In music,
just intonation (sometimes abbreviated as
JI) or
pure intonation is any
musical tuning in which the
frequencies of
notes are related by
ratios of
small whole numbers. Any
interval tuned in this way is called a
pure or
just interval. The two notes in any just interval are members of the same
harmonic series. Frequency ratios involving large integers such as 1024:729 are not generally said to be justly tuned. "Just intonation is the tuning system of the later ancient Greek modes as codified by
Ptolemy; it was the aesthetic ideal of the Renaissance theorists; and it is the tuning practice of a great many musical cultures worldwide, both ancient and modern."