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In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth is 3:2 ], 1.5, and may be approximated by an equal tempered perfect fifth ] which is 2. If the A above middle C is 440 Hz, the perfect fifth above it would be E, at 660 Hz, while the equal tempered E5 is 659.255 Hz.
Ratios, rather than direct frequency measurements, allow musicians to work with relative pitch measurements applicable to many instruments in an intuitive manner, whereas one rarely has the frequencies of fixed pitched instruments memorized and rarely has the capabilities to measure the changes of adjustable pitch instruments. Ratios have an inverse relationship to string length, for example stopping a string at two-thirds its length produces a pitch one and one-half that of the open string ].
Intervals may be ranked by relative consonance and dissonance. As such ratios with lower integers are generally more consonant than intervals with higher integers. For example, 2:1 ], 4:3 ], 9:8 ], 65536:59049 ], etc.
Consonance and dissonance may more subtly be defined by limit, wherein the ratios whose limit, which includes its integer multiples, is lower are generally more consonant. For example, the 3-limit 128:81 ] and the 7-limit 14:9 ]. Despite having larger integers 128:81 is less dissonant than 14:9, as according to limit theory.