The Jazz Sax & Improvisation Blog of Saxophonist Bobby Stern

0 1 3 Calling...Super Augmented!

11/29/2019

0 1 3 Calling...Super Augmented!
An Introduction to the 013 Trichord & Super Augmented Scale

The scale in the title of this latest Shortbook™ was originally referred to as "Super Augmented" in a previous blog post from several years ago.

Among other names, it's been identified primarily as the inverse of Messaen's 3rd mode of limited transposition, as well as "Tcherepnin Nonatonic Mode 1", "Genus Chromaticum", and "Augmented Nine".

I'll still go with "Super Augmented", however, since among other aspects of its scalar construction, it contains two overlapping 6-note Augmented Scales, linked by a common Augmented triad.

"Pretty super!", I'd say. It also contains a trio of 013 Trichords, a Major 3rd apart - forming a 9-note (nonetonic) scale.

"But..what", you ask "is an 013 Trichord?" Or - better yet - what is a trichord, period?

A trichord is a group, series or pitch collection consisting of three notes, usually in a configuration other than in 3rds (which would make it a triad). As part of the system of pitch organization, sometimes called "serialism" or 12-tone technique", the notes are numbered according to their position (0 through 11) in ascending series within the 12-note chromatic scale.

If C is designated as the root, then

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 12-tone technique features "12-tone rows", where each pitch is non-repeating within the row. It was developed in the late 19th and early 20th centuries and is identified most closely with composers, Arnold Schoenberg, Anton Webern & Alban Berg (the Austrian "Triple A's"). It's become a widely used compositional concept, as well as increasingly popular among contemporary improvisers.

While it's not within the scope of this book to cover 12-tone rows in any depth, it's touched upon briefly here in order to better understand the construction of the 013 trichord (which can be part of a row).

Its interval make-up, as shown below, is half-step + whole step (1+2) and is the Prime Form.

013 - Prime Form
0 1 3

Besides its prime form, a trichord can be expressed as the two inversions - called rotations - of itself.
013 - 1st Rotation 013 - 2nd Rotation

While attention is called here to a trichord's 1st and 2nd rotations, the focus of the exercises and sequences in this book is almost exclusively on the prime form.

To the traditional ear, these 3 notes might sound like scale steps 3-4-5 in Ab Major (or 7-Root-2 in Db). In fact, this can be an excellent way to visualize and practice 013, as it occurs twice in each Major, Melodic and Harmonic Minor scale - as well as in each of their modes.

Ex 1. - 013 Trichords ascending in half steps

Rather than focusing on its usage in a 12-tone row, a more traditional view of this 3 note grouping is taken in the form of its permutations - of which there are 6, including the prime form.

Ex 2. - 013 Trichords - Permutation #2 - ascending in half steps.

This same process is presented as an 013 sequence in whole steps as well as Maj 3rds. Why not in min 3rds? Because continuous 013 trichords, a minor 3rd apart, create a whole / half step diminished scale, which is already the subject of "The Diminished Scale Coloring Book".

The focus of the remainder of "013 Calling... Super Augmented" is based on the melodic structure formed by three 013 trichords a Major 3rd apart.

Ex 3. - Super Augmented Scale in C over a C6 chord.

Listen

Once we've recognized Super Augmented as its own unique nonetonic scale system, we can break it back down to its more conventional compounds.

The Super Augmented Scale is symmetrical and palindromic. It's scalar interval scheme is:
h - W - h h - W - h h - W - h

As a "mode of limited transposition", which means that - like the Augmented Scale - there are only 4 transpositions before repeating. Its 3 trichords divide the octave into 3 equal parts.

It contains 6 semitones (min 2nds), 6 whole tones, 9 Maj 3rds (one from each scale step), 6 perfect 4ths (C-F, Eb-Ab, E-A, G-C, Ab-Db, B-E) & 3 tritones (Db-G, Eb-A, F-B).

It hosts 6 Major Triads, 6 minor triads, 3 diminished & 3 augmented triads (with enharmonic inversions, an augmented triad is generated from all 9 scale steps).

Ex 4. - Super Augmented sequence - Maj triads as permutations

As mentioned, it's structure includes:

the fusion of 2 adjacent Augmented Scales (C-D#-E-G-Ab-B & C-Db-E-F-G#-A), linked by a common Augmented triad (C-E-G#), as well as
a complete Whole Tone Scale (Db-Eb-F-G-A-B).
3 Pentatonic b2's (C-Db-E-G-A, E-F-G#-B-C#, Ab-A-C-Eb-F)
3 Pentatonic b6's (Db-Eb-F-Ab-A, F-G-A-C-Db, A-B-C#-E-F)

Below are several ii-V7 sequences using material, including the accompanying harmonies, from a single C Super Augmented Scale - the exception being an occasional D in the bass, which is borrowed from outside the scale.

These examples, in the book, are transposed to all 12 keys..

Ex 5.

Listen

Ex 6.

Listen

Still using the same material from C Super Augmented, here's an example of a minor ii-V in the relative minor (A min).

Ex 7.

Listen

Since Super Augmented divides the octave into 3 equal parts, it stands to reason that the Cycle of Descending Major Thirds might be available.

Voila! Coltrane Changes!

Ex 8.

Listen

Exploring the 013 Trichord and Super Augmented scale system can be both entertaining and engaging. It provides a method of incorporating certain elements of chromaticism, in an effort to break old habits and create, from an individual standpoint, something fresh and distinctive as an improviser or composer.

B. Stern

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