Harmonic Series In Music

Harmonic Series in Music

In calculus we learn about sequences and series, and more specifically a series called the harmonic series, or overtones series in music, which gets its name from the mathematical relationships within music between notes and pitches and frequencies. When someone hears a note they are actually hearing a periodic sequence of vibrations in which the sound enters their ear as a sine wave that is compressed in the air in a periodic pattern. Similarly, when one hears a pitch, they aren’t hearing one pitch alone but rather a series of notes that when combined create that pitch. This is called the pitch’s harmonic series. For example, in a pitch producing source like a piano string vibrates not just as a whole string but as

The fundamental frequency of an instrument is the lowest frequency produced and is also called an instruments’ first harmonic. When multiplying a fundamental frequency by integers, an individual harmonic series will result. The numerator of the ratios from the harmonic series is the multiple from the fundamental frequency and the denominator is the number of octaves, the eighth degree from a given tone, that are between the

The numbers 1,2,3, and 4 are proportional to the frequencies of the tones; the larger the number the higher the pitch. The names fourth, fifth, and octave come from the ordering of tones of an 8-tone diatonic scale. (tone relating to 1 is called tonic). The notes that are played by an instrument are not heard in their pure and basic sound wave but rather along with something called overtones. The harmonic progression describes the change in wavelength between notes. halving the wavelength doubles the frequency giving the octave, then taking a third of the original frequency gives the fifth. Overtones are notes whose frequencies are an exact multiple of the fundamental, and are essentially