Foundations of Diatonic Theory is the first introductory, undergraduate-level book published on diatonic set theory, an important but often overlooked sub-field of music theory. It provides an easy entry point into this challenging field and is appropriate for introductory music majors, motivated non-majors, music theorists, and mathematicians with musical interests.
This book supplements any Music Theory or Fundamentals of Music course which includes music theory, and is suitable for self-study of basic music theory in a mathematical context. It requires only general mathematical knowledge, and provides the solution for nearly all exercises.
This book is part of the NSF-funded Mathematics Across the Curriculum (MATC) project at Dartmouth College developed to achieve the goal of allowing students to focus on their disciplines while improving their mathematical skills.
Timothy A. Johnson is Associate 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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Timothy A. Johnson is associate professor of music theory and chair of graduate studies in music at Ithaca College. He teaches in all areas of the theory and sightsinging curriculum, ranging from introductory courses for first-year students to upper-level and graduate courses.
Johnson received the PhD in Music Theory from the University at Buffalo in 1991, the MM in Music Composition from the University of Connecticut in 1986, and the BM in Music Theory-Composition from the University of Massachusetts-Lowell.
Nixon in China Johnson's most recent book is John Adams's Nixon in China: Musical Analysis, Historical and Cultural Perspectives (Ashgate 2011). This book ties together analytical observations about the opera with cultural, political, and historical aspects of the scenes, characters, and issues raised in the opera. Johnson received a Society for Music Theory publication subvention grant in 2010 for this book. In 2006-2007 he was on sabbatical, during which he began research on this project.
Ives and Baseball Baseball and the Music of Charles Ives: A Proving Ground (Scarecrow Press, 2004) discusses the importance of baseball in Ives's life, including his participation during his youth as a pitcher and shortstop, his baseball-related compositions musical depictions of ballplayers and baseball situations), and his use of baseball analogies in his writings. Baseball was a place where Ives felt he could prove himself as a man, and baseball provided a framework within which he could build new musical ideas. Johnson was awarded the 2004 Sporting News-SABR Baseball Research Award for this book.
Diatonic Theory His textbook, Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals (Scarecrow Press, 2008; originally Key College Publishing, 2003), is the first introductory, undergraduate-level book published on diatonic set theory. This textbook introduces a strong link between introductory pedagogy and recent scholarship in music theory by relating concepts in diatonic set theory directly to the study of music fundamentals through pedagogical exercises and instructions. This book is part of the Mathematics Across the Curriculum project at Dartmouth College, funded by the National Science Foundation. This innovative project was developed to achieve the goal of allowing students to concentrate on their disciplines while using and improving their mathematical skills.
He also has authored a chapter, "Some Pedagogical Implications of Diatonic and Neo-Riemannian Theory," in Music Theory and Mathematics: Chords, Collections, and Transformations. Edited by Jack Douthett, Martha M. Hyde, and Charles J. Smith (University of Rochester Press, 2008).
Other Research Areas In previous scholarship Johnson has focused on music and baseball, the songs of Charles Ives, minimalist music, and the music of John Adams (including the first dissertation written about this enormously successful contemporary composer, as well as several related articles). In addition, Johnson has published articles or presented papers in the areas of the music and baseball, music theory pedagogy, music technology, twelve-tone theory, and the history of music theory. Johnson serves on the advisory board of The Baseball Music Project, which, in cooperation with major symphony orchestras and concert halls throughout the USA, presents concerts celebrating the National Baseball Hall of Fame through the great lineage of baseball music.
Recent Presentations Johnson recently has given presentations at the Cooperstown Symposium on Baseball and American Culture at the Baseball Hall of Fame; the Second Conference on Music and Minimalism in Kansas City; the First International Conference on Music and Minimalism in Bangor, Wales; the Music Theory Society of New York State; the Joint Mathematics Meetings of the American Mathematical Society and Mathematics Association of America; and The Society for Music Theory.
One-Year Visiting Endowed Chair In 2005-2006 he was on leave from Ithaca College to teach at the University at Buffalo as the Visiting Frederick and Alice Slee Professor of Music Theory, the oldest endowed chair in the field. Publications
John Adams's Nixon in China: Musical Analysis, Historical and Cultural Perspectives (Ashgate Publishing, 2011 forthcoming) "I Never Get Back: How 'Take Me Out to the Ball Game' Succeeds in Celebrating Failure," The National Pastime: A Review of Baseball History 28 (2008): 138-143. "Some Pedagogical Implications of Diatonic and Neo-Riemannian Theory," in Music Theory and Mathematics: Chords, Collections, and Transformations. Edited by Jack Douthett, Martha M. Hyde, and Charles J. Smith (Rochester, N.Y.: University of Rochester Press, 2008), 161-173. Baseball and the Music of Charles Ives: A Proving Ground (Lanham, Md.: Scarecrow Press, 2004). Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals (Lanham, Md.: Scarecrow Press, 2008; originally published by Emeryville, Calif.: Key College Publishing, 2003). "Chromatic Quotations of Diatonic Tunes in Songs of Charles Ives," Music Theory Spectrum 18.2 (Fall 1996): 236-261. "The Computer Presentation of Musical Research: A Case Study," Music Theory Online 1.3 (May 1995). Typical Chord Successions in the Music of John Adams: An Interactive Computer Presentation (May 1995) [a computer program originally published by Music Theory Online via ftp; no longer available]. "Minimalism: Aesthetic, Style, or Technique?" Musical Quarterly 78, no. 4 (Winter 1994): 742-773. "Harmonic Vocabulary in the Music of John Adams: A Hierarchical Approach," Journal of Music Theory 37 (Spring 1993): 117-156. "Solmization in English Treatises Around the Turn of the Seventeenth Century: A Break From Modal Theory," Theoria 5 (1990-91): 42-60.
This review is from: Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals (Mathematics Across the Curriculum) (Paperback)
Part of the Mathematics Across the Curriculum series, Foundations of Diatonic Theory IS mathematically based, but only requires basic math skills. While it claims to serve as a intro or basic music theory text, the first few chapters do not introduce interval names and thus require prior knowledge. On the other hand, it introduces relatively little mathematical skills such as greatest common divisor and coprime, avoiding modulo 12.
This instructional text is based on the latest papers in diatonic set theory. For people who took a music theory intro class and left with more questions than they began, this book is likely what they want. Why major and minor? Why the modes? Why the diatonic scale? Why the diatonic triads and seventh chords? The book leads readers through the discovery of properties of these collections which help explain their general, and some specific, uses and qualities.
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Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
maximal evenness, series initial series, first circle diagram, melodic minor collections, cardinality equals variety, different interval patterns, dinner table analogy, diatonic set theory, diatonic collection, transposed series, chromatic universe, transpose the series, pentatonic collection, diatonic theory, spatial relation puzzles, other musical structures, major half steps, stepwise notes, ascending melodic minor scale, diatonic triads, octatonic scale, harmonic sonorities, adjacent dots, property cardinality, triad qualities
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Jack Douthett, Music Theory Spectrum, Journal of Music Theory, Suggested Reading Clough, David Clampitt, Maximally Even Sets, John Clough, Using Exercises, Aspects of Diatonic Sets
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