# Prime interval

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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⟩, ...)