the.com/harmonic
every musical sound is secretly a stack of pure tones hiding in plain hearing
means Relating to the series of overtones that sound above a fundamental pitch, or more broadly to anything pleasingly proportioned or related by simple whole-number ratios.
from From Greek 'harmonikos,' from 'harmonia' — a joining, fitting, or agreement — itself from 'harmos,' a joint or fastening (think of timbers fitted snugly together). The Greeks heard music as literal proportion: Pythagoras is credited with the discovery that pleasing intervals correspond to simple ratios of string lengths, so 'harmony' carried both the sense of things fitting together and the sense of concordant sound. English took it up through Latin 'harmonicus.'
- hidden ladder
- each note contains a whole series above it
- why timbre
- harmonic mix is why violins beat trumpets apart
- math twins
- frequencies climb in tidy integer multiples
- silent killers
- power grids fight harmonic distortion daily
- the sum
- adding 1+1/2+1/3 forever never stops growing
pythagorean comma — frequency ratio of 531441/524288, the 12-note tuning system imperfection discovered by ancient greeks
fourier series — mathematical decomposition of periodic waveforms into harmonics, developed by jean-baptiste fourier in 1822
overtone series — natural acoustic phenomenon where vibrating objects (strings, air columns) produce integer multiples of a fundamental frequency