Harmonic phases in wind instruments are fixed by pulse-driven resonance, not random.

Evidence

How indeed are the relative phases of the harmonics determined under any playing conditions? Certainly they are not random, since the vocal folds (or lips, in the case of a trumpet, for example) are open in pulses, and the pressure due to a given partial should be high in the mouthpiece at the moment of the pulse to resonantly enhance that partial. This suggests a more pulsed waveform than a random choice of phases is likely to produce. It appears that further investigation of the relative phases in wind instruments, as a function of the player, instrument, lipping up or down, and so on would be very rewarding. — Eric J. Heller, Why You Hear What You Hear- An…, 2259

Categorization

• QUESTION: Interesting open research question about phase as a function of player and technique — could be worth chasing.