A Musical Scale Generated from the Ratio of Consecutive Primes

Reginald Bain
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)
Pages 407–410 Short Papers


This paper describes a 12-note musical scale generated from the ratio of consecutive prime numbers that is used as the basis for the author's electronic composition The Music of the Primes. The scale is a type of extended just intonation, a tuning system whose intervals are derived from the harmonic (overtone) series and uses partials above the first six partials. The ratio of consecutive primes sequence makes a potentially infinite number of prime ratios available to the composer.