Prime interval

A prime interval or prime harmonic is a musical interval which as a ratio of frequencies is a prime number; that is, a number such as 2, 3, 5, 7, 11, … which is divisible only by itself and 1. Any musical interval in the p-limit can be expressed in terms of a product of prime numbers less than or equal to p.

For example, the octave is a prime interval whereas the intervals 5/3 or even 1/1 are not. In traditional ratio notation, the prime intervals are 2/1, 3/1, 5/1, 7/1, 11/1 etc.

The monzo notation of each prime interval consists of all-zeros except for a single unity entry: (2: [1⟩, 3: [0 1⟩, 5: [0 0 1⟩, 7: [0 0 0 1⟩, 11: [0 0 0 0 1⟩, …)

Individual pages

See Category: Prime harmonics.

See also

• Patent val
• Harmonic limit
• Prime harmonic series