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…
