1

So the most basic sound wave is a sinusoid

for a frequency F, we can create the wave using

sin(F*2pi)

We can add harmonic to make the sound richer:

sin(F*2pi) + sin(2F*2pi)

My question is regarding the phasing of the two sin, does it affect the resulting sound if I shift the harmonics by a constant K:

sin(F*2pi) + sin(2F*2pi + K)

I generated the sound and I can't hear a difference, but it's difficult to know for sure, especially what would happen with more than 2 sinusoid

3

The effect of changing the phase of a harmonic, might simply equate to (acoustically) that particular harmonic coming (to the ears) from a slightly different distance than the fundamental. Thinking about it like this, I would have to say that the probability of it 'changing' the sound is quite limited.

You are more likely to get a change in timbre of the overall sound if the relative level of the harmonic is changed than the phase. Additionally, a change in frequency of the harmonic would also result in a change in timbre.

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