I disagree. A sine wave has no overtones but we can still easily perceive the octave notes.
Also overtones don't have to be even multiples of the fundamental. Many organs have stops that are not multiples of the fundamental. 2-2⁄3′, 1-3⁄5' are common flute stops.
> I disagree. A sine wave has no overtones but we can still easily perceive the octave notes.
Sure we can. Does the explanation given above require that we shouldn't? Of course, laying sines an octave apart is a good first step to building a simple additive synth that doesn't sound as dull as a pure sine. In that case, are you adding a note or an overtone? If anything, to me this only makes the given explanation more credible. The relationship between common naturally occurring harmonic overtones and the octave.
> Also overtones don't have to be even multiples of the fundamental. Many organs have stops that are not multiples of the fundamental. 2-2⁄3′, 1-3⁄5' are common flute stops.
Sure, there are dissonant sounding instruments as well as instruments that can sound more like a chord when a single note is played. Of course, we can synthesize anything. On the other hand, many instruments are prone to producing overtones that increasingly deviate from the harmonic series. And many tricks are employed to try and reduce that effect, because it doesn't sound good.
Also overtones don't have to be even multiples of the fundamental. Many organs have stops that are not multiples of the fundamental. 2-2⁄3′, 1-3⁄5' are common flute stops.