limit

1. prime limit: A pitch system in Just Intonation where all ratios are of integers containing no prime factors higher than n is said to be an "n-limit" system.

2. odd limit: A chord in Just Intonation where all ratios are of integers containing no odd factors higher than n is said to be an "n-limit" chord. A composition or style where chords of the n-limit are considered consonant and chords of any higher limit are considered dissonant is said to be an "n-limit" composition or style. Note that this may not agree with the "prime limit" definition.

[from Paul Erlich]

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A pitch system in Just Intonation whose ratios contain the prime number n and no higher primes is said to be an "n-Prime-Limit" system.

By usage, certain odd non-primes such as 9, 15, and 21 may also be said to define "n-limit" systems.

[from John Chalmers, Divisions of the Tetrachord]

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