13-limit: Difference between revisions
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{{Prime limit navigation|13}} | |||
The '''13-limit''' or 13-prime-limit consists of [[just intonation]] intervals such that the highest [[prime number]] in all ratios is 13. Thus, [[40/39]] would be allowable, since 40 is 2 × 2 × 2 × 5 and 39 is 3 × 13, but 34/33 would not be allowable, since 34 is 2 × 17, and [[17-limit|17]] is a prime number higher than 13. An interval doesn't need to contain a 13 to be considered within the 13-limit. For instance, [[3/2]] is considered part of the 13-limit, since the primes 2 and 3 are smaller than 13. Also, an interval with a 13 in it is not necessarily within the 13-limit. [[23/13]] is not within the 13-limit, since [[23-limit|23]] is a prime number higher than 13. | The '''13-limit''' or 13-prime-limit consists of [[just intonation]] intervals such that the highest [[prime number]] in all ratios is 13. Thus, [[40/39]] would be allowable, since 40 is 2 × 2 × 2 × 5 and 39 is 3 × 13, but 34/33 would not be allowable, since 34 is 2 × 17, and [[17-limit|17]] is a prime number higher than 13. An interval doesn't need to contain a 13 to be considered within the 13-limit. For instance, [[3/2]] is considered part of the 13-limit, since the primes 2 and 3 are smaller than 13. Also, an interval with a 13 in it is not necessarily within the 13-limit. [[23/13]] is not within the 13-limit, since [[23-limit|23]] is a prime number higher than 13. | ||