A simple interval (i.e., an interval smaller than or equal to an octave) may be inverted by raising the lower pitch an octave, or lowering the upper pitch an octave. For example, the fourth from a lower C to a higher F may be inverted to make a fifth, from a lower F to a higher C.
There are two rules to determine the number and quality of the inversion of any simple interval:<ref>Kostka, Stephen; Payne, Dorothy (2008). Tonal Harmony, p. 21. First Edition, 1984.</ref>
- The interval number and the number of its inversion always add up to nine (4 + 5 = 9, in the example just given).
- The inversion of a major interval is a minor interval, and vice versa; the inversion of a perfect interval is also perfect; the inversion of an augmented interval is a diminished interval, and vice versa; the inversion of a doubly augmented interval is a doubly diminished interval, and vice versa.
For example, the interval from C to the E♭ above it is a minor third. By the two rules just given, the interval from E♭ to the C above it must be a major sixth.
Since compound intervals are larger than an octave, "the inversion of any compound interval is always the same as the inversion of the simple interval from which it is compounded."<ref>Prout, Ebenezer (1903). Harmony: Its Theory and Practice, 16th edition. London: Augener & Co. (facsimile reprint, St. Clair Shores, Mich.: Scholarly Press, 1970), p. 10. ISBN 0-403-00326-1.</ref>
For intervals identified by their ratio, the inversion is determined by reversing the ratio and multiplying by 2. For example, the inversion of a 5:4 ratio is an 8:5 ratio.
For intervals identified by an integer number of semitones, the inversion is obtained by subtracting that number from 12.
Since an interval class is the lower number selected among the interval integer and its inversion, interval classes cannot be inverted.
Interval (music) sections
Intro Size Main intervals Interval number and quality Shorthand notation Inversion Classification Minute intervals Compound intervals Intervals in chords Size of intervals used in different tuning systems Alternative interval naming conventions Pitch-class intervals Generic and specific intervals Generalizations and non-pitch uses See also Notes [[Interval_(music)?section=</a>_External_links_|</a> External links ]]
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