Generic interval
Encyclopedia
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)
In the diatonic collection the generic interval is one less than the corresponding diatonic interval:
The largest generic interval in the diatonic scale being 7-1 = 6.
Myhill's property
is the quality of musical scales or collections with exactly two specific interval
s 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 generic interval is the number of scale steps between notes of a collection
Set (music)
A set in music theory, as in mathematics and general parlance, is a collection of objects...
or scale. The largest generic 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 scale members. (Johnson 2003, p.26)
In the diatonic collection the generic interval is one less than the corresponding diatonic interval:
- Adjacent intervals, secondSecondThe second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
s, are 1 - ThirdThirdThird may refer to:*3 , such as the 3rd of something -see also Ordinal number *Fraction , such as 1/3*1/60 of a second, or 1/3,600 of a minute *Third World, economically underdeveloped nations...
s = 2 - FourthFourthFourth can refer to:* ¼, one quarter* Fourth, the ordinal number following third* Preceded by the, refers to the United States holiday of Independence Day, celebrated on the fourth of July.-Music:* Perfect fourth in music theory...
s = 3 - FifthFifthFifth is the ordinal form of the number five.Fifth may refer to:* Fifth Amendment to the United States Constitution, as in the expression "Pleading the Fifth"* Fifth column - a political term...
s = 4 - SixthSixthSixth can refer to:* The ordinal form of the number six* Sixth Amendment to the U.S. Constitution* A keg of beer equal to 5 U.S. gallons or 1/6 barrel of beer.* A fraction, such as 1/6-Music:*Interval*Major sixth*Minor sixth...
s = 5 - SeventhSeventhSeventh may refer to:* Seventh Amendment to the United States Constitution-Music:* Diminished seventh, a chromatically reduced minor seventh interval...
s = 6
The largest generic interval in the diatonic scale being 7-1 = 6.
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 interval
Specific interval
In diatonic set theory a specific interval is the shortest possible clockwise distance between pitch classes on the chromatic circle , 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...
s for every generic interval. 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.