Other Harmony: Beyond Tonal and Atonal

Hundreds of Harmony Books Have Been Devoted to Tonality, and Many Have Dealt with Atonality, but This Book Considers All the Other Harmony That Has Dominated Musical Practice for At Least 50 Years. After Considering the Theories of Allen Forte, Leonhard Euler, Oliver Messian, and a Few Lesser Known Theorists, Tom Johnson Considers All Sorts of Chord Families and Introduces His Own Harmonic Practices Having to Do with Heights, Sums Modulo N, Homometric Pairs and Combinatorial Designs. the Author Writes: When I Was Young, the Virtues of Tonal Music and Atonal Music Were Strongly Debated By Composers and Theorists, All of Whom Were Quite Divided On This Subject. Nobody Seemed to Really Notice That All This Time Bartok and Others Were Writing Fine Music Without Taking a Position On One Side or the Other. I Think We Finally Need a New Harmony Book That Goes Beyond Tonal and Atonal and Considers All the Other Harmony That Has Dominated and Continues to Dominate Music." the Book's Chapters Are: 1. Introduction 2. Tonality 3. Atonality 4. Euler Harmonies 5. Hauer 6. Slonimsky 7. Obouhow 8. Schillinger 9. Messian 10. Equal and Complete 11. Heights and Sums 12. Advancing 13. Adjacent Intervals 14. Sums Modulo N 15. All-interval Tetrachords and Other Homometries 16. Block Designs 17. Parallel Classes 18. Almost Not 19. References 20. Math Addendum