In his REH Video, Allan Holdsworth presented a sample of the scales he devised from the basic formula of ‘no more than three consecutive semi-tones’.
These were all one-octave scales (distributed across the fretboard). His motivation for this endeavour was a pronounced dissatisfaction with the orthodox scales (and chords) on offer, so he built his own to taste. His unique music reflects this.
In and amongst the scale presentation however, he casually 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…
My first thought was to use his formula, but I could not devise a pattern from it that actually sounded and felt like it was heading for the end of the second octave as the destination point for tonic resolution. I even asked Chatgpt4 to devise some patterns, but it failed too.
Anyway a few days later 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 13th arpeggio with a semitone before each note, but now 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 tried to improvise a melody.
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 using another 13th arpeggio from the same key e.g. D Dorian = D E F G A B C D arranged in ascending thirds = D F A C E G B D.
Then try the remains modes and even the Harmonic & Melodic Minor variants.
I never found out what 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 use them like Mike might or as standalone scales.
