Porcusmine - Revision history

FloraC: Fix linking

2025-09-11T12:17:17Z

Fix linking

Fredg999: Misc. edits

2024-08-12T19:07:58Z

Misc. edits

← Older revision		Revision as of 19:07, 12 August 2024
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	'''Porcusmine''' is a ~~[[Maximum variety\|max-variety-4]] or max-variety-3,~~ [[generator-offset]] scale with step pattern 4L 3M 1s. It is equivalent to the [[porcupine]] ([[7L 1s]]) mos with 4 of the large steps made bigger and the other 3 made smaller, or to the smitonic ([[4L 3s]]) with an extra-small step added. ~~Porcusmine~~ is not [[chiral]]. [[19edo]] is the smallest edo to support a non-degenerate porcusmine.		'''Porcusmine''' is a [[generator-offset]] scale with step pattern 4L 3M 1s. It is equivalent to the [[porcupine]] ([[7L 1s]]) mos with 4 of the large steps made bigger and the other 3 made smaller, or to the smitonic ([[4L 3s]]) with an extra-small step added. It is not [[chiral]] and it has [[Maximum variety\|maximum variety 3]] for certain tunings only (otherwise it has maximum variety 4 in general). [[19edo]] is the smallest edo to support a non-degenerate porcusmine.

	Porcusmine can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[27/25]], and s represents [[25/24]].		Porcusmine can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[27/25]], and s represents [[25/24]].

	"Porcusmine" is a name given by [[User:CellularAutomaton\|cellularAutomaton]], who discovered it as a detempering of porcupine. The name is a portmanteau of "porcupine" and "smitonic", since its step sizes are intermediate between those of the 8-note porcupine and 7-note smitonic mosses. It was also later called the [[The Pinetone System#Pinetone diminished octatonic\|Pinetone diminished octatonic]] when independently discovered by [[~~User:Lhearne\|Lhearne~~]]. Similar Porcupine[8] detemperings have also been [[Kite_Guitar_Translations_by_Kite_Giedraitis#Couples_Therapy_.28Jacob_Barton.2C_microtonal.29\|discussed]] by [[Kite Giedraitis]] as well as by ~~[[User:Lhearne\|Lhearne]]~~.		"Porcusmine" is a name given by [[User:CellularAutomaton\|cellularAutomaton]], who discovered it as a detempering of porcupine. The name is a portmanteau of "porcupine" and "smitonic", since its step sizes are intermediate between those of the 8-note porcupine and 7-note smitonic mosses. It was also later called the [[The Pinetone System#Pinetone diminished octatonic\|Pinetone diminished octatonic]] when independently discovered by [[Lillian Hearne]]. Similar Porcupine[8] detemperings have also been [[Kite_Guitar_Translations_by_Kite_Giedraitis#Couples_Therapy_.28Jacob_Barton.2C_microtonal.29\|discussed]] by [[Kite Giedraitis]] as well as by Lillian Hearne.

	== Modes ==		== Modes ==

Lhearne: Added reference to my more recent discovery of it and edited to reflect that the scale Kite discussed was actually slightly different

2024-03-13T02:43:35Z

Added reference to my more recent discovery of it and edited to reflect that the scale Kite discussed was actually slightly different

← Older revision		Revision as of 02:43, 13 March 2024
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	Porcusmine can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[27/25]], and s represents [[25/24]].		Porcusmine can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[27/25]], and s represents [[25/24]].

	"Porcusmine" is a name given by [[User:CellularAutomaton\|cellularAutomaton]], who discovered it as a detempering of porcupine~~, although the scale has also been [[Kite_Guitar_Translations_by_Kite_Giedraitis#Couples_Therapy_.28Jacob_Barton.2C_microtonal.29\|discussed]] by [[Kite Giedraitis]] and possibly others~~. The name is a portmanteau of "porcupine" and "smitonic", since its step sizes are intermediate between those of the 8-note porcupine and 7-note smitonic mosses.		"Porcusmine" is a name given by [[User:CellularAutomaton\|cellularAutomaton]], who discovered it as a detempering of porcupine. The name is a portmanteau of "porcupine" and "smitonic", since its step sizes are intermediate between those of the 8-note porcupine and 7-note smitonic mosses. It was also later called the [[The Pinetone System#Pinetone diminished octatonic\|Pinetone diminished octatonic]] when independently discovered by [[User:Lhearne\|Lhearne]]. Similar Porcupine[8] detemperings have also been [[Kite_Guitar_Translations_by_Kite_Giedraitis#Couples_Therapy_.28Jacob_Barton.2C_microtonal.29\|discussed]] by [[Kite Giedraitis]] as well as by [[User:Lhearne\|Lhearne]].

	== Modes ==		== Modes ==

CellularAutomaton: elaborated on the 5-limit AGS interpretation

2023-07-14T19:53:17Z

elaborated on the 5-limit AGS interpretation

← Older revision		Revision as of 19:53, 14 July 2023
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	!Other notes		!Other notes
	\|-		\|-
	\|JI (5-limit interpretation)		\|JI (5-limit AGS interpretation)
	\|2.581:1.885:1		\|2.581:1.885:1
	\|just 3/2, 6/5, 5/4, 9/8, and 10/9		\|just 3/2, 6/5, 5/4, 9/8, and 10/9
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	\|}		\|}

			== 5-limit AGS interpretation ==
			Porcusmine can be interpreted as a member of an [[AGS]] series AGS(9/5, 50/27), which is [[constant structure]] at 5, 6, 7, 8, 15, 23, 38, 61, and 99 notes. It is noteworthy for an AGS series to retain constant structure to this size.

			In this AGS interpretation, Whothic is the "root mode" of Porcusmine. The 5-limit tuning of Whothic generated by AGS(9/5, 50/27) is:

			1/1 25/24 125/108 5/4 25/18 3/2 5/3 9/5 2/1

			In this tuning, the interval 25/18 occurs frequently, and the scale could be more consonant by tempering out [[126/125]] to equate this interval with 7/5.
	[[Category:8-tone scales]]		[[Category:8-tone scales]]
	[[Category:19edo]]		[[Category:19edo]]

TallKite: /* Tunings */ added 41edo

2023-05-01T06:19:11Z

Tunings: added 41edo

← Older revision		Revision as of 06:19, 1 May 2023
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	\|6:3:1		\|6:3:1
	\|excellent 6/5; fairly good 9/8, 11/9, and 14/11		\|excellent 6/5; fairly good 9/8, 11/9, and 14/11
			\|
			\|-
			\|41edo
			\|6:5:2
			\|excellent 3-limit; good 7-limit; fairly good 5-limit
	\|		\|
	\|}		\|}

Xenwolf: link chiral -> chirality

2022-11-07T08:27:18Z

link chiral -> chirality

← Older revision		Revision as of 08:27, 7 November 2022
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	'''Porcusmine''' is a [[Maximum variety\|max-variety-4]] or max-variety-3, [[generator-offset]] scale with step pattern 4L 3M 1s. It is equivalent to the [[porcupine]] ([[7L 1s]]) mos with 4 of the large steps made bigger and the other 3 made smaller, or to the smitonic ([[4L 3s]]) with an extra-small step added. Porcusmine is not chiral. [[19edo]] is the smallest edo to support a non-degenerate porcusmine.		'''Porcusmine''' is a [[Maximum variety\|max-variety-4]] or max-variety-3, [[generator-offset]] scale with step pattern 4L 3M 1s. It is equivalent to the [[porcupine]] ([[7L 1s]]) mos with 4 of the large steps made bigger and the other 3 made smaller, or to the smitonic ([[4L 3s]]) with an extra-small step added. Porcusmine is not [[chiral]]. [[19edo]] is the smallest edo to support a non-degenerate porcusmine.

	Porcusmine can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[27/25]], and s represents [[25/24]].		Porcusmine can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[27/25]], and s represents [[25/24]].

CellularAutomaton: CellularAutomaton moved page User:CellularAutomaton/Porcusmine to Porcusmine: notable enough to be documented in the main namespace + i got it checked on discord (thanks inthar and fumica)

2022-11-03T17:34:29Z

CellularAutomaton moved page User:CellularAutomaton/Porcusmine to Porcusmine: notable enough to be documented in the main namespace + i got it checked on discord (thanks inthar and fumica)

← Older revision	Revision as of 17:34, 3 November 2022
(No difference)

CellularAutomaton: put the page in some categories

2022-11-03T17:20:50Z

put the page in some categories

← Older revision		Revision as of 17:20, 3 November 2022
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	\|		\|
	\|}		\|}

			[[Category:8-tone scales]]
			[[Category:19edo]]
			[[Category:23edo]]
			[[Category:26edo]]
			[[Category:27edo]]
			[[Category:31edo]]
			[[Category:34edo]]
			[[Category:Just intonation scales]]
			[[Category:5-limit]]
			[[Category:GO scales]]
			[[Category:Rank-3 scales]]
			[[Category:Scales]]

CellularAutomaton: finished tunings section

2022-11-03T17:14:29Z

finished tunings section

← Older revision		Revision as of 17:14, 3 November 2022
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	== Modes ==		== Modes ==
	Porcusmine has 8 modes. Names are provided based on porcupine (tuning-neutral) and smitonic (for tunings where s is small), as well as a unique portmanteau name. When M and s are close, the scale approaches [[Diminished\|diminshed]] ([[4L 4s]]), which has two distinct modes and is therefore not useful for naming. The porcupine mode names refer to William Lynch's names, and the smitonic mode names refer to [[User:Ayceman\|Alexandru Ianu]]'s names. Below are the modes arranged in cyclic order:		Porcusmine has 8 modes. Names are provided based on porcupine (tuning-neutral) and smitonic (for tunings where s is small), as well as a unique portmanteau name. When M and s are close, the scale approaches [[Diminished\|diminshed]] ([[4L 4s]]), which has only two distinct modes and is therefore not useful for naming. The porcupine mode names refer to William Lynch's names, and the smitonic mode names refer to [[User:Ayceman\|Alexandru Ianu]]'s names. Below are the modes arranged in cyclic order:
	{\| class="wikitable"		{\| class="wikitable"
	!Modes in cyclic order		!Modes in cyclic order
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	\|JI (5-limit interpretation)		\|JI (5-limit interpretation)
	\|2.581:1.885:1		\|2.581:1.885:1
	\|just 3/2~~, 4/3~~, 6/5, 5/4, 9/8, and 16/9		\|just 3/2, 6/5, 5/4, 9/8, and 10/9
	\|		\|
	\|-		\|-
Line 123:		Line 123:
	\|33edo		\|33edo
	\|5:4:1		\|5:4:1
	\|		\|excellent 10/9; fairly good 11/6 and 11/8
	\|		\|
	\|-		\|-
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	\|34edo		\|34edo
	\|6:3:1		\|6:3:1
	\|		\|excellent 6/5; fairly good 9/8, 11/9, and 14/11
	\|
	\|-
	~~\|35edo~~
	\|5~~:4:3~~
	\|
	\|
	\|-
	~~\|35edo~~
	~~\|6:3:2~~
	\|
	\|
	\|-
	~~\|35edo~~
	~~\|7:2:1~~
	\|
	\|		\|
	\|}		\|}

CellularAutomaton: fleshed out tunings section

2022-11-02T20:17:13Z

fleshed out tunings section

← Older revision		Revision as of 20:17, 2 November 2022
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	'''Porcusmine''' is a [[Maximum variety\|max-variety-3]], [[generator-offset]] scale with step pattern 4L 3M 1s. It is equivalent to the [[porcupine]] ([[7L 1s]]) mos with 4 of the large steps made bigger and the other 3 made smaller, or to the smitonic ([[4L 3s]]) with an extra-small step added. Porcusmine is not chiral. [[19edo]] is the smallest edo to support a non-degenerate porcusmine.		'''Porcusmine''' is a [[Maximum variety\|max-variety-4]] or max-variety-3, [[generator-offset]] scale with step pattern 4L 3M 1s. It is equivalent to the [[porcupine]] ([[7L 1s]]) mos with 4 of the large steps made bigger and the other 3 made smaller, or to the smitonic ([[4L 3s]]) with an extra-small step added. Porcusmine is not chiral. [[19edo]] is the smallest edo to support a non-degenerate porcusmine.

	Porcusmine can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[27/25]], and s represents [[25/24]].		Porcusmine can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[27/25]], and s represents [[25/24]].
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	== Tunings ==		== Tunings ==
			Porcusmine is MV3 when L+s=M+M, as reflected in the table below.
	{\| class="wikitable sortable"		{\| class="wikitable sortable"
	\|+Porcusmine tunings		\|+Porcusmine tunings
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	\|3:2:1		\|3:2:1
	\|excellent pental thirds, fairly good 3-limit		\|excellent pental thirds, fairly good 3-limit
	\|		\|MV3
	\|-		\|-
	\|23edo		\|23edo
	\|4:2:1		\|4:2:1
	\|excellent 6/5 and 9/8, fairly good 7/5		\|excellent 6/5 and 9/8, fairly good 7/5
	\|		\|
	\|-		\|-
Line 97:		Line 98:
	\|27edo		\|27edo
	\|4:3:2		\|4:3:2
	\|		\|excellent 10/9, 7/6, 6/5, and 7/5; fairly good 9/7 and 3/2
	\|		\|MV3
	\|-		\|-
	\|27edo		\|27edo
	\|5:2:1		\|5:2:1
	\|		\|excellent 5:6:7; fairly good 7/4, 11/9, and 3/2
	\|		\|
	\|-		\|-
	\|30edo		\|30edo
	\|5:3:1		\|5:3:1
	\|		\|excellent 15/14, 9/8, 6/5, and 9/7; fairly good 15/8, 7/4, and 11/8
	\|		\|MV3
	\|-		\|-
	\|31edo		\|31edo
	\|5:3:2		\|5:3:2
	\|		\|excellent 15/14 or 16/15, 7/6, 5/4, and 7/5; fairly good 6/5, 9/7, 3/2
	\|		\|meantone fifths
	\|-		\|-
	\|31edo		\|31edo
	\|6:2:1		\|6:2:1
	\|		\|excellent 7/4, 7/6, 11/9, 5/4, 7/5; fairly good 6/5, 3/2, and 11/8
	\|		\|single meantone fifth
	\|-		\|-
	\|33edo		\|33edo
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	\|5:4:2		\|5:4:2
	\|very close to 5-limit just tuning		\|very close to 5-limit just tuning
	\|~~offers slightly sharp~~ fifths		\|gentle fifths
	\|-		\|-
	\|34edo		\|34edo