David-Jubal
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This article or section contains multiple idiosyncratic terms. Such terms are used by only a few people and are not regularly used within the community.
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 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 guitars 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:
Theory
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).
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.
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 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.
Jubal's scale
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 has published a document describing rules for composition in David-Jubal tuning:
Scala file
! jubal.scl ! Jubal's scale, John O'Sullivan 9 ! 9/8 7/6 5/4 4/3 3/2 5/3 7/4 15/8 2/1
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 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.
Music
David-Jubal tuning
On his YouTube channel "@johnsmusic7", O'Sullivan has compiled the following playlist of 14 musical examples that use David-Jubal tuning: