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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, 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:  
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== 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.
; 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''.  


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


=== David's chord ===
; Harmonic contexts
'''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]].
In chord construction, every interval in a chord must have a strength value greater than 0.5.


David's chord consists of four [[pitch class]]es: E, B, G# and D when tuned to E.  
; Tempering
O'Sullivan allows a [[temperament|tempering]] of just intervals by up to plus or minus 6.7758 [[cents]] ([[256/255]]).


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]]).
=== David's chord ===
 
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.
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 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.  
 
=== 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.
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 ==
=== 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: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]]
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