Specific interval
Encyclopedia
In diatonic set theory
a specific interval is the shortest possible clockwise distance between pitch class
es 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)
Myhill's property
is the quality of musical scales or collections with exactly two specific intervals for every generic interval
. In other words, each generic interval can be made from one of two possible different specific intervals.
Diatonic set theory
Diatonic set theory is a subdivision or application of musical set theory which applies the techniques and insights of discrete mathematics to properties of the diatonic collection such as maximal evenness, Myhill's property, well formedness, the deep scale property, cardinality equals variety, and...
a specific interval is the shortest possible clockwise distance between pitch class
Pitch class
In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves...
es on the chromatic circle
Chromatic circle
The chromatic circle is a geometrical space that shows relationships among the 12 equal-tempered pitch classes making up the familiar chromatic scale...
(interval class
Interval class
In musical set theory, an interval class , also known as unordered pitch-class interval, interval distance, undirected interval, or interval mod...
), in other words the number of half steps between notes. The largest specific interval
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
is one less than the number of "chromatic" pitches. In twelve tone equal temperament the largest specific interval is 11. (Johnson 2003, p.26)
Myhill's property
Myhill's property
In diatonic set theory Myhill's property is the quality of musical scales or collections with exactly two specific intervals for every generic interval, and thus also have the properties of maximal evenness, cardinality equals variety, structure implies multiplicity, and be a well formed generated...
is the quality of musical scales or collections with exactly two specific intervals for every generic interval
Generic interval
In diatonic set theory a generic interval is the number of scale steps between notes of a collection or scale. The largest generic interval is one less than the number of scale members...
. In other words, each generic interval can be made from one of two possible different specific intervals.
Source
- Johnson, Timothy (2003). Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. ISBN 1-930190-80-8.