
 Comma list: 22/21, 36/35, 80/77
-Mapping: {{mapping| 1 2 3 3 4 | 0 -3 -5 -1 -4 }}
+{{Mapping|legend=0| 1 2 3 3 4 | 0 -3 -5 -1 -4 }}
 Optimal tunings:
@@ Line 452: / Line 449: @@
 Badness (Sintel): 0.886
-== Hedgehog ==
-{{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.
-edo 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.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 50/49, 245/243
-{{Mapping|legend=1| 2 1 1 2 | 0 3 5 5 }}
-: mapping generators: ~7/5, ~9/7
-[[Optimal tuning]]s:
-* [[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 }}
-{{Optimal ET sequence|legend=1| 8d, 14c, 22 }}
-[[Badness]] (Sintel): 1.11
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 50/49, 55/54, 99/98
-Mapping: {{mapping| 2 1 1 2 4 | 0 3 5 5 4 }}
-Optimal tunings:
-* WE: ~7/5 = 600.1133{{c}}, ~9/7 = 435.4680{{c}}
-* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4431{{c}}
-{{Optimal ET sequence|legend=0| 8d, 14c, 22, 58ce }}
-Badness (Sintel): 0.764
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 50/49, 55/54, 65/63, 99/98
-Mapping: {{mapping| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}
-Optimal tunings:
-* WE: ~7/5 = 600.3651{{c}}, ~9/7 = 436.1258{{c}}
-* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 436.0483{{c}}
-{{Optimal ET sequence|legend=0| 8d, 14cf, 22 }}
-Badness (Sintel): 0.889
-==== Urchin ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 40/39, 50/49, 55/54, 66/65
-Mapping: {{mapping| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}
-Optimal tunings:
-* WE: ~7/5 = 598.3303{{c}}, ~9/7 = 435.8617{{c}}
-* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 436.3485{{c}}
-{{Optimal ET sequence|legend=0| 14c, 22f }}
-Badness (Sintel): 1.04
-=== Hedgepig ===
-Subgroup: 2.3.5.7.11
-Comma list: 50/49, 245/243, 385/384
-Mapping: {{mapping| 2 1 1 2 12 | 0 3 5 5 -7 }}
-Optimal tunings:
-* WE: ~7/5 = 599.7917{{c}}, ~9/7 = 435.2737{{c}}
-* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4047{{c}}
-{{Optimal ET sequence|legend=0| 22 }}
-Badness (Sintel): 2.26
-; Music
-* [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 ==
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 Comma list: 49/48, 55/54, 245/242
-Mapping: {{mapping| 1 2 3 3 4 | 0 -6 -10 -3 -8 }}
+{{Mapping|legend=0| 1 2 3 3 4 | 0 -6 -10 -3 -8 }}
 Optimal tunings:
@@ Line 582: / Line 491: @@
 Comma list: 49/48, 55/54, 91/90, 100/99
-Mapping: {{mapping| 1 2 3 3 4 5 | 0 -6 -10 -3 -8 -19 }}
+{{Mapping|legend=0| 1 2 3 3 4 5 | 0 -6 -10 -3 -8 -19 }}
 Optimal tunings:
@@ Line 597: / Line 506: @@
 Comma list: 40/39, 49/48, 55/54, 66/65
-Mapping: {{mapping| 1 2 3 3 4 4 | 0 -6 -10 -3 -8 -4 }}
+{{Mapping|legend=0| 1 2 3 3 4 4 | 0 -6 -10 -3 -8 -4 }}
 Optimal tunings:
@@ Line 611: / Line 520: @@
 == 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.
@@ Line 636: / Line 546: @@
 Comma list: 55/54, 100/99, 686/675
-Mapping: {{mapping| 1 -4 -7 -9 -4 | 0 9 15 19 12 }}
+{{Mapping|legend=0| 1 -4 -7 -9 -4 | 0 9 15 19 12 }}
 Optimal tunings:
@@ Line 651: / Line 561: @@
 Comma list: 55/54, 91/90, 100/99, 169/168
-Mapping: {{mapping| 1 -4 -7 -9 -4 -5 | 0 9 15 19 12 14 }}
+{{Mapping|legend=0| 1 -4 -7 -9 -4 -5 | 0 9 15 19 12 14 }}
 Optimal tunings:
@@ Line 687: / Line 597: @@
 Comma list: 55/54, 100/99, 352/343
-Mapping: {{mapping| 1 2 3 3 4 | 0 -9 -15 -4 -12 }}
+{{Mapping|legend=0| 1 2 3 3 4 | 0 -9 -15 -4 -12 }}
 Optimal tunings:
@@ Line 702: / Line 612: @@
 Comma list: 55/54, 65/63, 100/99, 352/343
-Mapping: {{mapping| 1 2 3 3 4 4 | 0 -9 -15 -4 -12 -7 }}
+{{Mapping|legend=0| 1 2 3 3 4 4 | 0 -9 -15 -4 -12 -7 }}
 Optimal tunings:
@@ Line 712: / Line 622: @@
 Badness (Sintel): 1.85
+[[Category:Porcupine family| ]] <!-- main article -->
 [[Category:Temperament families]]
-[[Category:Pages with mostly numerical content]]
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Porcupine family| ]] <!-- main article -->
-[[Category:Porcupine| ]] <!-- key article -->
-[[Category:Rank 2]]

Porcupine family: Difference between revisions