David-Jubal: Difference between revisions

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'''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:

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== 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]])'''.

'''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''.

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

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.

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

; Harmonic contexts

In chord construction, every interval in a chord must have a strength value greater than 0.5.

; Tempering

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

=== David's chord ===

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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:

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=== 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 ==

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* ''[https://youtu.be/Na-tLZL82pw Elias]'' (2026)

[[Category:10-tone scales]]

[[Category:9-tone scales]]

[[Category:7-limit]]

[[Category:Just intonation scales]]

[[Category:Pages with Scala files]]

@@ 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 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:
@@ Line 10: / Line 12: @@
 == 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]])'''.
+'''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''.
-As regards chord construction, every interval in a chord must have a strength value greater than 0.5.
+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.
-O'Sullivan allows a tempering of just intervals by up to plus or minus 6.7758 cents ([[256/255]]).
+; Harmonic contexts
+In chord construction, every interval in a chord must have a strength value greater than 0.5.
+; Tempering
+O'Sullivan allows a [[temperament|tempering]] of just intervals by up to plus or minus 6.7758 [[cents]] ([[256/255]]).
 === David's chord ===
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 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:
@@ Line 50: / Line 60: @@
 === 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 ==
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 * ''[https://youtu.be/Na-tLZL82pw Elias]'' (2026)
-[[Category:10-tone scales]]
+[[Category:9-tone scales]]
 [[Category:7-limit]]
 [[Category:Just intonation scales]]
 [[Category:Pages with Scala files]]