His approach to soloing and his approach to chording (the latter of which, despite his own stated wishes, is as far away from horn playing as it gets) are deeply intertwined. Basically, it comes down to scales. He knows them all, no matter how exotic, plus a bunch that I’m pretty sure he invented.
He doesn’t think of scales like a guitarist. In other words, he doesn’t think, “Okay, in this position, the box for the scale looks like this, and in that position, it looks like that, etc.” An exceptionally daring guitar player might string together several boxes so they have more navigability on the neck and access to some cool wide fingerings, but that’s still thinking in terms of boxes. Holdsworth doesn’t think that way. He just knows every position of every degree on the scale through all the available octaves from the lowest note to the highest. In his instructional video, he shows a chart of how he looks at the neck and it’s just an explosion of dots from top to bottom without divisions by position.
Another thing most guitarists do that he doesn’t (or, at least, that isn’t really a part of his approach) is learn chords first by name and then how they work with certain scales. You know, you learn the fingerings for all the basic chords you need to know first–E major, D minor, G minor seventh, whatever. That’s as much as a lot of guitarists ever learn, because that’s the bare minimum you need to know to bang out a song.
Holdsworth’s approach, which I personally endorse but am obviously not nearly as good at, is to start with the scale and build chords out of certain degrees within that scale. Considering that many of the scales he uses are pretty exotic, and that he packs a lot of very highly-stacked chords into his progressions (a lot more than you hear in rock and metal, and even a lot of jazz), his compositions start to sound really elaborate and baffling. I’ve heard a lot of uninitiated listeners say that it just sounds like random stuff all thrown together… but of course it isn’t.
Then when it comes time to solo, he’s basically following the same sprawling roadmap of scale degrees across the whole neck as he does when he’s building chords out of those degrees. Because he doesn’t think in terms of boxes and tends to use a lot of slurs and string-skipping techniques (in other words, his saxophone-esque approach to lead playing), he tends to play with a lot more fluidity and doesn’t fall into patterns as much as a lot of electric guitarists do. His tone also sounds a lot smoother than it would if a more conventional guitarist played through his gear. He deliberately minimizes picking because he doesn’t like the noise-to-note ratio that comes with the attack of the pick.
Another crucial thing is that Holdsworth changes scales a lot, sometimes from chord to chord. It isn’t enough for him to know all the scales everywhere on the fretboard and to bang them every which way to get his dense and bizarre chord voicings. He switches them up constantly, which, to my ears, makes the mood of any given composition evolve constantly.
That, to me, is one of the craziest things about him. Not only does he have the entire book of roadmaps memorized, but the map is constantly changing and it never fazes him. His knowledge and ability to apply all those scales in both chords and lead playing is already astonishing as it is, but he can leap in and out of those scales, chain them together, and deal with the constant changes without ever losing his train of thought or breaking the fluency of his soloing technique. That is a depth of musical knowledge that I am certain I will never achieve.
And that is probably one percent of one percent of all there is to know about Allan Holdsworth.