harmonic series Algorithm

Its name infers from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's fundamental wavelength. Every term of the series after the first is the harmonic mean of the neighboring terms; the phrase harmonic mean besides infers from music. 

This was so particularly in the Baroque period, when architects used them to establish the proportions of floor plans, of elevations, and to establish harmonic relationships between both interior and exterior architectural details of churches and palaces. proof were given in the 17th century by Pietro Mengoli, Johann Bernoulli, and Jacob Bernoulli. The deviation of the harmonic series was first proven in the 14th century by Nicole Oresme, but this accomplishment fall into obscurity.

harmonic series source code, pseudocode and analysis