David-Jubal - Revision history

BudjarnLambeth at 13:14, 16 September 2026

2026-09-16T13:14:35Z

← Older revision		Revision as of 13:14, 16 September 2026
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	* ''[https://youtu.be/Na-tLZL82pw Elias]'' (2026)		* ''[https://youtu.be/Na-tLZL82pw Elias]'' (2026)

	[[Category:10-tone scales]]		[[Category:9-tone scales]]
	[[Category:7-limit]]		[[Category:7-limit]]
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
	[[Category:Pages with Scala files]]		[[Category:Pages with Scala files]]

BudjarnLambeth at 13:13, 16 September 2026

2026-09-16T13:13:05Z

BudjarnLambeth at 13:10, 16 September 2026

2026-09-16T13:10:20Z

← Older revision		Revision as of 13:10, 16 September 2026
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	== Theory ==		== Theory ==
	=== Interval strength ===		=== Interval strength ===
	'''Interval strength''' is a term invented by O'Sullivan to describe a measure of the strength of a just interval. It equals '''2/n + 2/d (where n/d is the simplified interval [[ratio]])'''.		'''Interval strength''' is a term invented by O'Sullivan to describe a measure of the strength of a just interval. It equals ''2/n + 2/d (where n/d is the simplified interval [[ratio]])''.

	Any just interval n/d is acceptable in a melodic context (notes or chords played sequentially, not simultaneously) if its interval strength is greater than 0.25. An interval with a strength value between 0.25 and 0.4999 is a '''neutral interval'''. An interval with a strength value between 0.5 and 0.9999 is a '''strong interval'''. An interval with a strength value greater than 1.0 is a '''very strong interval'''~~. Over a one octave range the very strong intervals are [[4/3]], [[3/2]] and [[5/3]]; these have a value greater than 1.0 using O'Sullivan's formula~~.		; Melodic contexts
			Any just interval n/d is acceptable in a melodic context (notes or chords played sequentially, not simultaneously) if its interval strength is greater than 0.25:
			* An interval with a strength value between 0.25 and 0.4999 is a '''neutral interval'''.
			* An interval with a strength value between 0.5 and 0.9999 is a '''strong interval'''.
			* An interval with a strength value greater than 1.0 is a '''very strong interval'''.

			Over a one octave range the very strong intervals are [[4/3]], [[3/2]] and [[5/3]]; these have a value greater than 1.0 using O'Sullivan's formula.

			; Harmonic contexts
	As regards chord construction, every interval in a chord must have a strength value greater than 0.5.		As regards chord construction, every interval in a chord must have a strength value greater than 0.5.

	O'Sullivan allows a tempering of just intervals by up to plus or minus 6.7758 cents ([[256/255]]).		; Tempering
			O'Sullivan allows a [[temperament\|tempering]] of just intervals by up to plus or minus 6.7758 [[cents]] ([[256/255]]).

	=== David's chord ===		=== David's chord ===

BudjarnLambeth: /* David-John tuning */

2026-09-16T13:00:56Z

David-John tuning

← Older revision		Revision as of 13:00, 16 September 2026
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	=== David-John tuning ===		=== David-John tuning ===
	'''David-John tuning''' is similar to David-Jubal tuning, but '''John's scale''' is used instead of Jubal's scale. John's scale is the 8 to 20 [[harmonic series]] segment, with 17 and 19, and numbers higher than 20, not allowed, as some illegal intervals would occur (interval strength less than 0.25). It looks like this: 8-9-10-11-12-13-14-15-16-18-20.		'''David-John tuning''' is similar to David-Jubal tuning, but '''John's scale''' is used instead of Jubal's scale.

			John's scale resembles the 8 to 20 [[harmonic series]] segment, but with 17 and 19, and numbers higher than 20, not allowed, as some illegal intervals would occur (interval strength less than 0.25). It looks like this: 8-9-10-11-12-13-14-15-16-18-20.

	== Music ==		== Music ==

BudjarnLambeth: corrections requested by O’Sullivan

2026-09-16T12:59:23Z

corrections requested by O’Sullivan

← Older revision		Revision as of 12:59, 16 September 2026
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	{{Idiosyncratic terms\|The terms ''David-Jubal tuning, David's chord, Jubal's scale, ~~harmonic~~ strength, David-John tuning'' and ''~~David-~~John scale'' were coined by John O'Sullivan in the mid 2020s and are not so far widely known to other microtonalists.}}		{{Idiosyncratic terms\|The terms ''David-Jubal tuning, David's chord, Jubal's scale, interval strength, illegal/neutral/strong/very strong interval, David-John tuning'' and ''John's scale'' were coined by John O'Sullivan in the mid 2020s and are not so far widely known to other microtonalists.}}

	'''David-Jubal tuning''' is a musical framework invented by [[John O'Sullivan]] in ~~the 2020s~~. It is a type of [[just intonation]]. It consists of the use of '''Jubal's scale''' as its pitch gamut, and '''David's chord''' as its primary sonority. (''For contrast, compare to most 21st century Western music which uses the [[12edo]] chromatic scale as its pitch gamut and the (tempered) major and minor triads as its primary sonorities'').		'''David-Jubal tuning''' is a musical framework invented by [[John O'Sullivan]] in August, 2026. It is a type of [[just intonation]]. It consists of the use of '''Jubal's scale''' as its pitch gamut, and '''David's chord''' as its primary sonority. (''For contrast, compare to most 21st century Western music which uses the [[12edo]] chromatic scale as its pitch gamut and the (tempered) major and minor triads as its primary sonorities'').

			David-Jubal tuning was designed for [[guitar]]s only, not keyboards. The guitar is tuned to an "open" just chord (David's chord), and fretted with frets corresponding to the notes of Jubal's scale (9 frets). The idea is to play David's chord on any or all of the notes of Jubal's scale, by barring with the index finger just beside the appropriate fret.

	O'Sullivan describes David-Jubal tuning, the reasoning behind it, and practical instructions for fretting a guitar or similar instrument, on his website:		O'Sullivan describes David-Jubal tuning, the reasoning behind it, and practical instructions for fretting a guitar or similar instrument, on his website:
Line 7:		Line 9:

	== Theory ==		== Theory ==
	=== ~~Harmonic~~ strength ===		=== Interval strength ===
	'''~~Harmonic~~ strength''' is a term invented by O'Sullivan to describe a measure of the strength of a just ~~sonority~~. It equals '''2/n + 2/d (where n/d is the simplified interval [[ratio]])'''.		'''Interval strength''' is a term invented by O'Sullivan to describe a measure of the strength of a just interval. It equals '''2/n + 2/d (where n/d is the simplified interval [[ratio]])'''.

	~~O'Sullivan considers~~ a ~~good tuning to be~~ a ~~tuning with as many intervals as possible~~ with a ~~harmonic~~ strength of 0.5 ~~or higher,~~ and ~~as few intervals as possible~~ with a ~~harmonic~~ strength of 0.~~25 or higher~~.		Any just interval n/d is acceptable in a melodic context (notes or chords played sequentially, not simultaneously) if its interval strength is greater than 0.25. An interval with a strength value between 0.25 and 0.4999 is a '''neutral interval'''. An interval with a strength value between 0.5 and 0.9999 is a '''strong interval'''. An interval with a strength value greater than 1.0 is a '''very strong interval'''. Over a one octave range the very strong intervals are [[4/3]], [[3/2]] and [[5/3]]; these have a value greater than 1.0 using O'Sullivan's formula.

	~~The goal~~ of ~~David-Jubal tuning is~~ to ~~be as 'good' as possible by those criteria~~.		As regards chord construction, every interval in a chord must have a strength value greater than 0.5.

			O'Sullivan allows a tempering of just intervals by up to plus or minus 6.7758 cents ([[256/255]]).

	=== David's chord ===		=== David's chord ===
	~~'''~~David's chord~~'''~~ is ~~the name O'Sullivan coined for the [[just intonation]] chord~~ [[1:2:3:4:5:7]]~~. This~~ chord ~~is derived by starting with the first 9 tones of the~~ [[~~harmonic series]] and removing all instances of the intervals O'Sullivan considers to be [[dissonance]]s~~: ~~[[6/~~5~~]], [[~~7/6]]~~, [[8/7]] and [[9/8]].~~		David's chord is a justly tuned [[1:2:3:4:5:7]] chord, or [[2:3:4:5:7]] on guitars (the 1 isn't feasible on a guitar, it's too low). How O'Sullivan arrived at David's chord is described on his website.

	~~David~~'~~s chord consists of four [[pitch class]]es: E~~, ~~B, G# and D when tuned to E.~~

	~~O'Sullivan discourages the use of minor triads in music build upon David~~'s ~~chord, considering them "destructive" to the harmonic affect of the chord. When retuning 12edo music to David-Jubal tuning, O'Sullivan recommends replacing minor triads with power chords ([[2:3:4]]~~).

	O'Sullivan ~~considers [[2:3:4:5:7]] to be an acceptable substitute for~~ David's chord~~, for practical use~~ on ~~instruments, given the difficulty of including an entire additional octave~~.

	=== Jubal's scale ===		=== Jubal's scale ===
	~~'''~~Jubal's scale~~'''~~ is the [[just intonation]] scale ~~'''8~~:9~~:10:10.666...:12:13.333...:14:~~15~~:16:18:20'''~~.		Jubal's scale is the [[just intonation]] scale: 1/1, 9/8, 7/6, 5/4, 4/3, 3/2, 5/3, 7/4, 15/8, 2/1.

	~~Its intervals are: 1/1~~, 9/8~~, 7/6, 5/4,~~ 4/3~~, 3~~/2, 5/3, 7/~~4, 15/8, 2/1~~.		O'Sullivan derived it from the harmonic series segment 8-9-10-11-12-13-14-15-16, but replaced [[11/8]] with [[4/3]] and replaced [[13/8]] with [[5/3]], and [[7/6]] was added as well. All the denominators in Jubal's scale are 3-[[prime limit]].

	O'Sullivan ~~replaced harmonics 11 and 13~~ in ~~the scale because the intervals between them and the other scale degrees do not have high 'harmonic strength'~~.		O'Sullivan has published a document describing rules for composition in David-Jubal tuning:
			* [https://www.johnsmusic7.com/david-jubal-rules.txt David-Jubal composition rules]

	==== Scala file ====		==== Scala file ====
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	! jubal.scl		! jubal.scl
	!		!
	Jubal's scale, John O'Sullivan~~, key of E~~		Jubal's scale, John O'Sullivan
	10		9
	!		!
	9/8		9/8
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	2/1		2/1
	</pre>		</pre>

			In practice, the root note (4) needs to be tuned a bit lower than usual, so that the tension in some of the strings is not too high.

	=== David-John tuning ===		=== David-John tuning ===
	'''David-John tuning''' is ~~an analogous concept~~ to David-Jubal tuning but ~~using the~~ '''~~David-~~John scale ~~(8:9:10:11:12:13:14:15:16:18:20)~~''' instead of Jubal's scale.		'''David-John tuning''' is similar to David-Jubal tuning, but '''John's scale''' is used instead of Jubal's scale. John's scale is the 8 to 20 [[harmonic series]] segment, with 17 and 19, and numbers higher than 20, not allowed, as some illegal intervals would occur (interval strength less than 0.25). It looks like this: 8-9-10-11-12-13-14-15-16-18-20.

	~~=== Relationship to other scales and concepts ===~~
	~~Within the framework of [[otonal]] and [[utonal]] analysis, David-Jubal tuning is a strongly otonal tuning, which deliberately avoids utonality.~~

	~~The intervals O'Sullivan removed from David's chord are all the [[superparticular]] intervals smaller than 5/4.~~

	~~Jubal's scale bears a slight resemblance to [[Paul Erlich]]'s 'pentachordal decatonic scale' (the [[pajara]][10] scale of [[22edo]]).~~

	~~Jubal~~'s scale is ~~a subset of [[24afdo]] (~~the ~~24th~~ [[~~overtone scale\|mode of the~~ harmonic series]]).

	~~The David-John scale is harmonic series~~ segment ~~8::~~20, ~~and it is a subset of [[8afdo]]~~ (~~the 8th mode of the harmonic series~~). ~~In fact it contains every pitch class from 8afdo at least once and sometimes twice. This makes the David~~-~~John scale an ''over~~-~~2 scale'' within [[primodality]] theory.~~

	~~Jubal's scale is a [[7~~-~~limit]] just intonation scale and the David~~-~~John scale is a [[~~13-~~limit]] just intonation scale~~.

	== Music ==		== Music ==

BudjarnLambeth at 10:42, 15 September 2026

2026-09-15T10:42:28Z

← Older revision		Revision as of 10:42, 15 September 2026
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	{{Idiosyncratic terms\|The terms ''David-Jubal tuning, David's chord, Jubal's scale'' and ''~~harmonic strength~~'' were coined by John O'Sullivan in the mid 2020s and are not so far widely known to other microtonalists.}}		{{Idiosyncratic terms\|The terms ''David-Jubal tuning, David's chord, Jubal's scale, harmonic strength, David-John tuning'' and ''David-John scale'' were coined by John O'Sullivan in the mid 2020s and are not so far widely known to other microtonalists.}}

	'''David-Jubal tuning''' is a musical framework invented by [[John O'Sullivan]] in the 2020s. It is a type of [[just intonation]]. It consists of the use of '''Jubal's scale''' as its pitch gamut, and '''David's chord''' as its primary sonority. (''For contrast, compare to most 21st century Western music which uses the [[12edo]] chromatic scale as its pitch gamut and the (tempered) major and minor triads as its primary sonorities'').		'''David-Jubal tuning''' is a musical framework invented by [[John O'Sullivan]] in the 2020s. It is a type of [[just intonation]]. It consists of the use of '''Jubal's scale''' as its pitch gamut, and '''David's chord''' as its primary sonority. (''For contrast, compare to most 21st century Western music which uses the [[12edo]] chromatic scale as its pitch gamut and the (tempered) major and minor triads as its primary sonorities'').
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	=== David-John tuning ===		=== David-John tuning ===
	'''David-John tuning''' is an analogous concept to David-Jubal tuning but using the ~~scale~~ '''8:9:10:11:12:13:14:15:16:18:20''' instead of Jubal's scale.		'''David-John tuning''' is an analogous concept to David-Jubal tuning but using the '''David-John scale (8:9:10:11:12:13:14:15:16:18:20)''' instead of Jubal's scale.

	=== Relationship to other scales and concepts ===		=== Relationship to other scales and concepts ===
Line 61:		Line 61:

	The David-John scale is harmonic series segment 8::20, and it is a subset of [[8afdo]] (the 8th mode of the harmonic series). In fact it contains every pitch class from 8afdo at least once and sometimes twice. This makes the David-John scale an ''over-2 scale'' within [[primodality]] theory.		The David-John scale is harmonic series segment 8::20, and it is a subset of [[8afdo]] (the 8th mode of the harmonic series). In fact it contains every pitch class from 8afdo at least once and sometimes twice. This makes the David-John scale an ''over-2 scale'' within [[primodality]] theory.

			Jubal's scale is a [[7-limit]] just intonation scale and the David-John scale is a [[13-limit]] just intonation scale.

	== Music ==		== Music ==
	=== David-Jubal tuning ===		=== David-Jubal tuning ===
	; by [[John O'Sullivan]]		; by [[John O'Sullivan]]
	On his YouTube channel "@johnsmusic7", O'Sullivan has compiled the following playlist of ~~music using~~ David-Jubal tuning:		On his YouTube channel "@johnsmusic7", O'Sullivan has compiled the following playlist of 14 musical examples that use David-Jubal tuning:
	* https://www.youtube.com/playlist?list=PLQkrE1MMrb9g		* https://www.youtube.com/playlist?list=PLQkrE1MMrb9g

	=== David-John tuning ===		=== David-John tuning ===
	; by [[John O'Sullivan]]		; by [[John O'Sullivan]]
	* https://youtu.be/ScI8TBk7y5E		* ''[https://youtu.be/ScI8TBk7y5E Arrival]'' (2026)
	* https://youtu.be/Na-tLZL82pw		* ''[https://youtu.be/Na-tLZL82pw Elias]'' (2026)

	[[Category:10-tone scales]]		[[Category:10-tone scales]]

BudjarnLambeth at 10:38, 15 September 2026

2026-09-15T10:38:24Z

← Older revision		Revision as of 10:38, 15 September 2026
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	2/1		2/1
	</pre>		</pre>

			=== David-John tuning ===
			'''David-John tuning''' is an analogous concept to David-Jubal tuning but using the scale '''8:9:10:11:12:13:14:15:16:18:20''' instead of Jubal's scale.

	=== Relationship to other scales and concepts ===		=== Relationship to other scales and concepts ===

	Within the framework of [[otonal]] and [[utonal]] analysis, David-Jubal tuning is a strongly otonal tuning, which deliberately avoids utonality.		Within the framework of [[otonal]] and [[utonal]] analysis, David-Jubal tuning is a strongly otonal tuning, which deliberately avoids utonality.

Line 57:		Line 59:

	Jubal's scale is a subset of [[24afdo]] (the 24th [[overtone scale\|mode of the harmonic series]]).		Jubal's scale is a subset of [[24afdo]] (the 24th [[overtone scale\|mode of the harmonic series]]).

			The David-John scale is harmonic series segment 8::20, and it is a subset of [[8afdo]] (the 8th mode of the harmonic series). In fact it contains every pitch class from 8afdo at least once and sometimes twice. This makes the David-John scale an ''over-2 scale'' within [[primodality]] theory.

	== Music ==		== Music ==
			=== David-Jubal tuning ===
			; by [[John O'Sullivan]]
	On his YouTube channel "@johnsmusic7", O'Sullivan has compiled the following playlist of music using David-Jubal tuning:		On his YouTube channel "@johnsmusic7", O'Sullivan has compiled the following playlist of music using David-Jubal tuning:
	* https://www.youtube.com/playlist?list=PLQkrE1MMrb9g		* https://www.youtube.com/playlist?list=PLQkrE1MMrb9g

			=== David-John tuning ===
			; by [[John O'Sullivan]]
			* https://youtu.be/ScI8TBk7y5E
			* https://youtu.be/Na-tLZL82pw

	[[Category:10-tone scales]]		[[Category:10-tone scales]]

BudjarnLambeth at 10:29, 15 September 2026

2026-09-15T10:29:46Z

← Older revision		Revision as of 10:29, 15 September 2026
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			{{Idiosyncratic terms\|The terms ''David-Jubal tuning, David's chord, Jubal's scale'' and ''harmonic strength'' were coined by John O'Sullivan in the mid 2020s and are not so far widely known to other microtonalists.}}

	'''David-Jubal tuning''' is a musical framework invented by [[John O'Sullivan]] in the 2020s. It is a type of [[just intonation]]. It consists of the use of '''Jubal's scale''' as its pitch gamut, and '''David's chord''' as its primary sonority. (''For contrast, compare to most 21st century Western music which uses the [[12edo]] chromatic scale as its pitch gamut and the (tempered) major and minor triads as its primary sonorities'').		'''David-Jubal tuning''' is a musical framework invented by [[John O'Sullivan]] in the 2020s. It is a type of [[just intonation]]. It consists of the use of '''Jubal's scale''' as its pitch gamut, and '''David's chord''' as its primary sonority. (''For contrast, compare to most 21st century Western music which uses the [[12edo]] chromatic scale as its pitch gamut and the (tempered) major and minor triads as its primary sonorities'').

BudjarnLambeth: Created page with "'''David-Jubal tuning''' is a musical framework invented by John O'Sullivan in the 2020s. It is a type of just intonation. It consists of the use of '''Jubal's scale''' as its pitch gamut, and '''David's chord''' as its primary sonority. (''For contrast, compare to most 21st century Western music which uses the 12edo chromatic scale as its pitch gamut and the (tempered) major and minor triads as its primary sonorities''). O'Sullivan describes David-Jubal tun..."

2026-09-15T10:27:48Z

Created page with "'''David-Jubal tuning''' is a musical framework invented by John O'Sullivan in the 2020s. It is a type of just intonation. It consists of the use of '''Jubal's scale''' as its pitch gamut, and '''David's chord''' as its primary sonority. (''For contrast, compare to most 21st century Western music which uses the 12edo chromatic scale as its pitch gamut and the (tempered) major and minor triads as its primary sonorities''). O'Sullivan describes David-Jubal tun..."

New page

'''David-Jubal tuning''' is a musical framework invented by [[John O'Sullivan]] in the 2020s. It is a type of [[just intonation]]. It consists of the use of '''Jubal's scale''' as its pitch gamut, and '''David's chord''' as its primary sonority. (''For contrast, compare to most 21st century Western music which uses the [[12edo]] chromatic scale as its pitch gamut and the (tempered) major and minor triads as its primary sonorities'').

O'Sullivan describes David-Jubal tuning, the reasoning behind it, and practical instructions for fretting a guitar or similar instrument, on his website:
* [https://www.johnsmusic7.com JohnsMusic7.com].

== Theory ==
=== Harmonic strength ===
'''Harmonic strength''' is a term invented by O'Sullivan to describe a measure of the strength of a just sonority. It equals '''2/n + 2/d (where n/d is the simplified interval [[ratio]])'''.

O'Sullivan considers a good tuning to be a tuning with as many intervals as possible with a harmonic strength of 0.5 or higher, and as few intervals as possible with a harmonic strength of 0.25 or higher.

The goal of David-Jubal tuning is to be as 'good' as possible by those criteria.

=== David's chord ===
'''David's chord''' is the name O'Sullivan coined for the [[just intonation]] chord [[1:2:3:4:5:7]]. This chord is derived by starting with the first 9 tones of the [[harmonic series]] and removing all instances of the intervals O'Sullivan considers to be [[dissonance]]s: [[6/5]], [[7/6]], [[8/7]] and [[9/8]].

David's chord consists of four [[pitch class]]es: E, B, G# and D when tuned to E.

O'Sullivan discourages the use of minor triads in music build upon David's chord, considering them "destructive" to the harmonic affect of the chord. When retuning 12edo music to David-Jubal tuning, O'Sullivan recommends replacing minor triads with power chords ([[2:3:4]]).

O'Sullivan considers [[2:3:4:5:7]] to be an acceptable substitute for David's chord, for practical use on instruments, given the difficulty of including an entire additional octave.

=== Jubal's scale ===
'''Jubal's scale''' is the [[just intonation]] scale '''8:9:10:10.666...:12:13.333...:14:15:16:18:20'''.

Its intervals are: 1/1, 9/8, 7/6, 5/4, 4/3, 3/2, 5/3, 7/4, 15/8, 2/1.

O'Sullivan replaced harmonics 11 and 13 in the scale because the intervals between them and the other scale degrees do not have high 'harmonic strength'.

==== Scala file ====
<pre>
! jubal.scl
!
Jubal's scale, John O'Sullivan, key of E
10
!
9/8
7/6
5/4
4/3
3/2
5/3
7/4
15/8
2/1
</pre>

=== Relationship to other scales and concepts ===

Within the framework of [[otonal]] and [[utonal]] analysis, David-Jubal tuning is a strongly otonal tuning, which deliberately avoids utonality.

The intervals O'Sullivan removed from David's chord are all the [[superparticular]] intervals smaller than 5/4.

Jubal's scale bears a slight resemblance to [[Paul Erlich]]'s 'pentachordal decatonic scale' (the [[pajara]][10] scale of [[22edo]]).

Jubal's scale is a subset of [[24afdo]] (the 24th [[overtone scale|mode of the harmonic series]]).

== Music ==
On his YouTube channel "@johnsmusic7", O'Sullivan has compiled the following playlist of music using David-Jubal tuning:
* https://www.youtube.com/playlist?list=PLQkrE1MMrb9g

[[Category:10-tone scales]]
[[Category:7-limit]]
[[Category:Just intonation scales]]
[[Category:Pages with Scala files]]

← Older revision		Revision as of 13:13, 16 September 2026
Line 3:		Line 3:
	'''David-Jubal tuning''' is a musical framework invented by [[John O'Sullivan]] in August, 2026. It is a type of [[just intonation]]. It consists of the use of '''Jubal's scale''' as its pitch gamut, and '''David's chord''' as its primary sonority. (''For contrast, compare to most 21st century Western music which uses the [[12edo]] chromatic scale as its pitch gamut and the (tempered) major and minor triads as its primary sonorities'').		'''David-Jubal tuning''' is a musical framework invented by [[John O'Sullivan]] in August, 2026. It is a type of [[just intonation]]. It consists of the use of '''Jubal's scale''' as its pitch gamut, and '''David's chord''' as its primary sonority. (''For contrast, compare to most 21st century Western music which uses the [[12edo]] chromatic scale as its pitch gamut and the (tempered) major and minor triads as its primary sonorities'').

	David-Jubal tuning was designed for [[guitar]]s only, not keyboards. The guitar is tuned to an "open" just chord (David's chord), and fretted with frets corresponding to the notes of Jubal's scale (9 frets). The idea is to play David's chord on any or all of the notes of Jubal's scale, by barring with the index finger just beside the appropriate fret.		David-Jubal tuning was designed for [[guitar]]s only, not keyboards.

			The guitar is tuned to an "open" just chord (David's chord), and fretted with frets corresponding to the notes of Jubal's scale (9 frets). The idea is to play David's chord on any or all of the notes of Jubal's scale, by barring with the index finger just beside the appropriate fret.

	O'Sullivan describes David-Jubal tuning, the reasoning behind it, and practical instructions for fretting a guitar or similar instrument, on his website:		O'Sullivan describes David-Jubal tuning, the reasoning behind it, and practical instructions for fretting a guitar or similar instrument, on his website:
Line 14:		Line 16:
	; Melodic contexts		; Melodic contexts
	Any just interval n/d is acceptable in a melodic context (notes or chords played sequentially, not simultaneously) if its interval strength is greater than 0.25:		Any just interval n/d is acceptable in a melodic context (notes or chords played sequentially, not simultaneously) if its interval strength is greater than 0.25:
	* An interval with a strength value between 0.25 and 0.4999 is a '''neutral interval'''.		* An interval with a strength value between 0.25 and 0.4999 is a ''neutral interval''.
	* An interval with a strength value between 0.5 and 0.9999 is a '''strong interval'''.		* An interval with a strength value between 0.5 and 0.9999 is a ''strong interval''.
	* An interval with a strength value greater than 1.0 is a '''very strong interval'''.		* An interval with a strength value greater than 1.0 is a ''very strong interval''.

	Over a one octave range the very strong intervals are [[4/3]], [[3/2]] and [[5/3]]; these have a value greater than 1.0 using O'Sullivan's formula.		Over a one octave range the very strong intervals are [[4/3]], [[3/2]] and [[5/3]]; these have a value greater than 1.0 using O'Sullivan's formula.

	; Harmonic contexts		; Harmonic contexts
	~~As regards~~ chord construction, every interval in a chord must have a strength value greater than 0.5.		In chord construction, every interval in a chord must have a strength value greater than 0.5.

	; Tempering		; Tempering
Line 32:		Line 34:
	Jubal's scale is the [[just intonation]] scale: 1/1, 9/8, 7/6, 5/4, 4/3, 3/2, 5/3, 7/4, 15/8, 2/1.		Jubal's scale is the [[just intonation]] scale: 1/1, 9/8, 7/6, 5/4, 4/3, 3/2, 5/3, 7/4, 15/8, 2/1.

	O'Sullivan derived it from the harmonic series segment 8-9-10-11-12-13-14-15-16, but replaced [[11/8]] with [[4/3]] and replaced [[13/8]] with [[5/3]], and [[7/6]] was added as well. All the denominators in Jubal's scale are 3-[[prime limit]].		O'Sullivan derived it from the [[harmonic series]] segment 8-9-10-11-12-13-14-15-16, but replaced [[11/8]] with [[4/3]] and replaced [[13/8]] with [[5/3]], and [[7/6]] was added as well. All the denominators in Jubal's scale are 3-[[prime limit]].

	O'Sullivan has published a document describing rules for composition in David-Jubal tuning:		O'Sullivan has published a document describing rules for composition in David-Jubal tuning: