The major scale is maximally even. For example, for every generic interval of a second there are only two possible specific intervals: 1 semitone (a minor second) or 2 semitones (a major second).
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 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 propertyedit
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 cardinality equals variety, structure implies multiplicity, and being a well formed generated collection. In other words, each generic interval can be made from one of two possible different specific intervals. For example, there are major or minor and perfect or augmented/diminished variants of all the diatonic intervals:
Diatonic interval
Generic interval
Diatonic intervals
Specific intervals
2nd
1
m2 and M2
1 and 2
3rd
2
m3 and M3
3 and 4
4th
3
P4 and A4
5 and 6
5th
4
d5 and P5
6 and 7
6th
5
m6 and M6
8 and 9
7th
6
m7 and M7
10 and 11
The diatonic and pentatonic collections possess Myhill's property. The concept appears to have been first described by John Clough and Gerald Myerson and named after their associate the mathematician John Myhill. (Johnson 2003, p. 106, 158)
Sourcesedit
Johnson, Timothy (2003). Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. ISBN1-930190-80-8.
Further readingedit
Clough, Engebretsen, and Kochavi. "Scales, Sets, and Interval Cycles": 78–84.
January 01, 1970
generic, specific, intervals, diatonic, theory, generic, interval, number, scale, steps, between, notes, collection, scale, largest, generic, interval, less, than, number, scale, members, johnson, 2003, major, scale, maximally, even, example, every, generic, i. 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 The major scale is maximally even For example for every generic interval of a second there are only two possible specific intervals 1 semitone a minor second or 2 semitones a major second 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 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 Myhill s property editMyhill 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 cardinality equals variety structure implies multiplicity and being a well formed generated collection In other words each generic interval can be made from one of two possible different specific intervals For example there are major or minor and perfect or augmented diminished variants of all the diatonic intervals Diatonic interval Generic interval Diatonic intervals Specific intervals 2nd 1 m2 and M2 1 and 2 3rd 2 m3 and M3 3 and 4 4th 3 P4 and A4 5 and 6 5th 4 d5 and P5 6 and 7 6th 5 m6 and M6 8 and 9 7th 6 m7 and M7 10 and 11 The diatonic and pentatonic collections possess Myhill s property The concept appears to have been first described by John Clough and Gerald Myerson and named after their associate the mathematician John Myhill Johnson 2003 p 106 158 Sources editJohnson Timothy 2003 Foundations of Diatonic Theory A Mathematically Based Approach to Music Fundamentals Key College Publishing ISBN 1 930190 80 8 Further reading editClough Engebretsen and Kochavi Scales Sets and Interval Cycles 78 84 Retrieved from https en wikipedia org w index php title Generic and specific intervals amp oldid 1070787604, wikipedia, wiki, book, books, library,
