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. (Johnson 2003, p.26) Diatonic set theory is a subdivision or application of musical set theory which applies the techniques and insights of set theory to properties of the diatonic collection such as maximal evenness, Myhills property, well formedness, the deep scale property, cardinality equals variety, and structure implies multiplicity. ... See also: Dance step, Stairway. ... In common usage, a collection is any group of items that has one or more properties in common. ... In music, a scale is an unordered collection of notes or pitches, as opposed to a series of intervals, which is a musical mode. ... In music theory, an interval is the distance in pitch between two notes, the lower and higher members of the interval. ...

In the diatonic collection the generic interval is one less than the corresponding diatonic interval:

• Adjacent intervals, seconds, are 1
• Thirds = 2
• Fourths = 3
• Fifths = 4
• Sixths = 5
• Sevenths = 6

The largest generic interval in the diatonic scale being 7-1 = 6. This article is about the unit of time. ... In music, see the following intervals: Major third Minor third The mediant, and the chord built on the mediant, is often called simply the third, as it is the third degree of the diatonic scale. ... In music, see: Perfect fourth Augmented fourth or tritone The subdominant, and the chord built on the subdominant, is often simply called the fourth as it is the fourth scale degree. ... A fifth may mean any of three things: 1. ... In music, see the intervals: Major sixth minor sixth The submediant, and the chord built on the submediant, is often simply called the sixth as it is the sixth scale degree. ... In music, see the intervals: Major seventh minor seventh The leading tone or subtonic, and the chord built on the leading tone, is often called simply the seventh as it is the seventh scale degree. ...

See also: specific interval.

Source

• Johnson, Timothy (2003). Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. ISBN 1930190808.