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Interval class Play ⓘ.. In musical set theory, an interval class (often abbreviated: ic), also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval mod 6'" (Rahn 1980, 29; Whittall 2008, 273–74), is the shortest distance in pitch class space between two unordered pitch classes.
Octave and augmented second on pitch class C. The ordered pitch class interval is 3. The unordered pitch class interval is 'interval class 3' which is also used to describe major 6th. Play ⓘ. In musical set theory, pitch-class intervals do not distinguish between octaves since pitch-classes themselves treat all octaves as being equivalent.
The difference between the interval vector of a set and that of its complement is <X, X, X, X, X, X/2>, where (in base-ten) X = 12 – 2C, and C is the cardinality of the smaller set. In nearly all cases, complements of unsymmetrical sets are inversionally related—i.e. the complement of an "A" version of a set of cardinality C is (usually ...
In this system, intervals are named according to the number of half steps, from 0 to 11, the largest interval class being 6. In atonal or musical set theory, there are numerous types of intervals, the first being the ordered pitch interval, the distance between two pitches upward or downward. For instance, the interval from C upward to G is 7 ...
Forte provided each set class with a number of the form c–d, where c indicates the cardinality of the set and d is the ordinal number. [18] Thus the chromatic trichord {0, 1, 2} belongs to set-class 3–1, indicating that it is the first three-note set class in Forte's list. [19]
Comparison between tunings: Pythagorean, equal-tempered, quarter-comma meantone, and others.For each, the common origin is arbitrarily chosen as C. The degrees are arranged in the order or the cycle of fifths; as in each of these tunings except just intonation all fifths are of the same size, the tunings appear as straight lines, the slope indicating the relative tempering with respect to ...
A specific interval is the clockwise distance between pitch classes on the chromatic circle (interval class), in other words the number of half steps between notes. The largest specific interval is one less than the number of "chromatic" pitches. In twelve tone equal temperament the largest specific interval is 11. (Johnson 2003, p. 26)
In music, an interval cycle is a collection of pitch classes created from a sequence of the same interval class. [1] In other words, a collection of pitches by starting with a certain note and going up by a certain interval until the original note is reached (e.g. starting from C, going up by 3 semitones repeatedly until eventually C is again reached - the cycle is the collection of all the ...