A term and acronym used to describe musical tunings calculated by ratios of integers. RI is generally specifically reserved for tunings whose ratios have large numbers, to distinguish these types of tunings from those with small-integer terms and/or an audible property of containing many very concordant intervals. The latter is a special case of RI subsets called "just intonation" or JI, whereas RI is the more general category of tunings which includes all JI tunings.
A notorious example of an RI which is not synonymous with JI is the original (1935 to 1975) tuning of the Hammond organ.
Another excellent example of an RI is the tuning of the frequencies actually used by Karlheinz Stockhausen in his landmark 1954 electronic composition Studie II, which depart (in some cases significantly) from his ideal 25ed5 tuning, because of the limitations of the oscillators at his disposal.
The rational-intonation acronym RI is not to be confused with the Sanskrit syllable "ri", which is used in Indian music and music-theory.
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