This reminded me of student-days discussion between me (physics student) and my wife (music theory student), when I explained harmonics from a physics standpoint. In musical acoustics, “overtones” are very important and are usually assumed to be harmonic (in the mathematical sense), but some instruments like kettledrums have overtones that are Bessel functions instead of integer harmonics since they are two-dimensional objects instead of one-dimensional violin strings or organ pipes.
Anyway, the library had very old books on music theory that discussed “undertones”. The proof of these alleged frequency components was that if you lift the dampers on a piano and hit middle-C, the lower Cs (octaves below the note) are excited. Spectral analysis can be subtle.