Note that in historical Byzantine musical culture, there are no absolute pitches at all. Their notational form is entirely intervals from some arbitrary root note.

Similarly, in Carnatic and Hindustani classical traditions, the note names (Sa, Re, Pa etc) do not denote pitches - Sa is always the root, whatever it is, and the rest have a somewhat well defined intervallic relationship to it.

I personally would not use "harmonic value" to describe this, since it occurs in music that (broadly speaking) lacks harmony. The key point, IMO, is that what matters are sets of intervals (ratios, if you prefer) rather than actual pitches (as frequencies).