Why do toneholes work well on some instruments but not others? I've noticed that with brass instruments, toneholes are almost never seen, while in woodwinds they are the primary method of changing pitch (with a few exceptions). What I have thought is that the higher registers of brass instruments no not facilitate tone holes (and the keyed trumpet actually was using register holes), though through my own experiments have noticed that even with a short lip reed instrument (well, actually, it was just a length of PVC pipe) toneholes were becoming weak even in the first register and with only a few holes uncovered. I have tried to find more information on this, but I've not found anything that covers why higher harmonics would have a problem with this.
The physical principles of tone holes are the same for all instruments, and in fact they were widely used in brass instruments before the invention of reliable valves. The problem is that too many holes in the thin metal material degrade the specific "metallic" tone quality that we want these instruments for.
(Why brass tubes are more susceptible to this problem than wooden tubes (material or geometry?), I don't know. Maybe instrumentalists and composers are just more nitpicking about their tone quality - many composers refused to allow either tone holes or valves in their brass instruments even after the modern versions were invented and continued to require at least some natural horns in their scores, to produce the purest possible rendering of important chords.)
Well, that's part of it. It's also because brass instruments produce near-perfect square waves, and tone holes break them up. The sine(flute) or triangle (reed) waveforms aren't so picky, so to speak. It's also a LOT harder to force the overtone series with a reed-based mouthpiece than with vibrating lips (which drive all brass instruments). Jul 30, 2013 at 18:08
@CarlWitthoft Brass instruments don't produce square waves. Clarinets do, however, even with all those tone holes.– phoogSep 11, 2020 at 3:58
@phoog It's not that simple. Single-reeds don't produce a square wave -ish thing except perhaps at very high frequencies. They only generate odd harmonics, but with amplitude ratios that don't make a very clean 'triangle' . Trumpet shape looks a lot like an asymmetric square wave with a little overshoot, but again player skill and note range affects that. Sep 11, 2020 at 12:33
@CarlWitthoft then why doesn't a trumpet sound anything like a square wave?– phoogSep 11, 2020 at 15:05