Prime interval: Difference between revisions
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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 [[Harmonic limit|''p''-limit]] can be expressed in terms of a product of prime numbers less than or equal to ''p''. | 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 [[Harmonic limit|''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. | For example, the [[2/1|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 | The [[monzo]] notation of each prime interval consists of all-zeros except for a single unity entry: (2: {{monzo| 1 }}, 3: {{monzo| 0 1 }}, 5: {{monzo| 0 0 1 }}, 7: {{monzo| 0 0 0 1 }}, 11: {{monzo| 0 0 0 0 1 }}, …) | ||
== See also == | == See also == | ||
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[[Category:Terms]] | [[Category:Terms]] | ||
[[Category:Prime]] | [[Category:Prime]] | ||
[[Category: | [[Category:Harmonic]] | ||
[[Category:Todo:review]] | [[Category:Todo:review]] | ||
[[Category:Todo:expand]] | [[Category:Todo:expand]] | ||
Revision as of 14:25, 1 April 2025
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⟩, …)