Whitewood - Revision history

FloraC: Wording & misc. additions

2026-06-12T19:52:15Z

Wording & misc. additions

← Older revision		Revision as of 19:52, 12 June 2026
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	'''Whitewood''' is the [[rank-2 temperament]] tempering out [[2187/2048]], the Pythagorean chromatic semitone. As a result, the [[circle of fifths]] is the same as that of [[7edo]], and every interval on the chain of fifths is [[neutral (interval quality)\|neutral]] in quality. The whitewood temperament adds prime [[5/1\|5]] as an independent [[generator]], adding subchromatically inflected intervals (notated with ups and downs below) on either side of the neutral ones.		'''Whitewood''' is the [[rank-2 temperament]] tempering out [[2187/2048]], the Pythagorean chromatic semitone. As a result, the [[circle of fifths]] is the same as that of [[7edo]], and every interval on the chain of fifths is [[neutral (interval quality)\|neutral]] in quality. The whitewood temperament adds prime [[5/1\|5]] as an independent [[generator]], adding subchromatically inflected intervals (notated with ups and downs below) on either side of the neutral ones.

	The canonical [[extension]] to ~~prime~~ [[7~~/1\|7~~]] adds [[36/35]] to the commas, thus equating ~~[[5-limit]]~~ major and minor intervals with ~~[[7-limit]]~~ subminor and supermajor ones. It finds [[7/4]] at the down seventh, [[7/6]] at the down third, and [[9/7]] at the up third.		The canonical [[extension]] to the [[7-limit]] adds [[36/35]] to the commas, thus equating classical major and minor intervals with septimal subminor and supermajor ones. It finds [[7/4]] at the down seventh, [[7/6]] at the down third, and [[9/7]] at the up third.

	Whitewood was named by [[Mike Battaglia]] in 2010 to serve in contrast with the [[blackwood]] temperament, which tempers out 256/243, the [[Pythagorean limma]].<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_95296.html Yahoo! Tuning Group \| ''7&14 temperament - 14 out of 35'']</ref> The [[2.3.7 subgroup\|2.3.7-subgroup]] [[restriction]] of whitewood is sometimes known as '''purpleheart'''.		Whitewood was named by [[Mike Battaglia]] in 2010 to serve in contrast with the [[blackwood]] temperament, which tempers out 256/243, the [[Pythagorean limma]].<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_95296.html Yahoo! Tuning Group \| ''7&14 temperament - 14 out of 35'']</ref> The [[2.3.7 subgroup\|2.3.7-subgroup]] [[restriction]] of whitewood is sometimes known as '''purpleheart'''.
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	\| 32/27, 81/64, 128/105		\| 32/27, 81/64, 128/105
	\| 392.7		\| 392.7
	\| '''5/4'''		\| '''5/4''', 9/7
	\|-		\|-
	\| 3		\| 3
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	\| [[7/4]]		\| [[7/4]]
	\| 402.603		\| 402.603
	\|		\| 2.3.7-subgroup CTE
	\|-		\|-
	\|		\|

Overthink: /* Tuning spectrum */ more edo tunings; links

2026-05-21T01:01:29Z

Tuning spectrum: more edo tunings; links

← Older revision		Revision as of 01:01, 21 May 2026
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	! Comments		! Comments
	\|-		\|-
	\| '''2\7'''		\| '''[[7edo\|2\7]]'''
	\|		\|
	\| '''342.857'''		\| '''342.857'''
	\| '''Lower bound of 5-odd-limit diamond monotone'''		\| '''Lower bound of 5-odd-limit [[diamond monotone]]'''
	\|-		\|-
	\|		\|
	\| 9/5		\| [[9/5]]
	\| 353.832		\| 353.832
	\|		\|
	\|-		\|-
	\|		\|
	\| 6/5		\| [[6/5]]
	\| 370.073		\| 370.073
	\|		\|
	\|-		\|-
	\| 11\35		\| [[35edo\|11\35]]
	\|		\|
	\| 377.143		\| 377.143
	\| 35d val		\| 35d [[val]]
	\|-		\|-
	\|		\|
	\| 25/24		\| [[25/24]]
	\| 378.193		\| 378.193
	\| 5-odd-limit minimax		\| 5-odd-limit minimax
	\|-		\|-
	\| '''9\28'''		\| '''[[28edo\|9\28]]'''
	\|		\|
	\| '''385.714'''		\| '''385.714'''
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	\|-		\|-
	\|		\|
	\| 5/4		\| [[5/4]]
	\| 386.314		\| 386.314
	\| 5-limit CTE		\| 5-limit CTE
	\|-		\|-
	\|		\|
	\| 21/20		\| [[21/20]]
	\| 386.338		\| 386.338
	\|		\|
	\|-		\|-
	\|		\|
	\| 21/16		\| [[21/16]]
	\| 386.362		\| 386.362
	\|		\|
	\|-		\|-
			\| [[49edo\|16\49]]
	\|		\|
	\| 7/5		\| 391.837
			\| 49b val
			\|-
			\|
			\| [[7/5]]
	\| 394.458		\| 394.458
	\| 7- and 9-odd-limit minimax		\| 7- and 9-odd-limit minimax
	\|-		\|-
	\| 7\21		\| [[21edo\|7\21]]
	\|		\|
	\| 400.000		\| 400.000
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	\|-		\|-
	\|		\|
	\| 15/8		\| [[15/8]]
	\| 402.554		\| 402.554
	\|		\|
	\|-		\|-
	\|		\|
	\| 15/14		\| [[15/14]]
	\| 402.579		\| 402.579
	\|		\|
	\|-		\|-
	\|		\|
	\| 7/4		\| [[7/4]]
	\| 402.603		\| 402.603
	\|		\|
	\|-		\|-
	\|		\|
	\| 49/48		\| [[49/48]]
	\| 410.723		\| 410.723
	\|		\|
			\|-
			\| [[35edo\|12\35]]
			\|
			\| 411.429
			\| 35c val
	\|-		\|-
	\|		\|
	\| 7/6		\| [[7/6]]
	\| 418.843		\| 418.843
	\|		\|
	\|-		\|-
	\| '''5\14'''		\| '''[[14edo\|5\14]]'''
	\|		\|
	\| '''428.571'''		\| '''428.571'''
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	\|-		\|-
	\|		\|
	\| 9/7		\| [[9/7]]
	\| 435.084		\| 435.084
	\|		\|
	\|-		\|-
	\| '''3\7'''		\| '''[[7edo\|3\7]]'''
	\|		\|
	\| '''514.286'''		\| '''514.286'''

FloraC at 11:23, 15 May 2026

2026-05-15T11:23:30Z

← Older revision		Revision as of 11:23, 15 May 2026
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	{{~~interwiki~~		{{Interwiki
			\| en = Whitewood
	\| de = Whitewood		\| de = Whitewood
	~~\| en = Whitewood~~		}}
	}}{{Infobox regtemp		{{Infobox regtemp
	\| Title = Whitewood		\| Title = Whitewood
	\| Subgroups = 2.3.5, 2.3.5.7		\| Subgroups = 2.3.5, 2.3.5.7
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	The canonical [[extension]] to prime [[7/1\|7]] adds [[36/35]] to the commas, thus equating [[5-limit]] major and minor intervals with [[7-limit]] subminor and supermajor ones. It finds [[7/4]] at the down seventh, [[7/6]] at the down third, and [[9/7]] at the up third.		The canonical [[extension]] to prime [[7/1\|7]] adds [[36/35]] to the commas, thus equating [[5-limit]] major and minor intervals with [[7-limit]] subminor and supermajor ones. It finds [[7/4]] at the down seventh, [[7/6]] at the down third, and [[9/7]] at the up third.

	Whitewood was named by [[Mike Battaglia]] in 2010 to serve in contrast with the [[blackwood]] temperament, which tempers out 256/243, the [[Pythagorean limma]].<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_95296.html Yahoo! Tuning Group \| ''7&14 temperament - 14 out of 35'']</ref>		Whitewood was named by [[Mike Battaglia]] in 2010 to serve in contrast with the [[blackwood]] temperament, which tempers out 256/243, the [[Pythagorean limma]].<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_95296.html Yahoo! Tuning Group \| ''7&14 temperament - 14 out of 35'']</ref> The [[2.3.7 subgroup\|2.3.7-subgroup]] [[restriction]] of whitewood is sometimes known as '''purpleheart'''.

	For technical data, see [[Whitewood family #Whitewood]].		For technical data, see [[Whitewood family #Whitewood]] and [[No-fives subgroup temperaments #Purpleheart]].

	== Intervals ==		== Intervals ==

Overthink: /* Tunings */ melodic consideration

2026-05-09T00:27:37Z

Tunings: melodic consideration

← Older revision		Revision as of 00:27, 9 May 2026
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	While blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning – targeting individually the [[5-limit\|2.3.5-]] or [[2.3.7 subgroup\|2.3.7-subgroup]]. Septimal whitewood entails a rather different tuning profile, as the vanishing of 36/35 means 5 and 7 should be tuned somewhat sharp.		While blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning – targeting individually the [[5-limit\|2.3.5-]] or [[2.3.7 subgroup\|2.3.7-subgroup]]. Septimal whitewood entails a rather different tuning profile, as the vanishing of 36/35 means 5 and 7 should be tuned somewhat sharp.

	Any multiple of [[7edo]], up until [[35edo]], contains 7edo's [[perfect fifth]], and thus supports whitewood, with all but 35edo supporting the canonical 7-limit extension by [[patent val]]. The most extreme tuning is [[14edo]], where up seconds and down thirds are equated, and every interval is either a 7edo interval or halfway between two 7edo intervals. While the 14edo tuning poorly approximates 5-limit intervals, it does approximate the [[6:7:9]] subminor and [[14:18:21\|1/(9:7:6)]] supermajor triads fairly well. A less extreme tuning is [[21edo]], tuning [[7/4]] close to just and tuning [[5/4]] to the same 400{{c}} major third as in [[12edo]], though [[6/5]] is still about 30 cents flat. The [[28edo]] tuning has a near-just 5/4, and tunes whitewood about as best as it can be tuned.		Any multiple of [[7edo]], up until [[35edo]], contains 7edo's [[perfect fifth]], and thus supports whitewood, with all but 35edo supporting the canonical 7-limit extension by [[patent val]]. The most extreme tuning is [[14edo]], where up seconds and down thirds are equated, and every interval is either a 7edo interval or halfway between two 7edo intervals. While the 14edo tuning poorly approximates 5-limit intervals, it does approximate the [[6:7:9]] subminor and [[14:18:21\|1/(9:7:6)]] supermajor triads fairly well. A less extreme tuning is [[21edo]], tuning [[7/4]] close to just and tuning [[5/4]] to the same 400{{c}} major third as in [[12edo]], though [[6/5]] is still about 30 cents flat. The [[28edo]] tuning has a near-just 5/4, and tunes whitewood about the best it can be tuned harmonically, though the small step of Whitewood[14] shrinks to just 42.9 cents, thus becoming less melodically viable.

	=== Norm-based tunings ===		=== Norm-based tunings ===

Hstraub: sound example

2026-05-08T22:40:13Z

sound example

← Older revision		Revision as of 22:40, 8 May 2026
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	Another interesting property is that it becomes possible to construct "super-linked" 5-limit chords. In Whitewood[14], or Blackwood[10], if one stacks alternating major and minor thirds on top of one another, one will eventually come back to the root without ever hitting a wall, and hence the pattern can continue forever. Since all of the diatonic modes can be thought of as a stacked chain of 7 alternating thirds, placed in inversion, this means that Whitewood[14] and Blackwood[10] also make for excellent "panmodal" scales, in which you can construct "modal" sounding sonorities in one key that will work in all keys.		Another interesting property is that it becomes possible to construct "super-linked" 5-limit chords. In Whitewood[14], or Blackwood[10], if one stacks alternating major and minor thirds on top of one another, one will eventually come back to the root without ever hitting a wall, and hence the pattern can continue forever. Since all of the diatonic modes can be thought of as a stacked chain of 7 alternating thirds, placed in inversion, this means that Whitewood[14] and Blackwood[10] also make for excellent "panmodal" scales, in which you can construct "modal" sounding sonorities in one key that will work in all keys.

			[[File:Whitewood14 21edo.mp3\|14-note Whitewood scale (major, sLsLsLsLsLsLsL) in 21edo tuning]]

			14-note Whitewood scale (major, sLsLsLsLsLsLsL) in 21edo tuning

	== Tunings ==		== Tunings ==

Hstraub at 19:50, 6 May 2026

2026-05-06T19:50:02Z

← Older revision		Revision as of 19:50, 6 May 2026
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	{{Infobox regtemp		{{interwiki
			\| de = Whitewood
			\| en = Whitewood
			}}{{Infobox regtemp
	\| Title = Whitewood		\| Title = Whitewood
	\| Subgroups = 2.3.5, 2.3.5.7		\| Subgroups = 2.3.5, 2.3.5.7

FloraC: + categories (see talk)

2026-05-01T05:31:19Z

+ categories (see talk)

← Older revision		Revision as of 05:31, 1 May 2026
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	== References ==		== References ==

			[[Category:Whitewood\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
			[[Category:Exotemperaments]]
	[[Category:Whitewood family]]		[[Category:Whitewood family]]
	[[Category:Mint temperaments]]		[[Category:Mint temperaments]]
			[[Category:Mirwomo temperaments]]

FloraC: /* Tunings */ mark 5-limit CTE. Phrasing

2026-04-30T10:26:31Z

Tunings: mark 5-limit CTE. Phrasing

← Older revision		Revision as of 10:26, 30 April 2026
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	== Tunings ==		== Tunings ==
	While blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning – as individually a [[5-limit\|2.3.5-]] or [[2.3.7 subgroup\|2.3.7-subgroup]] ~~temperament~~. Septimal whitewood entails a rather different tuning profile, as the vanishing of 36/35 means 5 and 7 should be tuned somewhat sharp.		While blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning – targeting individually the [[5-limit\|2.3.5-]] or [[2.3.7 subgroup\|2.3.7-subgroup]]. Septimal whitewood entails a rather different tuning profile, as the vanishing of 36/35 means 5 and 7 should be tuned somewhat sharp.

	Any multiple of [[7edo]], up until [[35edo]], contains 7edo's [[perfect fifth]], and thus supports whitewood, with all but 35edo supporting the canonical 7-limit extension by [[patent val]]. The most extreme tuning is [[14edo]], where up seconds and down thirds are equated, and every interval is either a 7edo interval or halfway between two 7edo intervals. While the 14edo tuning poorly approximates 5-limit intervals, it does approximate the [[6:7:9]] subminor and [[14:18:21\|1/(9:7:6)]] supermajor triads fairly well. A less extreme tuning is [[21edo]], tuning [[7/4]] close to just and tuning [[5/4]] to the same 400{{c}} major third as in [[12edo]], though [[6/5]] is still about 30 cents flat. The [[28edo]] tuning has a near-just 5/4, and tunes whitewood about as best as it can be tuned.		Any multiple of [[7edo]], up until [[35edo]], contains 7edo's [[perfect fifth]], and thus supports whitewood, with all but 35edo supporting the canonical 7-limit extension by [[patent val]]. The most extreme tuning is [[14edo]], where up seconds and down thirds are equated, and every interval is either a 7edo interval or halfway between two 7edo intervals. While the 14edo tuning poorly approximates 5-limit intervals, it does approximate the [[6:7:9]] subminor and [[14:18:21\|1/(9:7:6)]] supermajor triads fairly well. A less extreme tuning is [[21edo]], tuning [[7/4]] close to just and tuning [[5/4]] to the same 400{{c}} major third as in [[12edo]], though [[6/5]] is still about 30 cents flat. The [[28edo]] tuning has a near-just 5/4, and tunes whitewood about as best as it can be tuned.
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	\| 5/4		\| 5/4
	\| 386.314		\| 386.314
	\|		\| 5-limit CTE
	\|-		\|-
	\|		\|
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	\|		\|
	\| '''514.286'''		\| '''514.286'''
	\| 7cd val, '''~~Upper~~ bound of 5-odd-limit diamond monotone'''		\| 7cd val, '''upper bound of 5-odd-limit diamond monotone'''
	\|}		\|}
	<nowiki/>* Besides the octave		<nowiki/>* Besides the octave

FloraC: Move another chunk of info.. with a caveat

2026-04-30T09:28:25Z

Move another chunk of info.. with a caveat

← Older revision		Revision as of 09:28, 30 April 2026
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	== Tunings ==		== Tunings ==
			While blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning – as individually a [[5-limit\|2.3.5-]] or [[2.3.7 subgroup\|2.3.7-subgroup]] temperament. Septimal whitewood entails a rather different tuning profile, as the vanishing of 36/35 means 5 and 7 should be tuned somewhat sharp.

	Any multiple of [[7edo]], up until [[35edo]], contains 7edo's [[perfect fifth]], and thus supports whitewood, with all but 35edo supporting the canonical 7-limit extension by [[patent val]]. The most extreme tuning is [[14edo]], where up seconds and down thirds are equated, and every interval is either a 7edo interval or halfway between two 7edo intervals. While the 14edo tuning poorly approximates 5-limit intervals, it does approximate the [[6:7:9]] subminor and [[14:18:21\|1/(9:7:6)]] supermajor triads fairly well. A less extreme tuning is [[21edo]], tuning [[7/4]] close to just and tuning [[5/4]] to the same 400{{c}} major third as in [[12edo]], though [[6/5]] is still about 30 cents flat. The [[28edo]] tuning has a near-just 5/4, and tunes whitewood about as best as it can be tuned.		Any multiple of [[7edo]], up until [[35edo]], contains 7edo's [[perfect fifth]], and thus supports whitewood, with all but 35edo supporting the canonical 7-limit extension by [[patent val]]. The most extreme tuning is [[14edo]], where up seconds and down thirds are equated, and every interval is either a 7edo interval or halfway between two 7edo intervals. While the 14edo tuning poorly approximates 5-limit intervals, it does approximate the [[6:7:9]] subminor and [[14:18:21\|1/(9:7:6)]] supermajor triads fairly well. A less extreme tuning is [[21edo]], tuning [[7/4]] close to just and tuning [[5/4]] to the same 400{{c}} major third as in [[12edo]], though [[6/5]] is still about 30 cents flat. The [[28edo]] tuning has a near-just 5/4, and tunes whitewood about as best as it can be tuned.

FloraC: Move certain info here from the data page

2026-04-30T09:13:43Z

Move certain info here from the data page

← Older revision		Revision as of 09:13, 30 April 2026
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	The canonical [[extension]] to prime [[7/1\|7]] adds [[36/35]] to the commas, thus equating [[5-limit]] major and minor intervals with [[7-limit]] subminor and supermajor ones. It finds [[7/4]] at the down seventh, [[7/6]] at the down third, and [[9/7]] at the up third.		The canonical [[extension]] to prime [[7/1\|7]] adds [[36/35]] to the commas, thus equating [[5-limit]] major and minor intervals with [[7-limit]] subminor and supermajor ones. It finds [[7/4]] at the down seventh, [[7/6]] at the down third, and [[9/7]] at the up third.

			Whitewood was named by [[Mike Battaglia]] in 2010 to serve in contrast with the [[blackwood]] temperament, which tempers out 256/243, the [[Pythagorean limma]].<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_95296.html Yahoo! Tuning Group \| ''7&14 temperament - 14 out of 35'']</ref>

	For technical data, see [[Whitewood family #Whitewood]].		For technical data, see [[Whitewood family #Whitewood]].
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	\|}		\|}

	<nowiki/>*in 7-limit CWE tuning		<nowiki/> * In 7-limit CWE tuning, octave reduced

			== Scales ==
			The [[7L 7s]] 14-note [[mos]] of whitewood, like the [[5L 5s]] 10-note mos of blackwood, shares a number of interesting properties which derive from the relatively small circle of fifths common to both. From any major or minor triad in the scale, one can always move away by ~3/2 or ~4/3 to reach another triad of the same type. This contrasts with the [[5L 2s\|diatonic scale]], in which one will eventually "hit a wall" if one moves by perfect fifth for long enough; the chain of fifths will eventually "stop" and make the next fifth a diminished fifth. This means that this scale is, in a sense, "pantonal", since resolutions that work in one key will work in all other keys in the scale, at least keys that share the same chord quality.

			Another interesting property is that it becomes possible to construct "super-linked" 5-limit chords. In Whitewood[14], or Blackwood[10], if one stacks alternating major and minor thirds on top of one another, one will eventually come back to the root without ever hitting a wall, and hence the pattern can continue forever. Since all of the diatonic modes can be thought of as a stacked chain of 7 alternating thirds, placed in inversion, this means that Whitewood[14] and Blackwood[10] also make for excellent "panmodal" scales, in which you can construct "modal" sounding sonorities in one key that will work in all keys.

	== Tunings ==		== Tunings ==
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	\|}		\|}
	<nowiki/>* Besides the octave		<nowiki/>* Besides the octave

			== References ==

	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Whitewood family]]		[[Category:Whitewood family]]
	[[Category:Mint temperaments]]		[[Category:Mint temperaments]]