Chapter Two. Flip-Flop Circles and Their Groups

Chapters in this book

1. Frontmatter i
2. Contents v
3. Preface vii
4. Introduction 1
5. Chapter One “Cardinality Equals Variety for Chords” in Well-Formed Scales, with a Note on the Twin Primes Conjecture 9
6. Chapter Two. Flip-Flop Circles and Their Groups 23
7. Chapter Three. Pitch-Time Analogies and Transformations in Bartók’s Sonata for Two Pianos and Percussion 49
8. Chapter Four. Filtered Point-Symmetry and Dynamical Voice-Leading 72
9. Chapter Five The “Over-Determined” Triad as a Source of Discord: Nascent Groups and the Emergent Chromatic Tonality in Nineteenth-Century German Harmonic Theory 107
10. Chapter Six. Signature Transformations 137
11. Chapter Seven. Some Pedagogical Implications of Diatonic and Neo-Riemannian Theory 161
12. Chapter Eight. A Parsimony Metric for Diatonic Sequences 174
13. Chapter Nine. Transformational Considerations in Schoenberg’s Opus 23, Number 3 197
14. Chapter Ten. Transformational Etudes: Basic Principles and Applications of Interval String Theory 222
15. Works Cited 245
16. Contributors 253
17. Index 257