the.com/harmonic series

means A sequence of numbers or frequencies built from whole-number ratios of a fundamental (1, 1/2, 1/3, 1/4…) — in math it's the sum 1 + 1/2 + 1/3 + 1/4 + … which diverges, and in music/physics it's the stack of overtones above a fundamental pitch.

from The name comes from music theory: the overtones a vibrating string produces sit at frequencies that are whole-number multiples of the fundamental, and these pleasing, consonant ratios were called 'harmonic.' Mathematicians borrowed the term for the sequence 1, 1/2, 1/3, 1/4… because each term is related to the one before it the same way harmonic frequencies relate to each other — specifically, each term is the 'harmonic mean' pattern of its neighbors. So the math use is a direct loan from acoustics, not the other way around.