Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals

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Scarecrow Press, 2008 - Mathematics - 194 pages
Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals is an introductory, undergraduate-level textbook that provides an easy entry point into the challenging field of diatonic set theory, a division of music theory that applies the techniques of discrete mathematics to the properties of diatonic scales. After introducing mathematical concepts that relate directly to music theory, the text concentrates on these mathematical relationships, firmly establishing a link between introductory pedagogy and recent scholarship in music theory. It then relates concepts in diatonic set theory directly to the study of music fundamentals through pedagogical exercises and instructions. Ideal for introductory music majors, the book requires only a general knowledge of mathematics, and the exercises are provided with solutions and detailed explanations. With its basic description of musical elements, this textbook is suitable for courses in music fundamentals, music theory for non-music majors, music and mathematics, and other similar courses that allow students to improve their mathematics skills while pursuing the study of music.
 

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Contents

Introduction
1
Mathematics and Music
2
How to Use this Book
4
Spatial Relations and Musical Structures
5
Musical Structures form Geometric Figures
15
An Intervallic Definition
26
Summary and Extensions
39
Interval Patterns and Musical Structures
45
Summary and Extensions
103
Triads and Seventh Chords and Their Structures
107
Maximally Even Triads and Seventh Chords
108
Variety and Multiplicity of Diatonic Chords
129
Summary and Extensions
141
Conclusion
143
For Further Study
147
Notes
153

Interval Patterns in Other Scales
66
Interval Patterns and the Circle of Fifths
79
Structure in Other Collections
95
Sources Cited
159
Index
163
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About the author (2008)

Timothy A. Johnson is Professor of Music Theory at Ithaca College and Chair of Graduate Studies in Music. He is the author of Baseball and the Music of Charles Ives: A Proving Ground (Scarecrow Press, 2004).

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