Is our thinking of "audio" in terms of frequencies correct?
We do know sound is composed of vibrations, and hence sine waves.
But audio is not sound, audio is the brain's response to a specific range of sound.
Audio could be a macroscopic effect fundamentally, and a single frequency could simply be perceived as a combination of tones.
For example, as ((tone a + tone b) - (tone c + tone d))
The combination of the tones 'a' and 'b' could have a set of harmonics close to the combination of the tones 'c' and 'd'.
That is to say, the brain could only understand tones, not individual frequencies.
This is similar to how our eyes do not really understand specific frequencies of electromagnetic waves, but only the spectral response of the Tristimulus from the different types of photocells in our eyes.
As for mathematical modelling, that would mean audio is not an effect formed directly sound, but is an effect formed from the perceived tones, which are directly formed from sound.
In another way of thinking, is music composed of "beats"?

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