The hierarchy of chords and scales in music harmony

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

Coming in early 2026

If you would like to be notified when the book and the PDF download are available, click on  

this link

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 and Pitch
6. Enharmonic Equivalence
7. Interval and Interval Class
8. The Overtone Series
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. Consonance and Dissonance
14. The Magnetism of Consonance and the Repulsion of Dissonance
15. The Resolution of the Tritone
16. Sharp and Flat Projections
17. Span
18. The Quintal Prime Form
19. The Numeric Quintal Prime 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 and its Numbering System
26. Modalities and the Modal Harmonic Procession
27. Modulation
28. The Natural Harmonic Procession and Dissonance Levels
29. The Interval-Class Vector
30. The Interval-Class Vector of the Diatonic Set
31. The Interval-Class Dissonance Gradient and the Dissonance Curve
32. Quantifying Dissonance Levels of Sets
33. The Interval-Class Signature
34. Building and Resolving Harmonic Tension
35. Tonal Ambiguity
36. Z-Relation and Dissonance Level
37. Modes of the Diatonic Scale
38. Tritone Substitution
39. The Forte Numbers
40. Further Thoughts

Harmonic Processions Tables

1. The Natural Harmonic Procession of All Sets in Dual Exposition
2. The Natural Harmonic Procession of All Sets
3. The Natural Harmonic Procession of All Sets, Including the Numeric Quintal and the Chromatic Prime Form
4. The Natural Harmonic Procession of Sharp Projecting Sets
5. The Natural Harmonic Procession of Flat-Projecting Sets
6. The Natural Harmonic Procession of Symmetrical Sets in Sharp-Projecting Form
7. The Natural Harmonic Procession of Symmetrical Sets in Flat-Projecting Form
8. The Natural Harmonic Procession of Dyads
9. The Natural Harmonic Procession of Trichords
10. The Natural Harmonic Procession of Tetrachords
11. The Natural Harmonic Procession of Pentachords
12. The Natural Harmonic Procession of Hexachords
13. The Natural Harmonic Procession of Heptachords
14. The Natural Harmonic Procession of Octachords
15. The Natural Harmonic Procession of Nonachords
16. The Natural Harmonic Procession of Decachords
17. The Natural Harmonic Procession of Undecachords
18. The Natural Harmonic Procession of Dodecachords

19. The Modal Harmonic Procession of All Sets
20. The Modal Harmonic Procession of Dyads
21. The Modal Harmonic Procession of Trichords
22. The Modal Harmonic Procession of Tetrachords
23. The Modal Harmonic Procession of Pentachords
24. The Modal Harmonic Procession of Hexachords
25. The Modal Harmonic Procession of Heptachords
26. The Modal Harmonic Procession of Octachords
27. The Modal Harmonic Procession of Nonachords
28. The Modal Harmonic Procession of Decachords
29. The Modal Harmonic Procession of Undecachords
30. The Modal Harmonic Procession of Dodecachords

31. The Dissonance-Gradient Harmonic Procession of All Sets
32. The Dissonance-Gradient Harmonic Procession of All Sets, Including the Numeric Quintal and the Chromatic Prime Form
33. The Dissonance-Gradient Harmonic Procession of Dyads
34. The Dissonance-Gradient Harmonic Procession of Trichords
35. The Dissonance-Gradient Harmonic Procession of Tetrachords
36. The Dissonance-Gradient Harmonic Procession of Pentachords
37. The Dissonance-Gradient Harmonic Procession of Hexachords
38. The Dissonance-Gradient Harmonic Procession of Heptachords
39. The Dissonance-Gradient Harmonic Procession of Octachords
40. The Dissonance-Gradient Harmonic Procession of Nonachords
41. The Dissonance-Gradient Harmonic Procession of Decachords
42. The Dissonance-Gradient Harmonic Procession of Undecachords
43. The Dissonance-Gradient Harmonic Procession of Dodecachords

44. The Natural Harmonic Procession with Interval-Class Dissonance Gradients
45. Sets with Identical Dissonance Levels, including Z-Related Sets
46. Sets Sorted by Forte Numbers
47. Sets Sorted by Forte Numbers, Including the Numeric Quintal and Chromatic Prime Form