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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.
Interval cycles, "unfold [i.e., repeat] a single recurrent interval in a series that closes with a return to the initial pitch class", and are notated by George Perle using the letter "C", for cycle, with an interval-class integer to distinguish the interval. Thus the diminished-seventh chord would be C3 and the augmented triad would be C4.
Similarly, the 'augmented fourth' and the 'diminished fifth' both correspond to 'interval class 6'. There is no 'interval class 7' therefore, since counting down five semitones can describe the perfect fifth more parsimoniously that counting up seven semitones can. A visual way to do determine an unordered pitch-class interval is to place the ...
Sets marked with a "Z" refer to a pair of different set classes with identical interval class content unrelated by inversion, with one of each pair listed at the end of the respective list when they occur. ("Z" is derived from the prefix zygo-, from Ancient Greek ζυγόν, "yoke". Hence: zygosets.) "T" and "E" are conventionally used in sets ...
One method is to use intervals as a basis. The smallest value in the above data is 8 and the largest is 34. The interval from 8 to 34 is broken up into smaller subintervals (called class intervals). For each class interval, the number of data items falling in this interval is counted. This number is called the frequency of that
By definition, every interval in a given limit can also be part of a limit of higher order. For instance, a 3-limit unit can also be part of a 5-limit tuning and so on. By sorting the limit columns in the table below, all intervals of a given limit can be brought together (sort backwards by clicking the button twice).
Successive Z-related hexachords from act 3 of Wozzeck [4]: 79 Play ⓘ. In musical set theory, a Z-relation, also called isomeric relation, is a relation between two pitch class sets in which the two sets have the same intervallic content (and thus the same interval vector) but they are not transpositionally related (are of different T n-type ) or inversionally related (are of different T n /T ...
The largest generic interval is one less than the number of scale members. (Johnson 2003, p. 26) 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 ...