Humming seems to map to the vocal-nasal tract.
Here is a mapping with the Vocal Tract, Western Scale and Indian Solfege.
C Lower throat Sa(1)
D Adams’s Apple Re(2)
E Throat Opening Ga(3)
F Vibrating Thing Ma(4)
G Below nose opening Pa(5)
A Nasal roof Dha(6)
B Highest pitch Ni(7)
Going by numbers alone instead of letters is useful for mod 7 arithmetic.
Given l the length of the string, all notes in ratios of 3^m / 2^n between l and l / 2 are harmonic.