Xjyuk

An interval holds two pitches (C an G). Those two pitches have a fundamental frequency which represents their pitch names, along with their harmonic series/overtones.

When we turn that interval into a ratio (2:3) which demonstrates that intervals level of consonance from the two pitches wave cycle synchronicity, does that ratio account for the two pitches harmonic series also or just the fundamental?

If the ratio just accounts for the fundamental frequency, is that sufficient enough to establish two pitches wave relationships without taking into account their overtone relationships also?

Thank you.

When we say that the pitch ratio between notes is 2:3, that ratio only expresses the ratio of the fundamental frequencies. However, there will of course be lots of other ratios between the harmonics of those notes which may be relevant to the perceived consonance.

Let's consider two notes each with 3 partials:

one note has a fundamental at 100Hz, and harmonics 200Hz, 300Hz
the other note has a fundamental at 150Hz, and harmonics at 300Hz, and 450Hz.

This would mean that there are actually a number of ratios going on there:

100:200 (=1:2)

100:300 (=1:3)

100:150 (=2:3)

100:450 (=2:9)

200:300 (=2:3)

200:150 (=4:3)

200:450 (=4:9)

300:150 (=2:1)

300:300 (=1:1)

300:450 (=2:3)

150:300 (=1:2)

150:450 (=1:3)

300:450 (=2:3)

Have I missed any out? anyway, you can see that even with just 3 partials in each sound, there are a whole bunch of ratios that contribute to the overall level of consonance. Imagine how many more ratios there are in a sound with more harmonics.

It is fundamentals only. Apart from the mathematical problem (how to reduce a long series of overtone coefficients into a simple ratio) just the fundamental is accessible to normal tuning. The harmonics are called tone color since they are specific to an instrument. Even for piano a different octave will exhibit different overtones.

I believe it's usually just the fundamentals, because how far in the overtone series would you be willing to go to analyse each pitch or interval set? Depending on the timbre of the sound, or the room you're in, certain overtones might resonate, and others might not. This is acoustically, though. In electronic music, you may have other ways of measuring and analyzing these things.

I'll make this an answer, because you can't embed a picture in a comment.

There are two notes, with six partials each, a total of 12 separately sounding partials, many frequency pairs. Clearly only some of the frequency pairs have a 2:3 ratio.

It's only the ratio between fundamentals. Of course, corresponding harmonics have the same ratio as their fundamentals.

The spectrum of overtones of a note depends not only on the fundamental but also on the instrument being played. Flutes have very little sound energy in their overtones; they are about as close as one can get to a pure sine wave with orchestral instruments. Clarinets lack even numbered intervals (clarinets have no octave key; it's a twelvth key.) (Because of irregularities, the clarinet does produce some even overtones.

A piano is so tightly strung (not to meant pianists), their overtones are generally sharper that the overtone series would indicate.

Taking overtones into account would complicate things without explaining much. However, Helmholtz did discuss dissonance with respect to overtones of intervals but didn't really explain things fully.