It's true, I'm writing a book.

As if making this website, and a few thousand YouTube videos isn't enough.

I've studied music theory for about 43 years. I'm a bit of a nerd. In the past decade I've worked on creating software to calculate the many interesting properties of musical scales, and in doing that I've scoured academia and music theory literature for advanced, geeky arcane stuff about musical scales. The result of that work can be seen (in part) on the pages of this website. All of that and more is going in the book.

That's right, there is stuff in the book that you will not find on this website, or in the YouTube videos. Sneaky, huh?

I've spent the past 7 years working on it, and it is still not finished. It's massive. Here is the cover (as a fake 3D photo) of Volume 1: The Splaining

See that guy on the cover? He is reading about all the properties of musical scales, and there is so much material it's making his brain hurt.

Take note: this is not a printed book. It's a PDF document, and it's a big one. If you choose to print it out, the lives of all those trees are on your conscience, not mine.

In Volume 1, I explain all the concepts and ideas that you will need — actually, more than you'll need — to understand everything in Volume 2: The Scales.

This one is also not a printed book, it's another PDF document and it's even bigger than Volume 1. There is one page for every scale, and as you will read in Volume 1 (spoiler alert!!), there are 2048 of those. So yeah. It's a 2048 page book. That seems crazy when you read about it here, but once you see the book and how it's organized, you'll understand.

Here is the Table of Contents for Volume 1: The Splaining (so far):

  1. Preface
  2. Contents
  3. Introduction
    1. Preamble: The Goal Of This Book
    2. Typographic Conventions
    3. Explaining Pitch
      1. Hertz
      2. Cents
    4. Necessary Topics
      1. Pitch Classes
      2. Generic and Specific Intervals
      3. Modulo Arithmetic
    5. Scale Candidacy
    6. What Universe Is This?
      1. Octave Equivalence
      2. Twelve Tone Division
      3. Equal Temperament
    7. Summary
  4. Making Scales
    1. Preamble
    2. Binary Representation
    3. Power Set
    4. Applying Limitations
      1. Tonic Inclusion
      2. Maximum Interval
      3. Interval Neighbours
    5. Cardinality
    6. Summary
  5. Representing Scales
    1. Preamble
    2. Pitch Class Set
    3. Interval Structure
    4. Staff Notation
    5. Bracelet Notation
    6. Tonnetz Diagram
    7. Instrument-specific diagrams
    8. Summary
  6. Modifying Scales
    1. Preamble
    2. Rotation
    3. Modes
      1. Diatonic Modes
    4. Reflection
    5. Forte Set Classes
      1. Inversions
    6. Transpositional/Inversional Set Classes
      1. Z-relations
    7. Prime Form
    8. Multiplication
      1. Self M-related
    9. Unified Transformation Operations
    10. Mutation
      1. Levenshtein Distance
      2. A Better Method
    11. Complement
      1. Hypermodes
    12. Invariant Properties
    13. Summary
  7. Symmetries
    1. Preamble
    2. Reflective Symmetry
    3. Palindromicity
    4. Chirality
    5. Ridge Tones
    6. Rotational Symmetry
    7. Summary
  8. Observing Intervals
    1. Preamble
    2. Steps, Skips, Leaps, and Spans
    3. Cyclic Correlation
    4. Interval Vector
      1. Saturation
      2. Deep Scale
      3. Hemitonia
      4. Cohemitonia
    5. Imperfections
    6. Propriety & Coherence
    7. Heteromorphic Profile
      1. Contradictions
      2. Ambiguities
      3. Differences and Samenesses
    8. Coherence Quotient
    9. Sameness Quotient
    10. Distribution Spectra
      1. Spectra Variation
      2. Trivalence
      3. Myhill’s Property
      4. Reduced and Semireduced Scales
      5. Consecutivity Property
      6. Spectrum Filtering
    11. Summary
  9. Generators
    1. Preamble
    2. Three Gap Theorem
    3. Generators
      1. Degenerate Scales
      2. Chopin’s Theorem
      3. Distance Models
    4. Bisectors
    5. Well-Formedness
      1. Symmetry Condition
      2. Closure Condition
      3. Degenerate Well-Formed Scales
      4. Cardinality Equals Variety
      5. Structure Yields Multiplicity
      6. Pairwise Well-Formed Scales
    6. Summary
  10. Evenness
    1. Preamble
    2. Maximal Evenness
      1. Distributional Evenness
      2. Cohn’s Property and Hexatonic Cycles
      3. Euclidean Distance
    3. Maximally Smooth Cycles
    4. Maximal Area
    5. Polygon Perimeter
    6. Centrifuge Balance
    7. Self-complements
    8. Lewin-Quinn FC-components
    9. Summary
  11. Fragments
    1. Preamble
    2. Tetrachords
    3. Hierarchization
    4. Triad Inclusion
    5. Bi-Triadics
    6. Summary
  12. Appendix
    1. Set Theory Notation
    2. Pascal’s Triangle
    3. Coherence Data
  13. Lists
    1. Non-degenerate Well-formed Scales
    2. Degenerate Well-formed Scales
    3. Scales with the Myhill Property
    4. Prime scales that are Self-M-Related
    5. Balanced Scales
    6. Maximally Even Scales
    7. Maximally Even Scales With The Myhill Property
    8. Proper Scales
    9. Strictly Proper Scales
    10. Deep Scales
    11. Palindromic Scales
    12. Scales With Rotational Symmetry
    13. Trivalent Scales
    14. Scales with Contradictions but no Ambiguities
    15. Prime Scales Of Hierarchizability 3 with k=2
    16. Prime Scales Of Hierarchizability 2 with k=2
    17. Prime Scales Of Hierarchizability 1 with k=2
    18. Prime Scales Of Hierarchizability 3 with k=4
    19. Prime Scales that increase hierarchizability when k increases from 2 to 3
    20. Prime Scales with Consecutivity Property
  14. Bibliography
  15. Glossary
  16. Alphabetical Index

Things this book will not do:

Things this book will do:

OK Ian, take my money already

Keep your wallet closed, it's not fully written yet. I will accept your money once I have a book to give you.

But I have a deal for you. If you join my Patreon crew as a supporter, I will give you a copy of the book when it comes out. No matter what your pledge is. You could pledge for $1 and quit after a month, and you'll get this book for $1, no strings attached*. My patrons are currently giving enough that it keeps this web server going, and occasionally I get to buy a theory book! In gratitude for that support, you will be signed up to get the book, and you'll also be treated to occasional glimpses of chapters as they're completed. I send an update to my Patrons every couple of months to let them know how things are coming along, and with alerts to new stuff that I release on the website.

* Since you would be getting an early pre-release copy of the book, I will ask that you write a review on Amazon. Ideally a favourable one, but I know that's not a given, I have to earn that by writing an incredible book.

Go to My Patreon Page and join others like yourself who totally geek out on all this nerdy stuff.