Porcupine family - Revision history

FloraC: - interwiki (the German article corresponds to Porcupine); - redundant category

2026-07-02T07:55:56Z

- interwiki (the German article corresponds to Porcupine); - redundant category

← Older revision		Revision as of 07:55, 2 July 2026
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	~~{{interwiki~~
	~~\| de = Porcupine~~
	~~\| en = Porcupine family~~
	~~\| es =~~
	~~\| ja =~~
	}}
	{{Technical data page}}		{{Technical data page}}
	The '''porcupine family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis.		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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	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Porcupine family\| ]] <!-- main article -->		[[Category:Porcupine family\| ]] <!-- main article -->
	~~[[Category:Porcupine\| ]] <!-- key article -->~~
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Review & make undecimation a septimal porcupine extension as it seems it was never explicitly no-7

2026-07-02T07:55:15Z

Review & make undecimation a septimal porcupine extension as it seems it was never explicitly no-7

← Older revision		Revision as of 07:55, 2 July 2026
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	Badness (Sintel): 0.303		Badness (Sintel): 0.303

	~~==== Undecimation (no-7s) ====~~
	~~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 ==		== Septimal porcupine ==
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	Badness (Sintel): 1.08		Badness (Sintel): 1.08

	===== Undecimation =====		==== Undecimation ====
	This ~~temperament~~ is used by most patent ~~edos~~ that ~~have septimal~~ porcupine and tune 13 well.		This weak extension is used by most patent vals that support porcupine and tune 13 well.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: 55/54, 64/63, 100/99, ~~512~~/~~507~~		Comma list: 55/54, 64/63, 100/99, 169/168

	Mapping: {{mapping\| 1 ~~5 8~~ -4 8 2\| 0 -6 -10 12 -8 3 }}		Mapping: {{mapping\| 1 -1 -2 8 0 5 \| 0 6 10 -12 8 -3 }}
			: mapping generators: ~2, ~35/26
	mapping generators: ~2, ~52/35

	Optimal tunings:		Optimal tunings:
			* WE: ~2 = 1198.4569{{c}}, ~35/26 = 517.9375{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~35/26 = 518.5822{{c}}

	*WE: ~2 = 1198.457{{c}}, ~52/35 = 680.519{{c}}		{{Optimal ET sequence\|legend=0\| 7, 30, 37, 81bd }}
	* CWE: ~2 = 1200.000{{c}}, ~52/35 = 681.418{{c}}

	{{Optimal ET sequence\|legend=0\|7, 30, 37, 44}}

	Badness (Sintel): 1.~~679~~		Badness (Sintel): 1.68

	== Opossum ==		== Opossum ==

VectorGraphics at 07:17, 2 July 2026

2026-07-02T07:17:04Z

← Older revision		Revision as of 07:17, 2 July 2026
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	Badness (Sintel): 0.303		Badness (Sintel): 0.303

	==== Undecimation ====		==== Undecimation (no-7s) ====
	Subgroup: 2.3.5.11.13		Subgroup: 2.3.5.11.13

VectorGraphics at 07:16, 2 July 2026

2026-07-02T07:16:45Z

@@ Line 87: / Line 87: @@
 Badness (Sintel): 1.21
 == Septimal porcupine ==
@@ Line 252: / Line 232: @@
 Badness (Sintel): 1.08
 == Opossum ==

VectorGraphics at 06:30, 2 July 2026

2026-07-02T06:30:22Z

← Older revision		Revision as of 06:30, 2 July 2026
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	===== Full 13-limit =====		===== Full 13-limit =====
	This temperament is used by most edos that have porcupine and tune 13 well.		This temperament is used by most patent edos that have porcupine and tune 13 well.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

VectorGraphics at 06:29, 2 July 2026

2026-07-02T06:29:49Z

← Older revision		Revision as of 06:29, 2 July 2026
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	Badness (Sintel): 1.21		Badness (Sintel): 1.21

			===== Full 13-limit =====
			This temperament is used by most edos that have porcupine and tune 13 well.

			Subgroup: 2.3.5.7.11.13

			Comma list: 55/54, 64/63, 100/99, 512/507

			Mapping: {{mapping\| 1 5 8 -4 8 2\| 0 -6 -10 12 -8 3 }}

			mapping generators: ~2, ~52/35

			Optimal tunings:

			*WE: ~2 = 1198.457{{c}}, ~52/35 = 680.519{{c}}
			* CWE: ~2 = 1200.000{{c}}, ~52/35 = 681.418{{c}}

			{{Optimal ET sequence\|legend=0\|7, 30, 37, 44}}

			Badness (Sintel): 1.679

	== Septimal porcupine ==		== Septimal porcupine ==

FloraC: /* Porcupine */ update a link

2026-06-08T11:43:41Z

Porcupine: update a link

← Older revision		Revision as of 11:43, 8 June 2026
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	{{Mapping\|legend=1\| 1 2 3 \| 0 -3 -5 }}		{{Mapping\|legend=1\| 1 2 3 \| 0 -3 -5 }}

	: mapping generators: ~2, ~10/9		: mapping generators: ~2, ~10/9

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	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
	* [[Oxygen]] → [[Very low accuracy temperaments #Oxygen\|Very low accuracy temperaments]].		* ''[[Oxygen]]'' → [[Very low accuracy temperaments #Oxygen\|Very low accuracy temperaments]]
	* [[Jamesbond]] → [[~~7th-octave temperaments~~ #Jamesbond\|~~7th-octave temperaments~~]].		* ''[[Jamesbond]]'' → [[Whitewood family #Jamesbond\|Whitewood family]]

	==== Subgroup extensions ====		==== Subgroup extensions ====

Overthink: /* Ammonite */ see also

2026-02-05T04:15:39Z

Ammonite: see also

← Older revision		Revision as of 04:15, 5 February 2026
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	== 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.

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:31:04Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:31, 27 November 2025
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	[[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]]

FloraC: Fixes

2025-09-06T10:41:32Z

Fixes

← Older revision		Revision as of 10:41, 6 September 2025
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	Optimal tunings:		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 }}		{{Optimal ET sequence\|legend=0\| 7, 15, 22, 73ce, 95ce }}
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	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 }}
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	{{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.