Whitewood family - Revision history

FloraC: Oops. Left one out

2026-06-08T11:46:15Z

Oops. Left one out

@@ Line 211: / Line 211: @@
 Badness (Sintel): 0.951
 [[Category:Temperament families]]
 [[Category:Whitewood family| ]] <!-- main article -->
 [[Category:Rank 2]]

FloraC: Jamesbond belongs here for the same reason catler belongs to the compton family

2026-06-08T11:38:21Z

Jamesbond belongs here for the same reason catler belongs to the compton family

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The '''whitewood family''' of [[temperament]]s [[tempering out|tempers out]] the apotome, [[2187/2048]]. Consequently the [[3/2|fifth]]s are always 4/7 of an [[octave]], a distinctly flat 685.714 [[cent]]s. While quite flat, this is close enough to a just fifth to serve as one, and some people are fond of it.
+The '''whitewood family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the Pythagorean apotome, [[2187/2048]]. Consequently the [[3/2|fifth]]s are always 4/7 of an [[octave]], a distinctly flat 685.714 [[cent]]s. While quite flat, this is close enough to a just fifth to serve as one, and some people are fond of it.
 == Whitewood ==
@@ Line 27: / Line 27: @@
 === Overview to extensions ===
 Temperaments discussed elsewhere include:
 * ''[[Sept]]'' → [[Very low accuracy temperaments #Sept|Very low accuracy temperaments]]
-Considered below are septimal whitewood, redwood, and greenwood.
+Considered below are septimal whitewood, redwood, greenwood, and jamesbond.
 == Septimal whitewood ==
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 Badness (Sintel): 2.23
 [[Category:Temperament families]]
 [[Category:Whitewood family| ]] <!-- main article -->
 [[Category:Rank 2]]

FloraC: - mujannab (covered in very low accuracy temps)

2026-05-29T10:55:59Z

- mujannab (covered in very low accuracy temps)

@@ Line 1: / Line 1: @@
 {{Technical data page}}
 The '''whitewood family''' of [[temperament]]s [[tempering out|tempers out]] the apotome, [[2187/2048]]. Consequently the [[3/2|fifth]]s are always 4/7 of an [[octave]], a distinctly flat 685.714 [[cent]]s. While quite flat, this is close enough to a just fifth to serve as one, and some people are fond of it.
 == Whitewood ==
@@ Line 28: / Line 25: @@
 Scales: [[7L 7s in 140edo]]
 == Septimal whitewood ==
@@ Line 109: / Line 113: @@
 Badness (Sintel): 2.59
 == Greenwood ==

FloraC: - redundant category

2026-05-01T05:32:09Z

- redundant category

← Older revision		Revision as of 05:32, 1 May 2026
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Whitewood family\| ]] <!-- main article -->		[[Category:Whitewood family\| ]] <!-- main article -->
	~~[[Category:Whitewood\| ]] <!-- key article -->~~
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: - duplicate info (all moved to whitewood's dedicated article)

2026-04-30T09:29:03Z

- duplicate info (all moved to whitewood's dedicated article)

← Older revision		Revision as of 09:29, 30 April 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''whitewood family''' of [[temperament]]s [[tempering out\|tempers out]] the apotome, [[2187/2048]]. Consequently the [[3/2\|fifth]]s are always 4/7 of an [[octave]], a distinctly flat 685.714 [[cent]]s. While quite flat, this is close enough to a just fifth to serve as one, and some people are fond of it.		The '''whitewood family''' of [[temperament]]s [[tempering out\|tempers out]] the apotome, [[2187/2048]]. Consequently the [[3/2\|fifth]]s are always 4/7 of an [[octave]], a distinctly flat 685.714 [[cent]]s. While quite flat, this is close enough to a just fifth to serve as one, and some people are fond of it.

	The 5-limit version of this temperament is called ''whitewood'', to serve in contrast with the [[blackwood]] temperament which tempers out [[256/243]], the pythagorean limma. Whereas blackwood temperament can be thought of as a closed chain of 5 fifths and a major third generator, whitewood is a closed chain of 7 fifths and a major third generator. This means that blackwood is generally supported by 5''n''-edos, and whitewood is supported by 7''n''-edos, and the [[mos]] of both scales follow a similar pattern.

	The 14-note mos of whitewood, like the 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 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.

	~~Lastly, 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.~~

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
Line 15:		Line 7:
	== Whitewood ==		== Whitewood ==
	{{Main\| Whitewood }}		{{Main\| Whitewood }}

			Whitewood is the natural counterpart of [[blackwood]]: whereas blackwood can be thought of as a closed chain of five fifths and a [[5/4]] major third generator, whitewood is a closed chain of seven fifths and a 5/4 major third generator. This means that blackwood is generally supported by 5''n''-edos, and whitewood is supported by 7''n''-edos, and the [[mos]] of both scales follow a similar pattern.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

FloraC: + links

2026-04-30T08:40:15Z

+ links

← Older revision		Revision as of 08:40, 30 April 2026
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	== Whitewood ==		== Whitewood ==
			{{Main\| Whitewood }}

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

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	{{Mapping\|legend=1\| 7 11 0 \| 0 0 1 }}		{{Mapping\|legend=1\| 7 11 0 \| 0 0 1 }}

	: mapping generators: ~9/8, ~5		: mapping generators: ~9/8, ~5

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	== Septimal whitewood ==		== Septimal whitewood ==
			{{Main\| Whitewood }}

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Overthink: note jamesbond discussed elsewhere

2026-01-10T20:01:57Z

note jamesbond discussed elsewhere

← Older revision		Revision as of 20:01, 10 January 2026
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	Lastly, 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.		Lastly, 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.

			Temperaments discussed elsewhere include:
			* ''[[Jamesbond]]'' → [[7th-octave temperaments#Jamesbond\|7th-octave temperaments]]

	== Whitewood ==		== Whitewood ==

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

2025-11-27T12:31:32Z

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:Whitewood family\| ]] <!-- main article -->		[[Category:Whitewood family\| ]] <!-- main article -->
	[[Category:Whitewood\| ]] <!-- key article -->		[[Category:Whitewood\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

BudjarnLambeth: /* Whitewood */ add scales line

2025-10-05T08:47:37Z

Whitewood: add scales line

← Older revision		Revision as of 08:47, 5 October 2025
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	[[Badness]] (Sintel): 3.63		[[Badness]] (Sintel): 3.63

			Scales: [[7L 7s in 140edo]]

	== Septimal whitewood ==		== Septimal whitewood ==

FloraC: /* Redwood */ corrections

2025-09-28T15:50:18Z

Redwood: corrections

← Older revision		Revision as of 15:50, 28 September 2025
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~9/8 = ~~171~~.~~5524~~{{c}}, ~5/4 = ~~392~~.~~9834~~{{c}} (~36/35 = 49.~~8786~~{{c}})		* [[WE]]: ~9/8 = 172.0521{{c}}, ~5/4 = 379.5277{{c}} (~36/35 = 35.4234{{c}})
	: [[error map]]: {{val\| +0.~~867~~ -14.~~879~~ +8.~~403~~ +12.~~343~~ }}		: [[error map]]: {{val\| +4.365 -9.382 +1.944 +1.370 }}
	* [[CWE]]: ~9/8 = 171.4286{{c}}, ~5/4 = ~~392~~.~~7412~~{{c}} (~36/35 = 49.~~8841~~{{c}})		* [[CWE]]: ~9/8 = 171.4286{{c}}, ~5/4 = 377.7903{{c}} (~36/35 = 34.9331{{c}})
	: error map: {{val\| 0.000 -16.241 +6.~~428 +9~~.~~861~~ }}		: error map: {{val\| 0.000 -16.241 -8.523 -10.121 }}

	{{Optimal ET sequence\|legend=1\| 7, 28d, 35 }}		{{Optimal ET sequence\|legend=1\| 7, 28d, 35 }}