The overtone series above results from the fact that a vibrating body, such as an acoustic instrument, subdivides itself into an infinite series of integer fractions (1/2, 1/3, 1/4, 1/5, etc). These subdivisions produce frequencies (harmonics)that are integral multiples of the fundamental (2F, 3F, 4F, 5F, etc.). The series above is based on the fundamental C and is limited to the first sixteen overtones. A series may be built on any pitch and is infinite. Overtone 7 and 11 are approximately half way between the two pitches indicated. They are naturally occurring “blue notes.” Instruments that are rich in overtones produce vibrant, brilliant tones.

You can calculate the frequency ratio of any interval by locating it on the harmonic series. For example, the ratio of an octave is 2:1. The ratio of a perfect 5th is 3:2.