Comprehensive guide to musical harmony, chord progressions, and arrangements.

• Provides a detailed analyses of harmonic structures, modal borrowing, secondary dominants, and harmonic vectors through many popular songs

• Suitable for musicians, composers, arrangers, singers, improvisers, and music enthusiasts
  

This book presents a systematic framework for understanding functional harmony, chord relationships, and tonal motionthrough the concept of harmonic vectors. Designed for musicians, composers, arrangers, and advanced students of music theory, the text connects traditional tonal analysis with deeper structural concepts such as harmonic classes, overtone-derived chords, alternate roots, and symmetrical pitch systems.

Inside you’ll learn:

• How intervals and chord roots define harmonic structure

• The meaning of tonic, tonality, modality, and diatonic function

• How Roman numerals and harmonic classes reveal chord relationships

• The mechanics behind ii–V progressions and dominant motion

• How secondary dominants expand tonal harmony

• The role of diminished seventh structures as leading-tone and common-tone chords

• How modal borrowing reshapes tonal color

• Techniques for root substitutions, alternate roots, and implied harmony

• How deceptive resolutions and retrogression affect musical motion

• The harmonic logic behind non-diatonic chords and multi-vectored harmony

• How the overtone series and acoustic ratios shape tonal systems

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