In his REH Video, Allan Holdsworth presented a sample of the scales he had devised from the basic formula of ‘no more than three consecutive semi-tones’. His motivation for this endeavour was a dissatisfaction with the orthodox scales (and chords) on offer - so he built his own to taste. His unique music reflects this.
These were all one-octave scales (which he distributed across the fretboard and presented them on those infamous fretboard charts).
It seems he was also getting bored of these because towards the end of the video he referred to scales he’d been exploring that did not resolve at the first octave - but unfortunately did not elaborate.
That was years ago and I did not take the bait at the time, but recently I found myself dwelling on these hypothetical structures…
Initially the task did not inspire any useful ideas but after a few days of dwelling on it, I woke up with the realisation that I already know a group of structures that only resolve over two octaves and which could be adapted to achieve the goal.
If you take a C Major Scale = C D E F G A B C = R 2 3 4 5 6 7 R, and rearrange it so that it ascends in thirds, this will give you what is known as a 13th arpeggio (or chord, depending on how you play it), with these notes and intervals:
C E G B D F A C = R 3 5 7 9 11 13 R
This set of notes spans two octaves and also sounds and feels like it’s resolving at the end of the second octave.
The next step was inspired by listening to Mike Stern talk about one of his ways of generating Bebop lines - by hitting the safe notes of chords from a semi-tone either side, these being some decorative chromatic notes he likes to use to achieve his trademark fusion sound e.g. imagine you had the CEGB arpeggio lined up over the C maj7 chord and then slid an F# into a G, or a C# into the C.
So here is the original 13th arpeggio with a semitone before each note, but the idea is that the new notes are now main players in the scale rather than chromatic.
Its intervals are: R b3 3 b5 5 b7 7 b9 9 10 11 b13 13 14 R.
This is what I chose for the video. I played it twice and then improvised a melody. Its flavour is suitably ambiguous.
Here is one for you to try where the semitones are before or after:
Its intervals are: R b2 b3 3 5 b6 b7 7 b9 9 10 11 13 b14 R
Try your own variation.
Then try starting from a minor 13th arpeggio e.g. D F A C E G B D from D Dorian.
I have never found out what shapes Allan had in mind (if anyone knew him or read any more about these scales then please share) but I like to think he would approve of the attempt because I think these transformed arpeggios sound like independent scales, once you get used their sound and start to improvise - but bear in mind that if you play the original arpeggio first, then the extra notes will just sound like chromatic notes. This is similar to how you must approach modes of a scale - if you want them to have a distinct sound from their source, you have to approach and appreciate things with fresh ears and an open mind so that your imagination can get to work with it as if it is something novel.
The neat thing about this approach is that you can still use them like Mike or as standalone scales as Allan intended.
PS:
In December 2024 I asked both ChatGPT4 and Gemini to suggest a solution to Allan’s scale based on this prompt below and they failed miserably and repeatedly despite me pointing out where their errors were:
‘The task is to devise a scale which takes two octaves to resolve back to the tonic. The only parameters are that it can have no more than three consecutive semitones and the maximum interval is a major 3rd. Please use C as the tonic and good luck.’
In late Jan 2025 I asked Deepseek and it failed initially like the others but passed on the 2nd attempt after I pointed out the errors with this solution:
> R 2 3 4 5 6 7 9 10 11 #11 12 13 14 R = C D E F G A B D E F# G A B C
It also recognised other solutions.
One week later in early feb 2025 ChatGPT4 managed first time in its new Reason mode with this solution:
> R 2 3 #4 #5 #6 7 9 10 #11 12 13 = C D E F♯ G♯ A♯ B D E F♯ G A C.
However, when I gave it my interval formula from the article above (R b3 3 b5 5 b7 7 b9 9 10 11 b13 13 14 R ) and asked it to spell the scale from C it made errors.
Composers choose a particular scale as a source for their creations because of its characteristic tonal and emotive properties - and this relies on the overall interval structure being cohesive, including feeling like it wants to resolve to the tonic. Currently the bots cannot ‘sense’ the notes and savour the qualities of melodies and harmonies like humans - this is reflected in their scales.
I await the next upgrades.
