# natural harmonic series

A natural harmonic series consists of the frequencies that emanate from any plucked string or other vibrating musical instrument.

If you take a string tuned to C, pinch it in the middle, and pluck it on
one side, the tone will rise exactly one octave to the next higher C. If
you divide the length by a third, it will rise a fifth, to G. As you repeat
the procedure with smaller fractions, you will produce the fourth (landing
on a yet higher C) and the third (E). These intervals are, however, different
from the ones that occur in standard modern Western tuning. The fifths are
a little wider, the thirds a little narrower. **Equal-tempered tuning**,
which came into general use in the 19th century, adjusted the intervals
so that composers could move freely and naturally among the 24 major and
minor keys. The chromatic scale was tuned into twelve equal semitones. Some
20th-century composers, among them Harry Partch, Lou Harrison, and La Monte
Young, advocated a return to 'natural' tuning, or **just intonation** as it widely known – meaning that every note you hear can be related
to the natural harmonic series.