Oh-Two-Six (026)
An Improviser's Guide to Practical Usage of the 026 Trichord
An Improviser's Guide to Practical Usage of the 026 Trichord
Since the inception of the improvisational art form we know and love as “Jazz”, melodic and harmonic techniques have steadily expanded in all directions – in some cases even disappearing altogether.
Presently growing within the collective consciousness of many contemporary improvisers (guitarist Bruce Arnold and saxophonist John O'Gallagher lead the way), is the awareness and usage of the 12-tone techniques pioneered by the early 20th century European “serialist” composers – Berg, Webern & Schoenberg - being the most prominent among them.
The basic premise of this system is the construction of 12-tone rows – the 12 tones of the chromatic scale as equal entities, non-repeating and organized into different “pitch class sets”, or note groupings of varying lengths.
Presently growing within the collective consciousness of many contemporary improvisers (guitarist Bruce Arnold and saxophonist John O'Gallagher lead the way), is the awareness and usage of the 12-tone techniques pioneered by the early 20th century European “serialist” composers – Berg, Webern & Schoenberg - being the most prominent among them.
The basic premise of this system is the construction of 12-tone rows – the 12 tones of the chromatic scale as equal entities, non-repeating and organized into different “pitch class sets”, or note groupings of varying lengths.
Each semitone of the chromatic scale is numbered from 0 -11.
C (0), Db (1), D (2), Eb (3), E (4), F (5), F# (6), G (7), Ab (8), A (9), Bb (10), B (11):
Any note can be designated as 0, with all other notes relative to that.
This volume of “Oh-Two-Six” explores areas of practical usage, for the improviser, of the 026 pitch class set. As it contains 3 pitches, it's also known as an 026 Trichord.
Each 026 Trichord contains a whole tone (2 semitones) between 0 (C) and 2 (D) and a tritone (6 semitones) 6 (F#), as listed above. This relationship can be transposed throughout the chromatic cycle (Db-Eb-G, D-E-Ab, Eb-F-A, etc. - are all 026's).
Also considered 026 would be C-E-F#, Db-F-G, D-F#-G#, etc. Wouldn't they be 046's, you ask?
Well actually, no. The reason being, is that each numerical pitch class set designation describes the smallest interval content available within that configuration. Since C-E-F# still contains a whole step (E-F#) and a tritone (C-F#, unchanged) ... 026 it is!
However, this can be somewhat confusing, since C-D-F# and C-E-F# have slightly (or not so slightly) different sounds, especially when expressed in their 1st or 2nd rotations (inversions).
So for purposes of clarity in that regard, I took the idea from pioneering saxophonist John O'Gallagher's aptly titled, ground breaking book “Twelve-Tone Improvisation” (Advance Music) in which he differentiates between the two by labeling C-D-F#, etc as 2+4 (2 semitones from C, plus 4 semitones from D), and C-E-F# as 4+2 (4 semitones from C, plus 2 semitones from E).
Works for me!
Below is a sequence from “Oh-Two-Six” which shows alternating 026's (2+4 & 4+2) in prime form ascending chromatically. It's important to feel and hear the difference between the two.
C (0), Db (1), D (2), Eb (3), E (4), F (5), F# (6), G (7), Ab (8), A (9), Bb (10), B (11):
Any note can be designated as 0, with all other notes relative to that.
This volume of “Oh-Two-Six” explores areas of practical usage, for the improviser, of the 026 pitch class set. As it contains 3 pitches, it's also known as an 026 Trichord.
Each 026 Trichord contains a whole tone (2 semitones) between 0 (C) and 2 (D) and a tritone (6 semitones) 6 (F#), as listed above. This relationship can be transposed throughout the chromatic cycle (Db-Eb-G, D-E-Ab, Eb-F-A, etc. - are all 026's).
Also considered 026 would be C-E-F#, Db-F-G, D-F#-G#, etc. Wouldn't they be 046's, you ask?
Well actually, no. The reason being, is that each numerical pitch class set designation describes the smallest interval content available within that configuration. Since C-E-F# still contains a whole step (E-F#) and a tritone (C-F#, unchanged) ... 026 it is!
However, this can be somewhat confusing, since C-D-F# and C-E-F# have slightly (or not so slightly) different sounds, especially when expressed in their 1st or 2nd rotations (inversions).
So for purposes of clarity in that regard, I took the idea from pioneering saxophonist John O'Gallagher's aptly titled, ground breaking book “Twelve-Tone Improvisation” (Advance Music) in which he differentiates between the two by labeling C-D-F#, etc as 2+4 (2 semitones from C, plus 4 semitones from D), and C-E-F# as 4+2 (4 semitones from C, plus 2 semitones from E).
Works for me!
Below is a sequence from “Oh-Two-Six” which shows alternating 026's (2+4 & 4+2) in prime form ascending chromatically. It's important to feel and hear the difference between the two.
Since the effect of the tritone is so strong, the effect of the middle note is rendered somewhat subtle. Because of the tritone effect, this chromatic trichord sequence parallels the Cycle of Fifths - while ascending, and the Cycle of Fourths - while descending.
As part of the same sequence in 1st rotation (inversion) from (below), the non-tritonic tone becomes more distinguishable as the interval relationships within each trichord change - from the lowest note to the highest (0-4-10 & 0-2-8) - spanning min 7ths & min 6ths, respectively.
As part of the same sequence in 1st rotation (inversion) from (below), the non-tritonic tone becomes more distinguishable as the interval relationships within each trichord change - from the lowest note to the highest (0-4-10 & 0-2-8) - spanning min 7ths & min 6ths, respectively.
...etc.
From the 2nd rotation, another set of interval relationships (0-6-8 & 0-6-10), as the non-tritonic tone becomes extrapolated. All trichords in each example still belong to the 026 pitch class set.
From the 2nd rotation, another set of interval relationships (0-6-8 & 0-6-10), as the non-tritonic tone becomes extrapolated. All trichords in each example still belong to the 026 pitch class set.
...etc.
The 026 trichord is closely associated with the Whole Tone Scale, from which both versions of an 026 (2+4 & 4+2) can be formed on each of its 6 scale tones.
Below is a partial example, of alternating 026 trichords derived exclusively from a single Whole Tone Scale.
The 026 trichord is closely associated with the Whole Tone Scale, from which both versions of an 026 (2+4 & 4+2) can be formed on each of its 6 scale tones.
Below is a partial example, of alternating 026 trichords derived exclusively from a single Whole Tone Scale.
...etc.
Various combinations of 026 pairs form shortened, hexatonic versions of the Diminished Scale.
In the example below, a 4+2 & 2+4, a half step apart, form an abridged half /whole step Diminished Scale hexatonic. A pair of 4+2's separated by a half step, would do the trick, as well.
Various combinations of 026 pairs form shortened, hexatonic versions of the Diminished Scale.
In the example below, a 4+2 & 2+4, a half step apart, form an abridged half /whole step Diminished Scale hexatonic. A pair of 4+2's separated by a half step, would do the trick, as well.
Common tones between trichords are important to recognize. As in the example below, which focuses on the note “C”, there are 6 trichord possibilities for each note of the chromatic scale.
The major feature of 12-tone technique is the 12-tone row. In the strictest sense, a row employs all 12 tones before one is repeated. For the improviser, this rule is thankfully, a bit more relaxed. As a basic unit in our case is the trichord, a 12-tone row consists of 4 of them. Notes can repeat within a trichord, but not between them in the row.
The bulk of “Oh-Two-Six” presents I - VI - II - V chord sequences based on 4 different rows. They are:
Row #1: C-E-F# / A-C#-D# / Ab-Bb-D / F-G-B
Row #2: Bb-C-E / G-A-C# / D-F#-G# / B-Eb-F
Row #3: E-Gb-Bb / A-Db-Eb / Ab-C-D / F-G-B
Row #4: E-Ab-Bb / C#-D#-G / C-D-F# / F-A-B
In this section, all rows and sequences are presented in all 12 tonal centers.
The example below is from Row #1. Ascending arpeggios, rhythmically basic eighth notes, bottom note repeats at the top. Both 026 trichords in each measure stem from different Whole Tone scales, but from the same Diminished Scale. The 4 trichords alternate between Whole Tone scales through both measures, while the implied half / whole step Diminished Scales between measures are a whole step apart.
The bulk of “Oh-Two-Six” presents I - VI - II - V chord sequences based on 4 different rows. They are:
Row #1: C-E-F# / A-C#-D# / Ab-Bb-D / F-G-B
Row #2: Bb-C-E / G-A-C# / D-F#-G# / B-Eb-F
Row #3: E-Gb-Bb / A-Db-Eb / Ab-C-D / F-G-B
Row #4: E-Ab-Bb / C#-D#-G / C-D-F# / F-A-B
In this section, all rows and sequences are presented in all 12 tonal centers.
The example below is from Row #1. Ascending arpeggios, rhythmically basic eighth notes, bottom note repeats at the top. Both 026 trichords in each measure stem from different Whole Tone scales, but from the same Diminished Scale. The 4 trichords alternate between Whole Tone scales through both measures, while the implied half / whole step Diminished Scales between measures are a whole step apart.
Listen
The next example, also from Row #1, breaks up the line rhythmically with rests and triplets, as well as melodically anticipating the harmony (but part of the same Diminished Scale) on beats 2 & 4 of measure #2.
Listen
From Row #2, this next one features 4 dominant 7ths chords. As in the previous two examples, the implied relationships of the four trichords between alternating whole tone and diminished scales remains intact.
Listen
These are just a few examples of what is really only the tip of the iceberg of possibilities.
The 026 trichord is familiar to the ear, and because of its inherent tritone, it tends toward tonal resolution. It's relationship to both the Whole Tone and Diminished Scale systems, as well as the Cycle of 5ths, allows one to create intervallic melodic lines that avoid shop worn cliches.
“Oh-Two-Six” 24-7, 365!
B Stern
The 026 trichord is familiar to the ear, and because of its inherent tritone, it tends toward tonal resolution. It's relationship to both the Whole Tone and Diminished Scale systems, as well as the Cycle of 5ths, allows one to create intervallic melodic lines that avoid shop worn cliches.
“Oh-Two-Six” 24-7, 365!
B Stern
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