More...SUPER 4!
More SUPER 4? OK, You got it!
Since the release last month of "The SUPER 4" Shortbook™ and blogpost, I've subsequently come across a few additional interesting and potentially useful musical relationships between aspects of this "super" 4-note grouping, known technically as a tetratonic.
Specifically, I've been checking out the effect of expressing them in intervals of a minor 3rd, which divides the octave into four equal parts - forming the diminished cycle.
As mentioned, the results proved to be quite interesting - and musically useful to boot.
Since the release last month of "The SUPER 4" Shortbook™ and blogpost, I've subsequently come across a few additional interesting and potentially useful musical relationships between aspects of this "super" 4-note grouping, known technically as a tetratonic.
Specifically, I've been checking out the effect of expressing them in intervals of a minor 3rd, which divides the octave into four equal parts - forming the diminished cycle.
As mentioned, the results proved to be quite interesting - and musically useful to boot.
As explained in "The SUPER 4" Shortbook™, as well as in the previous post, the four shapes / inversions of the tetratonic reveals 5 basic chord types:
Dom7 13
Maj7#11
min6 9
Dom7 alt
min7b5.
After all, they're really just melodic expressions of time-honored piano voicings to begin with. Why should keyboard players have all the fun?!
In Ex. 1 below, a sequence made up of four identical tetratonic shapes descends in minor 3rds in bars #1 & 2. Each 4-note shape consists of a tritone and a Perfect 5th. This creates a neat, symmetrical, intervallic line which, after several repeats, resolves to a singular tetratonic in bars #3 & 4.
The chord choices, from the five listed above, are interesting in that, while attempting to create some type of ii-V7 movement, I realized that a line with the tetratonics ascending in minor 3rds (instead of descending, as it is here), would lend itself to a more traditional ii7b5 - V7alt (the ACE method).
To clarify that, and hopefully not to confuse; if we were to work backwards from the end of bar #2 to the beginning of bar #1 (creating an ascending line with exact same notes, retrograde or not), instead of B7 13 and F-7b5 in bar #2, we could have D#(Eb)-7b5 G#(Ab)7alt.
In bar #1, it would be A-7b5 D7alt.
In either case, the relationship between bars #1 & 2 remains a tritone.
Ex. 1
Dom7 13
Maj7#11
min6 9
Dom7 alt
min7b5.
After all, they're really just melodic expressions of time-honored piano voicings to begin with. Why should keyboard players have all the fun?!
In Ex. 1 below, a sequence made up of four identical tetratonic shapes descends in minor 3rds in bars #1 & 2. Each 4-note shape consists of a tritone and a Perfect 5th. This creates a neat, symmetrical, intervallic line which, after several repeats, resolves to a singular tetratonic in bars #3 & 4.
The chord choices, from the five listed above, are interesting in that, while attempting to create some type of ii-V7 movement, I realized that a line with the tetratonics ascending in minor 3rds (instead of descending, as it is here), would lend itself to a more traditional ii7b5 - V7alt (the ACE method).
To clarify that, and hopefully not to confuse; if we were to work backwards from the end of bar #2 to the beginning of bar #1 (creating an ascending line with exact same notes, retrograde or not), instead of B7 13 and F-7b5 in bar #2, we could have D#(Eb)-7b5 G#(Ab)7alt.
In bar #1, it would be A-7b5 D7alt.
In either case, the relationship between bars #1 & 2 remains a tritone.
Ex. 1
All that aside, the ii-V7 harmonic choices for the descending sequences, as they are in Ex. 1, work just fine. The resolution to E Maj7#11 (another one of the 5 chord choices) in bars #3 & 4 sounds smooth and natural as a tonic choice. The whole line reads: bvi-7b5 bII7 13 | ii-7b5 V7 13 | I Maj7#11.
The first two measures are tritone substitutions for each other. Which led me to a startling discovery!
The first two measures are tritone substitutions for each other. Which led me to a startling discovery!
Listen
Two consecutive "SUPER 4" tetratonics a min 3rd apart do not share any common tones. For example, if we combine all the notes of each tetratonic in bar #1 (Ex. 1) and form an 8-note scale, we get:
Bb-C-D-Eb-F-Gb-G-A, which is non other than a Bb Major BeBop Scale, aka Bb 6th/ Diminished Scale.
Are you startled yet? Logically, the same thing would be happening in bar # 2 - a tritone away: E-F#-G#-A-B-C-C#-D# = E 6th/ Diminished (BeBop) Scale.
The significance of this earth-shattering revelation, as far as I can tell, is in the ascending version of this sequence (described above the Ex. 1 graphic), whereas D#-7b5 G#7alt (bar #2) is the ii-V7 of C# min, the relative minor of E Maj. Likewise in bar #1; A-7b5 D7alt is the ii-V of G min - the relative minor of Bb Maj. Make sense?
Whew! I´m glad that´s out of the way!
Bb-C-D-Eb-F-Gb-G-A, which is non other than a Bb Major BeBop Scale, aka Bb 6th/ Diminished Scale.
Are you startled yet? Logically, the same thing would be happening in bar # 2 - a tritone away: E-F#-G#-A-B-C-C#-D# = E 6th/ Diminished (BeBop) Scale.
The significance of this earth-shattering revelation, as far as I can tell, is in the ascending version of this sequence (described above the Ex. 1 graphic), whereas D#-7b5 G#7alt (bar #2) is the ii-V7 of C# min, the relative minor of E Maj. Likewise in bar #1; A-7b5 D7alt is the ii-V of G min - the relative minor of Bb Maj. Make sense?
Whew! I´m glad that´s out of the way!
More SUPER 4 means there's more...
Ex. 2 below again shows the same sequence - four SUPER 4 tetratonics (tritone & P5th) descending in minor 3rds - transposed and rhythmically broken up with triplets and rests. The chords, again chosen from the basic 5, have their roots ascending in min 3rds - in contrary motion to the line itself - before resolving V7-I7 to a Bb7 13 tonic dominant.
Can you tell which 6th / Diminished Scales are in play here?
(Answer: E & Bb, in bars #1 & 2 respectively - the reverse of Ex. 1.)
Ex. 2
Ex. 2 below again shows the same sequence - four SUPER 4 tetratonics (tritone & P5th) descending in minor 3rds - transposed and rhythmically broken up with triplets and rests. The chords, again chosen from the basic 5, have their roots ascending in min 3rds - in contrary motion to the line itself - before resolving V7-I7 to a Bb7 13 tonic dominant.
Can you tell which 6th / Diminished Scales are in play here?
(Answer: E & Bb, in bars #1 & 2 respectively - the reverse of Ex. 1.)
Ex. 2
Listen
Similarly, a transposed and rhythmically juxtaposed version of same descending sequence is depicted in Ex. 3 below (notice the octave displacement in bar #2). The chosen chords are all of the same min6/9 quality, and descend in parallel with the line itself.
The BeBop Scale equivalents here are C (bar #1) & F# (bar #2).
Ex. 3
The BeBop Scale equivalents here are C (bar #1) & F# (bar #2).
Ex. 3
Listen
The free, downloadable PDF (link above) contains 9 more versions of this sequence, each transposed and rhythmically modified, for the most part. Download it, check it out, agonize and grow - and remember to have fun doing so.
The SUPER 4 tetratonic is a great little tool for the improviser - allowing for a leaner, meaner set of note choices.
Make it work for you!
B. Stern
The SUPER 4 tetratonic is a great little tool for the improviser - allowing for a leaner, meaner set of note choices.
Make it work for you!
B. Stern
For deeper insights into The SUPER 4 and more,
the following Shortbooks™ break it down even further.
Available for immediate download!
the following Shortbooks™ break it down even further.
Available for immediate download!
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