Goldonic series

A goldonic series or golden series is a series of frequencies that form a geometric progression whose generating interval is the golden ratio (φ = 1.618...).

Unique properties

The goldonic series is unique among geometric sequences because only φ satisfies the equation [math]x^{n-1} + x^n = x^{n+1}[/math].

From an acoustic standpoint, the goldonic series contains some "harmonic-like" characteristics despite being inharmonic. Because each term is equal the difference between the next highest and next lowest terms, a phenomenon similar to modelocking can occur (in which each oscillator becomes entrained to the difference tone generated by its nearest-neighbors).

Also, unlike the harmonic series, the goldonic series can be in theory extended infinitely in both directions and contains no fundamental.