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variations in timbreGood insight, but these variations are correlated with variations in pitch. It's a single note in the sense that it's always a C; not necessarily always the same octave.
> horns [...] can only play one note
A piece in bugle scale doesn't sound like one note to an average listener, nor does playing such an instrument feel like staying on one note. I'd rather compare this to a didgeridoo than a horn.
But if I concede that we don't need to adhere to lower grade music theory and that the performer will not use advanced techniques that can alter pitch without the use of a slide or valve, what argument could be made to support the "one note" claim?
To clarify what I'm looking for, here's an example of such an argument (but I don't know how much, if at all, it applies to actual fixed-length horn instruments): If the exact frequencies of a note's overtones deviate from a pure harmonic series, one could make a distinction between pitch-shifting a note and varying the timbre. I.e. playing the next note above the instrument's fundamental pitch doesn't multiply the individual frequencies by a constant factor, but repeats the exact frequencies of the fundamental's overtones, thus reordering the frequency ratios between adjacent overtones.