Blackwood - Revision history

Unque at 15:51, 18 July 2026

2026-07-18T15:51:28Z

← Older revision		Revision as of 15:51, 18 July 2026
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	[[File:Vector Blackwood.mp3\|thumb\|An example of Blackwood temperament in a song by Vector]]		[[File:Vector Blackwood.mp3\|thumb\|An example of Blackwood temperament in a song by Vector]]
	'''Blackwood''' is a regular temperament primarily supported by 15edo but in technicality by any EDO with 5edo's fifth (such as 25edo or 10edo) which takes 5edo as its 2.3.7, and treats 5 as an independent generator. Its 10-note scale (LsLsLsLsLs, '''pentawood''') is unique among scales of its complexity for making a perfect fifth available on every note of the scale, at the cost of a ~18c detuned fifth. This means that every step of the scale has either a major or a minor triad built on it. Blackwood has [[Zarlino]] as a subset, specifically tunings wherein the difference between the large and medium steps is the same size as the small step. This overlaps with [[Porcupine]] tunings of ~~zarlino~~ only at [[15edo]].		'''Blackwood''' is a regular temperament primarily supported by 15edo but in technicality by any EDO with 5edo's fifth (such as 25edo or 10edo) which takes 5edo as its 2.3.7, and treats 5 as an independent generator. Its 10-note scale (LsLsLsLsLs, '''pentawood''') is unique among scales of its complexity for making a perfect fifth available on every note of the scale, at the cost of a ~18c detuned fifth. This means that every step of the scale has either a major or a minor triad built on it. Blackwood has [[Diatonic#Greek diatonic scales\|Zarlino]] as a subset, specifically tunings wherein the difference between the large and medium steps is the same size as the small step. This overlaps with [[Porcupine]] tunings of Zarlino only at [[15edo]].

	There is also a 15-note, 20-note, etc. Blackwood scale, but these are much less common than the 10-note version which will be the main version discussed here.		There is also a 15-note, 20-note, etc. Blackwood scale, but these are much less common than the 10-note version which will be the main version discussed here.
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	Blackwood is named after Easley Blackwood Jr., a microtonal composer and theorist who extensively used what we now know as the Blackwood[10] scale.		Blackwood is named after Easley Blackwood Jr., a microtonal composer and theorist who extensively used what we now know as the Blackwood[10] scale.

	The 7-limit version of Blackwood was called "Blacksmith" originally; this name is ~~almost~~ obsolete.		The 7-limit version of Blackwood was called "Blacksmith" originally; this name is largely obsolete.

	== Generator chain ==		== Generator chain ==
	''The provided tuning is DR 4:5:6.''		''The provided tuning is DR 4:5:6.''

	Cells highlighted in gray are intervals found in 5edo, which Blackwood expands. Yellow intervals are found in major blackwood[10], and green intervals in minor blackwood[10]. Blackwood[15] can thus be considered the "chromatic scale" of blackwood, and in ~~any reasonable tuning closely approximates 15edo, which is the best edo tuning~~.		Cells highlighted in gray are intervals found in 5edo, which Blackwood expands. Yellow intervals are found in major blackwood[10], and green intervals in minor blackwood[10]. Blackwood[15] can thus be considered the "chromatic scale" of blackwood, and generally approaches equal temperament in most useful ranges.
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
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	== Blackwood tonality ==		== Blackwood tonality ==
	Like in diatonic, the fourth and fifth may be considered stable tones; another consideration is consider the unilatus and antilatus, and thus all perfect intervals, also stable. However, note that the unilatus creates a tendency tone towards the minor third, much as the perfect fourth creates a tendency tone towards the major third. So they may be considered dissonant in that context. While the tritone of blackwood is not a perfect antitonic, the sharp tritone regardless leads up to the fifth, and the flat tritone down to the fourth. The flat tritone also resolves inward to a major third.{{Navbox regtemp}}
			=== Tendency tones ===
			Like in diatonic, the fourth and fifth may be considered stable tones; another consideration is consider the unilatus and antilatus, and thus all perfect intervals, also stable. However, note that the unilatus creates a tendency tone towards the minor third, much as the perfect fourth creates a tendency tone towards the major third. So they may be considered dissonant in that context. While the tritone of blackwood is not a perfect antitonic, the sharp tritone regardless leads up to the fifth, and the flat tritone down to the fourth. The flat tritone also resolves inward to a major third.

			=== Chord functions ===
			In Blackwood[10], chords can be built by taking every third step of the scale; thus, the tonic chord contains steps 0, 3, and 6 (the root, third, and fifth of 10-form notation). Because the relative fifth interval over every degree is necessarily perfect, these chords come exclusively in major and minor forms.

			The functional paradigm for the major tonality can be decompiled as tonic, mediant, subdominant, predominant, dominant, and tonic; note that the subdominant and predominant are considered different functions. The mediant function is almost exclusively built on the major third degree (step 3 of the scale), and the subdominant on the perfect fourth (step 5). The predominant, however, can be variously built from the perfect latus or the major tritone degrees (both chords containing the major tritone tendency tone), and the dominant built on either the perfect fifth or major seventh (both chords containing the major seventh tendency tone). Thus the basal chord paradigm is thus I - iv - V - {III, vi} - {VII, x} - I, using 1-indexed roman numerals.

			The primary difference between the major and minor mode is that the minor intervals lead downward into the perfect intervals below, whereas their major forms lead upward to the perfect intervals above. As such, the minor mode paradigm can be seen as an inversion of the major paradigm, with the mediant function being taken by the chord built on the minor tritone, and the dominant can be built on the minor second, both functions making use of the downwards lead. The minor paradigm can be regularized i - bVI - v - {iii, bVIII} - bII - i.

			{{Navbox regtemp}}
	{{Cat\|temperaments}}		{{Cat\|temperaments}}

Vector at 07:01, 1 May 2026

2026-05-01T07:01:49Z

← Older revision		Revision as of 07:01, 1 May 2026
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	\|}		\|}

	{{Navbox regtemp}}		== Blackwood tonality ==
			Like in diatonic, the fourth and fifth may be considered stable tones; another consideration is consider the unilatus and antilatus, and thus all perfect intervals, also stable. However, note that the unilatus creates a tendency tone towards the minor third, much as the perfect fourth creates a tendency tone towards the major third. So they may be considered dissonant in that context. While the tritone of blackwood is not a perfect antitonic, the sharp tritone regardless leads up to the fifth, and the flat tritone down to the fourth. The flat tritone also resolves inward to a major third.{{Navbox regtemp}}
	{{Cat\|temperaments}}		{{Cat\|temperaments}}

Vector at 23:17, 20 April 2026

2026-04-20T23:17:16Z

← Older revision		Revision as of 23:17, 20 April 2026
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	The 7-limit version of Blackwood was called "Blacksmith" originally; this name is almost obsolete.		The 7-limit version of Blackwood was called "Blacksmith" originally; this name is almost obsolete.

			== Generator chain ==
			''The provided tuning is DR 4:5:6.''

			Cells highlighted in gray are intervals found in 5edo, which Blackwood expands. Yellow intervals are found in major blackwood[10], and green intervals in minor blackwood[10]. Blackwood[15] can thus be considered the "chromatic scale" of blackwood, and in any reasonable tuning closely approximates 15edo, which is the best edo tuning.
			{\| class="wikitable"
			\|+
			!
			! colspan="2" rowspan="1" \|Period 0
			! colspan="2" rowspan="1" \|Period 1
			! colspan="2" rowspan="1" \|Period 2
			! colspan="2" rowspan="1" \|Period 3
			! colspan="2" rowspan="1" \|Period 4
			\|-
			!Generators
			!Cents
			!JI
			!Cents
			!JI
			!Cents
			!JI
			!Cents
			!JI
			!Cents
			!JI
			\|-
			!-2
			\|'''1034.4'''
			\|50/27
			\|'''74.4'''
			\|25/24
			\|'''314.4'''
			\|25/21
			\|'''554.4'''
			\|25/18
			\|'''794.4'''
			\|100/63
			\|-
			!-1
			\| class="prime11" \|'''1117.2'''
			\| class="prime11" \|15/8, 40/21
			\| class="prime11" \|'''157.2'''
			\| class="prime11" \|10/9
			\| class="prime11" \|'''397.2'''
			\| class="prime11" \|5/4
			\| class="prime11" \|'''637.2'''
			\| class="prime11" \|10/7
			\| class="prime11" \|'''877.2'''
			\| class="prime11" \|5/3
			\|-
			!0
			\| class="prime2" \|'''0'''
			\| class="prime2" \|1/1
			\| class="prime2" \|'''240'''
			\| class="prime2" \|8/7
			\| class="prime2" \|'''480'''
			\| class="prime2" \|4/3
			\| class="prime2" \|'''720'''
			\| class="prime2" \|3/2
			\| class="prime2" \|'''960'''
			\| class="prime2" \|7/4
			\|-
			!1
			\| class="prime5" \|'''82.8'''
			\| class="prime5" \|21/20, 16/15
			\| class="prime5" \|'''322.8'''
			\| class="prime5" \|6/5
			\| class="prime5" \|'''562.8'''
			\| class="prime5" \|7/5
			\| class="prime5" \|'''802.8'''
			\| class="prime5" \|8/5
			\| class="prime5" \|'''1042.8'''
			\| class="prime5" \|10/9
			\|-
			!2
			\|'''165.6'''
			\|27/25
			\|'''405.6'''
			\|63/50
			\|'''645.6'''
			\|36/25
			\|'''885.6'''
			\|42/25
			\|'''1125.6'''
			\|48/25
			\|}

	== Blackwood[10] modes ==		== Blackwood[10] modes ==

Inthar at 18:18, 14 April 2026

2026-04-14T18:18:33Z

← Older revision		Revision as of 18:18, 14 April 2026
Line 7:		Line 7:
	Blackwood is named after Easley Blackwood Jr., a microtonal composer and theorist who extensively used what we now know as the Blackwood[10] scale.		Blackwood is named after Easley Blackwood Jr., a microtonal composer and theorist who extensively used what we now know as the Blackwood[10] scale.

	The 7-limit version of Blackwood was called "Blacksmith" originally; this name is ~~now rare~~.		The 7-limit version of Blackwood was called "Blacksmith" originally; this name is almost obsolete.

	== Blackwood[10] modes ==		== Blackwood[10] modes ==

Inthar at 14:43, 14 April 2026

2026-04-14T14:43:40Z

← Older revision		Revision as of 14:43, 14 April 2026
Line 53:		Line 53:
	\| 1200c		\| 1200c
	\|}		\|}

			{{Navbox regtemp}}
			{{Cat\|temperaments}}

Inthar: /* Name */

2026-04-14T11:27:32Z

Name

← Older revision		Revision as of 11:27, 14 April 2026
Line 7:		Line 7:
	Blackwood is named after Easley Blackwood Jr., a microtonal composer and theorist who extensively used what we now know as the Blackwood[10] scale.		Blackwood is named after Easley Blackwood Jr., a microtonal composer and theorist who extensively used what we now know as the Blackwood[10] scale.

	The 7-limit version of Blackwood was called "Blacksmith" originally; this name is ~~no longer used~~.		The 7-limit version of Blackwood was called "Blacksmith" originally; this name is now rare.

	== Blackwood[10] modes ==		== Blackwood[10] modes ==

Inthar: /* Bame */

2026-04-14T11:26:15Z

Bame

← Older revision		Revision as of 11:26, 14 April 2026
Line 4:		Line 4:
	There is also a 15-note, 20-note, etc. Blackwood scale, but these are much less common than the 10-note version which will be the main version discussed here.		There is also a 15-note, 20-note, etc. Blackwood scale, but these are much less common than the 10-note version which will be the main version discussed here.

	== ~~Bame~~ ==		== Name ==
	Blackwood is named after Easley Blackwood Jr., a microtonal composer and theorist who extensively used what we now know as the Blackwood[10] scale.		Blackwood is named after Easley Blackwood Jr., a microtonal composer and theorist who extensively used what we now know as the Blackwood[10] scale.

Vector: (don't remove information)

2026-04-14T05:14:53Z

(don't remove information)

← Older revision		Revision as of 05:14, 14 April 2026
Line 3:		Line 3:

	There is also a 15-note, 20-note, etc. Blackwood scale, but these are much less common than the 10-note version which will be the main version discussed here.		There is also a 15-note, 20-note, etc. Blackwood scale, but these are much less common than the 10-note version which will be the main version discussed here.

			== Bame ==
			Blackwood is named after Easley Blackwood Jr., a microtonal composer and theorist who extensively used what we now know as the Blackwood[10] scale.

			The 7-limit version of Blackwood was called "Blacksmith" originally; this name is no longer used.

	== Blackwood[10] modes ==		== Blackwood[10] modes ==

Vector: nobody uses that name. nobody used it while it was official except like, one guy. it was deprecated. there's no reason to consider blackwood as a 5-limit-only temperament

2026-04-14T05:09:13Z

nobody uses that name. nobody used it while it was official except like, one guy. it was deprecated. there's no reason to consider blackwood as a 5-limit-only temperament

← Older revision		Revision as of 05:09, 14 April 2026
Line 1:		Line 1:
	[[File:Vector Blackwood.mp3\|thumb\|An example of Blackwood temperament in a song by Vector]]		[[File:Vector Blackwood.mp3\|thumb\|An example of Blackwood temperament in a song by Vector]]
	'''Blackwood''' ~~(technically '''Blacksmith''' in the 7-limit)~~ is a regular temperament primarily supported by 15edo but in technicality by any EDO with 5edo's fifth (such as 25edo or 10edo) which takes 5edo as its 2.3.7, and treats 5 as an independent generator. Its 10-note scale (LsLsLsLsLs, '''pentawood''') is unique among scales of its complexity for making a perfect fifth available on every note of the scale, at the cost of a ~18c detuned fifth. This means that every step of the scale has either a major or a minor triad built on it. Blackwood has [[Zarlino]] as a subset, specifically tunings wherein the difference between the large and medium steps is the same size as the small step. This overlaps with [[Porcupine]] tunings of zarlino only at [[15edo]].		'''Blackwood''' is a regular temperament primarily supported by 15edo but in technicality by any EDO with 5edo's fifth (such as 25edo or 10edo) which takes 5edo as its 2.3.7, and treats 5 as an independent generator. Its 10-note scale (LsLsLsLsLs, '''pentawood''') is unique among scales of its complexity for making a perfect fifth available on every note of the scale, at the cost of a ~18c detuned fifth. This means that every step of the scale has either a major or a minor triad built on it. Blackwood has [[Zarlino]] as a subset, specifically tunings wherein the difference between the large and medium steps is the same size as the small step. This overlaps with [[Porcupine]] tunings of zarlino only at [[15edo]].

	There is also a 15-note, 20-note, etc. Blackwood scale, but these are much less common than the 10-note version which will be the main version discussed here.		There is also a 15-note, 20-note, etc. Blackwood scale, but these are much less common than the 10-note version which will be the main version discussed here.

Inthar at 00:48, 14 April 2026

2026-04-14T00:48:29Z

← Older revision		Revision as of 00:48, 14 April 2026
Line 1:		Line 1:
	[[File:Vector Blackwood.mp3\|thumb\|An example of Blackwood temperament in a song by Vector]]		[[File:Vector Blackwood.mp3\|thumb\|An example of Blackwood temperament in a song by Vector]]
	'''Blackwood''' (technically '''Blacksmith''') is a regular temperament primarily supported by 15edo but in technicality by any EDO with 5edo's fifth (such as 25edo or 10edo) which takes 5edo as its 2.3.7, and treats 5 as an independent generator. Its 10-note scale (LsLsLsLsLs, '''pentawood''') is unique among scales of its complexity for making a perfect fifth available on every note of the scale, at the cost of a ~18c detuned fifth. This means that every step of the scale has either a major or a minor triad built on it. Blackwood has [[Zarlino]] as a subset, specifically tunings wherein the difference between the large and medium steps is the same size as the small step. This overlaps with [[Porcupine]] tunings of zarlino only at [[15edo]].		'''Blackwood''' (technically '''Blacksmith''' in the 7-limit) is a regular temperament primarily supported by 15edo but in technicality by any EDO with 5edo's fifth (such as 25edo or 10edo) which takes 5edo as its 2.3.7, and treats 5 as an independent generator. Its 10-note scale (LsLsLsLsLs, '''pentawood''') is unique among scales of its complexity for making a perfect fifth available on every note of the scale, at the cost of a ~18c detuned fifth. This means that every step of the scale has either a major or a minor triad built on it. Blackwood has [[Zarlino]] as a subset, specifically tunings wherein the difference between the large and medium steps is the same size as the small step. This overlaps with [[Porcupine]] tunings of zarlino only at [[15edo]].

	There is also a 15-note, 20-note, etc. Blackwood scale, but these are much less common than the 10-note version which will be the main version discussed here.		There is also a 15-note, 20-note, etc. Blackwood scale, but these are much less common than the 10-note version which will be the main version discussed here.