Study multi-dimensional musical space through Symmetrical Polytonality, a theoretical framework for polysymmetrical pitch systems and harmonic environments. This advanced music theory text delves into the following topics:
Symmetrical Polytonality: Understand the interplay between harmonic symmetry and the overtone series, and how they drive tonal harmony.
Multi-Dimensional Harmonic Vectors: Explore how symmetrical harmonic elements create multi-directional relationships and dimensionality in musical space.
Harmonic Drive and Resolution: Learn about the mechanisms of harmonic tension and resolution, including the role of symmetrical intervals like tritones, augmented triads, and diminished seventh chords.
Symmetrical Pitch Sets: Discover the structural characteristics of polysymmetrical scales, including DimSet, BiOct, and NSet, and their unique chord pods.
Chord Progressions: Analyze progressions within pods and symmsets, guided by Normal Harmonic Progression (NHP) principles.
Augmented and Diminished Subsets: Examine subsets like the Augmented Scale and DimHex, and their role in creating rich harmonic textures.
Overtone Series and Scale Derivatives: Investigate the natural harmonic foundation of the overtone series and its connection to major scales and other pitch sets.
Notation and Analysis: Gain insights into the challenges of chord spelling, roots, and analysis in polysymmetrical environments
