Four'll Get You Twenty-Four
A few half-diminished permutations to get started
A few half-diminished permutations to get started
According to an online permutation calculator I stumbled upon recently, the number of unique combinations of the 12 pitches of the Western chromatic scale comes to exactly 479,001,600 - and that's just the pitches! Add to that the variations in rhythm, tone and timbre, etc., and that number grows to infinity.
Not to worry! In this post, we'll cover just a few of the permutations of just four notes - which yield the measly number of 24 possible unique combinations - definitely enough to deal with!
The 4-note cell focused on here is commonly known as a min7b5, or half-diminished chord and is similar in concept to a previous post and book, "Permutation Station 1235".
Not to worry! In this post, we'll cover just a few of the permutations of just four notes - which yield the measly number of 24 possible unique combinations - definitely enough to deal with!
The 4-note cell focused on here is commonly known as a min7b5, or half-diminished chord and is similar in concept to a previous post and book, "Permutation Station 1235".
The 24 possible permutations of C min7b5 (C, Eb, Gb, Bb) are:
{C,Eb,Gb,Bb} {C,Eb,Bb,Gb} {C,Gb,Eb,Bb} {C,Gb,Bb,Eb} {C,Bb,Eb,Gb} {C,Bb,Gb,Eb}
{Eb,C,Gb,Bb} {Eb,C,Bb,Gb} {Eb,Gb,C,Bb} {Eb,Gb,Bb,C} {Eb,Bb,C,Gb} {Eb,Bb,Gb,C}
{Gb,C,Eb,Bb} {Gb,C,Bb,Eb} {Gb,Eb,C,Bb} {Gb,Eb,Bb,C} {Gb,Bb,C,Eb} {Gb,Bb,Eb,C}
{Bb,C,Eb,Gb} {Bb,C,Gb,Eb} {Bb,Eb,C,Gb} {Bb,Eb,Gb,C} {Bb,Gb,C,Eb} {Bb,Gb,Eb,C}
The notation graphic below (Ex. 1) shows the first possibility - a root position half-diminished arpeggio, ascending in perfect 4ths around the Cycle. A half-diminished chord can be considered as part of a dominant 9th by adding the root a Maj 3rd below it (C min7b5 = Ab 9). The numbers on the left (35b79) represent this as third, fifth, flat-seventh & ninth. The letter names on top indicate the full 9th chord, as well as its tritone substitution (in smaller letters). In parenthesis is the half-diminished chord name, as notated.
Ex. 1 - Root position half-diminished arpeggio as dominant 9th around the cycle.
{C,Eb,Gb,Bb} {C,Eb,Bb,Gb} {C,Gb,Eb,Bb} {C,Gb,Bb,Eb} {C,Bb,Eb,Gb} {C,Bb,Gb,Eb}
{Eb,C,Gb,Bb} {Eb,C,Bb,Gb} {Eb,Gb,C,Bb} {Eb,Gb,Bb,C} {Eb,Bb,C,Gb} {Eb,Bb,Gb,C}
{Gb,C,Eb,Bb} {Gb,C,Bb,Eb} {Gb,Eb,C,Bb} {Gb,Eb,Bb,C} {Gb,Bb,C,Eb} {Gb,Bb,Eb,C}
{Bb,C,Eb,Gb} {Bb,C,Gb,Eb} {Bb,Eb,C,Gb} {Bb,Eb,Gb,C} {Bb,Gb,C,Eb} {Bb,Gb,Eb,C}
The notation graphic below (Ex. 1) shows the first possibility - a root position half-diminished arpeggio, ascending in perfect 4ths around the Cycle. A half-diminished chord can be considered as part of a dominant 9th by adding the root a Maj 3rd below it (C min7b5 = Ab 9). The numbers on the left (35b79) represent this as third, fifth, flat-seventh & ninth. The letter names on top indicate the full 9th chord, as well as its tritone substitution (in smaller letters). In parenthesis is the half-diminished chord name, as notated.
Ex. 1 - Root position half-diminished arpeggio as dominant 9th around the cycle.
Listen
Example 2 again shows a 35b79 permutation - this time with the first note displaced up an octave - combined with a b7953 configuration, as the second grouping in each measure. Notice that the first note of each grouping descends in half-steps, indicating how the Cycle of 5ths and the chromatic cycle are related through tritone substitutions (the 3rd and b7 are a tritone apart).
Ex. 2 - Octave displaced 35b79 combined with b7953 permutations per measure.
Ex. 2 - Octave displaced 35b79 combined with b7953 permutations per measure.
Listen
The Free-B. downloadable pdf contains an additional pair of these permutation examples.
This permutation technique works with any group of four notes. See how many you can come up with and integrate into your own playing.
B. Stern
This permutation technique works with any group of four notes. See how many you can come up with and integrate into your own playing.
B. Stern
Related:
* Permutation Station 1 2 3 5 - Twenty-four roads to Rome *
* Return of the SUPER 4 - A minor ii-V7 Sequence *
* NIDIAN & Her Sisters - Maj7sus4 Chords & Tetratonic Modes *
* Permutation Station 1 2 3 5 - Twenty-four roads to Rome *
* Return of the SUPER 4 - A minor ii-V7 Sequence *
* NIDIAN & Her Sisters - Maj7sus4 Chords & Tetratonic Modes *
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