5-limit: Difference between revisions
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{{Wikipedia|Five-limit tuning}} | {{Wikipedia|Five-limit tuning}} | ||
The '''5-limit''' consists of all [[just intonation]] intervals whose numerators and denominators are both products of the primes 2, 3, and 5; these are sometimes called [[wikipedia: Regular number|regular numbers]]. Some examples of 5-limit intervals are [[5/4]], [[6/5]], [[10/9]] and [[81/80]]. The [[5-odd-limit]] consists of intervals whose numerators and denominators, when all factors of two have been removed, are less than or equal to 5. Reduced to an octave, these are the ratios 1/1, 6/5, 5/4, [[4/3]], [[3/2]], [[8/5]], [[5/3]], [[2/1]]. Approximating these ratios has been basic to Western common-practice music since the Renaissance. | The '''5-limit''' consists of all [[just intonation]] intervals whose numerators and denominators are both products of the primes 2, 3, and 5; these are sometimes called [[wikipedia: Regular number|regular numbers]]. Some examples of 5-limit intervals are [[5/4]], [[6/5]], [[10/9]] and [[81/80]]. The [[5-odd-limit]] consists of intervals whose numerators and denominators, when all factors of two have been removed, are less than or equal to 5. Reduced to an octave, these are the ratios 1/1, 6/5, 5/4, [[4/3]], [[3/2]], [[8/5]], [[5/3]], [[2/1]]. Approximating these ratios has been basic to Western common-practice music since the Renaissance. | ||