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Intro -- Preface -- Organization -- Contents -- Algebraic Models -- Primal-Circular Substitutions -- Abstract -- 1 Introduction -- 2 Aesthetic and Philosophical Concerns -- 3 Primal-Circular Substitutions -- Appendix A: Primal-Circular Substitution Charts (Reproductions) -- Appendix B: Neo-Riemannian Analogues of Primal-Circular Substitutions -- References -- On the Group of Transformations of Classical Types of Seventh Chords -- 1 Introduction -- 2 The neo-Riemannian Group PLR -- 3 Transformations Between Seventh Chords -- 3.1 Transformations Between Seventh Chords -- 4 The PLRQ Group -- References -- Pairwise Well-Formed Modes and Transformations -- 1 Introduction: Authentic and Triadic Modes -- 2 Non-singular Pairwise Well-Formed Modes -- 3 Apo-syntonic Conversion -- 4 PWWF Substitutions and Automorphisms of F3 -- 5 Conclusion -- References -- Homometry in the Dihedral Groups: Lifting Sets from Zn to Dn -- 1 Introduction -- 2 The Dihedral Group Dn as a Semi-direct Product -- 3 Link with the T/I and the PLR-groups in the Case n=12 -- 4 Homometry in Dn: Formulas and Enumeration -- 5 The Concept of Lift -- Using the Fourier Transform -- 6 Conclusion -- References -- A Symmetric Quantum Theory of Modulation in ZZ20 -- 1 Introduction -- 2 Construction of the Diatonic 11-Note Microtonal Scale -- 3 Group Theory and the Harmonic Structure of Microtonal Scales -- 4 Symmetry and Modulation in ZZ ZZ ZZ ZZ12 -- 5 Symmetry and Modulation in ZZ ZZ ZZ ZZ20 -- References -- Almost Difference Sets in Transformational Music Theory -- 1 Introduction -- 2 Mathematical Preliminaries -- 2.1 Difference Sets -- 2.2 Almost Difference Sets -- 3 Musical Preliminaries -- 3.1 Generalized Interval Systems -- 3.2 Intervals and Differences -- 3.3 Total Intervallic Content and Interval Vector -- 4 PADSs in GISs -- 4.1 FLIDs and NFLIDs -- 4.2 PADSs with n = 2 -- 4.3 PADSs with n = 3 -- 4.4 PADSs with n = 4 -- 4.5 PADSs with n = 5 -- 4.6 PADSs with n = 6 -- 5 Conclusions and Future Work -- References -- Algebra of Harmony: Transformations of Just Consonances -- 1 Introduction -- 2 Harmonies -- 2.1 Basic Definitions: In the Footsteps of Euler -- 2.2 Multiplication of Harmonies -- 2.3 Inverses and Symmetries -- 2.4 Transpositional Intersection -- 3 Transformations of Harmonies -- 3.1 Schritts and Wechsels -- 3.2 Harmonic Neighborhood -- 3.3 Transformational Networks of Neighborhoods -- References -- Computer Assisted Performance -- Developing Software for Dancing Tango in Compás -- 1 Introduction -- 2 Difficulties in Dancing Tango -- 2.1 Practice of Argentinian Tango Dancing -- 2.2 Three Genres -- 2.3 Complexity of Beat -- 2.4 Instrumentation -- 3 The Problem -- 4 Compass Trainer: What, Why, How -- 4.1 Goal and Means -- 4.2 Consulting Experts -- 4.3 Abstracting the Relevant Rhythmic Information -- 4.4 User Interface -- 5 Conclusion -- References -- Using Inharmonic Strings in Musical Instruments -- 1 Ideal and Non-ideal Strings -- 2 The Hyperpiano -- 2.1 The Hyperoctave System .