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 nineteenth 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 twentieth-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.