The hierarchy of chords and scales in music harmony

A theory of consonance and dissonance for the modern composer and music theorist

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About the Harmonic Processions Theory

The Harmonic Processions Theory is a system for classifying all 350 possible sets—commonly referred to as chords or scales—found in Western music. The name reflects the system’s structure in which harmonies process sequentially from simple to complex, revealing shared origins and interrelationships. This journey traverses a gradient from consonance to dissonance and organizes sonorities by distinct harmonic flavors, that is, modalities.

Guided by mathematical principles, the theory of Harmonic Processions unveils an expressive world, elegant in its logic. It serves as a powerful tool for composers, music theorists, musicologists, and enthusiasts seeking to explore the nature of music harmony. More than a theoretical framework, it is a practical reference—a catalog of harmonic swatches or a harmonic color wheel—designed to aid in identifying and understanding the character and potential of all chords and scales.

Why This Book?

Painters have color swatches, color wheels, and gray scales. Architects consult reference books on the properties of steel, concrete, and timber. Chemists have the Mendeleev’s periodic table of elements. But what do composers have to guide their harmonic explorations? How do they find that perfect chord or scale—one suitable for the occasion, not too cliché but also not too jarring—something with a base of vanilla, a touch of melancholy, yet still bright and open?

Music students learn about harmony gradually from various sources. As children, they encounter happy and sad chords (major and minor). Guitarists soon discover the richness of added 7ths and 9ths, while the pianists spend hours practicing the harmonic and the melodic minor scales. In college, students meet the pentatonic and the diatonic modes. Venturing further—perhaps while playing in a wind ensemble or orchestra—they encounter the octatonic and the whole-tone scales, unlocking yet another layer of harmonic depth.

Many college programs require music majors to take post-tonal theory, a course that dazzles and confounds with interval-class vectors, hexachordal combinatoriality, and transpositional symmetries. Amid this strange and exhilarating landscape, one steadfast element emerges: the list of set classes—the complete catalog of 350 possible chords and scales encountered in Western music. Among them are the familiar major chord and major scale, the hexatonic, the octatonic, the chromatic scale, and many others, repeatedly used by composers and catalogued by theorists. Still many more remain like distant stars: identified by a number but unnamed and unexplored. With barely a six-digit interval vector assigned to each set, there is little to indicate the character, the modality, the flavor, or the level of dissonance of these sonorities. If this system is meant to be the composer’s periodic table or a color swatch book, it is not particularly inviting.

Where does a composer turn when seeking to convey sorrow, bitterness, bliss, brashness, joy, or ambiguity? Traditionally, they rely on instinct and luck while experimenting with harmonies at the piano until something interesting emerges. One can always imitate other composers by adopting their favorite chords or avoid exploration altogether by reusing the tried and true—the diatonic scale is quite powerful, thank you very much.

But what about those who know there is so much more to discover, who are ready to claim some of those unnamed distant stars for themselves? Now they can.

The purpose of this book is to explore every chord and scale and to catalog them in such a way that makes their content, qualities, and relationships easy to reference, intuitive to understand, and practical to apply in creative work. If you have ever wished for a color wheel of harmony—a true reference guide to sonic possibilities—this is where your search ends and creativity begins.

How to Use This Book?

This book assumes that the reader is already familiar with basic music theory concepts such as scale, chord, interval, accidentals (sharps and flats), and transposition. The ability to read music notation in both treble and bass clefs is also beneficial. The knowledge of post-tonal theory is helpful although not essential. As more advanced ideas are introduced, they are explained in an accessible manner.

The heart of the book lies in the enclosed tables, which invite the reader to bypass the introductory material and immediately explore new chords and scales through improvisation or composition. However, readers who value a deeper understanding of the theory’s methodology, will find detailed explanations, examples, and exercises in the preceding chapters.

Chapters

1. The Harmonic Processions Theory
2. Why This Book?
3. How to Use This Book
4. Is It a Chord or a Scale?
5. Note, Pitch, and Pitch Class
6. Enharmonic Equivalence
7. Interval and Interval Class
8. The Overtone Series and the Circle of Fifths
9. The Interval of Perfect Fifth and the Circle of Fifths
10. The Role of the Circle of Fifths in the Harmonic Processions
11. The Triadic Form and Transposition
12. The Row of Fifths
13. The Forte Number
14. Consonance and Dissonance
15. The Magnetism of Consonance and the Repulsion of Dissonance
16. The Resolution of the Tritone
17. Span
18. Sharp and Flat Projections
19. The Quintal Normal Form
20. Symmetrical Sets
21. Mirror Sets
22. The Natural Harmonic Procession
23. The Natural Order of Sharp-Projecting Sets
24. The Natural Order of Flat-Projecting Sets
25. The Duality of the Natural Harmonic Procession
26. Modulation
27. Modalities
28. The Natural Harmonic Procession and the Dissonance Levels
29. The Interval Class Vector
30. The Interval Class Vector of the Diatonic Set and the Dissonance Gradient
31. The Interval Class Dissonance Gradient
32. Quantifying Dissonance through Interval Class Dissonance Gradient
33. The Interval Class Signature
34. Building and Resolving Harmonic Tension
35. Tonal Ambiguity
36. Modes of the Diatonic Scale
37. Tritone Substitution
38. Z-Relation and Dissonance Level

Harmonic Processions Tables

1. The Natural Procession of All Sets
2. The Natural Procession with the Chromatic Normal Form
3. The Natural Procession of Sharp Projecting Sets
4. The Natural Procession of Flat-Projecting Sets
5. The Natural Procession of Symmetrical Sets in Sharp-Projecting Form
6. The Natural Procession of Symmetrical Sets in Flat-Projecting Form
7. The Natural Procession of Trichords
8. The Natural Procession of Tetrachords
9. The Natural Procession of Pentachords
10. The Natural Procession of Hexachords
11. The Natural Procession of Hepctachords
12. The Natural Procession of Octachords
13. The Natural Procession of Nonachords
14. The Natural Procession of Decachords
15. The Natural Procession of Undecachords
16. The Natural Procession of Dodecachords

17. The Modal Procession of All Sets
18. The Modal Procession of Trichords
19. The Modal Procession of Tetrachords
20. The Modal Procession of Pentachords
21. The Modal Procession of Hexachords
22. The Modal Procession of Heptachords
23. The Modal Procession of Octachords
24. The Modal Procession of Nonachords
25. The Modal Procession of Decachords
26. The Modal Procession of Undecachords
27. The Modal Procession of Dodecachords

28. The Dissonance Gradient Procession of All Sets
29. The Dissonance Gradient Procession with the Chromatic Normal Form
30. The Dissonance Gradient Procession of Trichords
31. The Dissonance Gradient Procession of Tetrachords
32. The Dissonance Gradient Procession of Pentachords
33. The Dissonance Gradient Procession of Hexachords
34. The Dissonance Gradient Procession of Heptachords
35. The Dissonance Gradient Procession of Octachords
36. The Dissonance Gradient Procession of Nonachords
37. The Dissonance Gradient Procession of Decachords
38. The Dissonance Gradient Procession of Undecachords
39. The Dissonance Gradient Procession of Dodecachords

40. Z-Related Sets with Dissonance Level Related Sets
41. Interval Class Gradients
42. Sets Sorted by Forte Number