History
The Cambridge History of Western Music Theory
Music Theory
Music Theory for the 21st Century Classroom (Free)
Open Music Theory (Free)
The Geometry of Musical Rhythm – Godfried T. Toussaint
Music Theory for Computer Musicians – Michael Hewitt
Composition for Computer Musicians – Michael Hewitt
Harmony for Computer Musicians – Michael Hewitt
Music Theory for the Digital Age (Udemy) – Michael Hewitt
Dr. B Music Theory (Youtube) (Free) – Dr. Christopher Brellochs
Steps to Parnassus (Gradus Ad Parnassum) – Johann Joseph Fux, Alfred Mann
The Musical Guide – Friederich Erhardt Niedt
Audio
Musimathics (1 & 2) – Gareth Loy
Why You Hear What Your Hear – Eric J. Heller
Digital Music
The Computer Music Tutorial – Curtis Roads
Synth Secrets (Sound on Sound) (Free) – Gordon Reid
Creating Sounds from Scratch – Andrea Pejrolo, Scott Metcalf
Sound Synthesis and Sampling – Martin Russ
Mixing Secrets – Mike Senior
Mastering Audio – Robert A. Katz
Hands-On Practice
Adult Piano Adventures All-In-One (Books 1 & 2) – Nancy & Randall Faber
Pianoforall (Udemy) – Robin Hall
Syntorial – Joe Hanley
Scale Intervals
| Major Scale | T | T | S | T | T | T | S |
| Minor Scale | T | S | T | T | S | T | T |
T = Tone
S = Semitone
Mode Intervals
| Aeolian | T | S | T | T | S | T | T |
| Locrian | S | T | T | S | T | T | T |
| Ionian | T | T | S | T | T | T | S |
| Dorian | T | S | T | T | T | S | T |
| Phrygian | S | T | T | T | S | T | T |
| Lydian | T | T | T | S | T | T | S |
| Mixolydian | T | T | S | T | T | S | T |
More Scale Intervals
| Natural Minor Scale | T | S | T | T | S | T | T |
| Harmonic Minor Scale | T | S | T | T | S | T+S | S |
| Melodic Minor Scale (Asc.) | T | S | T | T | T | T | S |
| Melodic Minor Scale (Desc.) | T | S | T | T | S | T | T |
| Whole Tone Scale | T | T | T | T | T | T | ||
| Octatonic Scale (T-first) | T | S | T | S | T | S | T | S |
| Octatonic Scale (S-first) | S | T | S | T | S | T | S | T |
| Acoustic Scale | T | T | T | S | T | S | T |
The Diatonic Polygon
Diatonic Polygon in Major Scale (Ionian Mode) orientation
This slightly rotated “Ionian Mode” orientation accounts not only for C Ionian, but also accounts for A Aeolian, B Locrian, D Dorian, E Phrygian, F Lydian, and G Mixolydian, which all contain the same set of notes (A, B, C, D, E, F, G). No sharps and no flats:
| C Ionian | C | D | E | F | G | A | B |
| A Aeolian | A | B | C | D | E | F | G |
| B Locrian | B | C | D | E | F | G | A |
| D Dorian | D | E | F | G | A | B | C |
| E Phrygian | E | F | G | A | B | C | D |
| F Lydian | F | G | A | B | C | D | E |
| G Mixolydian | G | A | B | C | D | E | F |
Switching between C Ionian and A Aeolian in this way, only depends on where you choose your starting point in this orientation. As is, if you start on C (labeled as 1 in the image), and move along the shape, all the way back to C, then you’re in C Ionian. If you start on A (labeled 6 in the image), and move along and all the way back to A, then you’ve traced A Aeolian. If you start on D and do the same, then you’re in D Dorian, and so on.
That’s all if the polygon shape above stays in the same orientation.
Rotating the polygon allows you to change the set of notes included in the group (e.g., going from A, B, C, D, E, F, G to Ab, Bb, C, Db, Eb, F, Gb), and thereby change the set of Key-Mode combinations that are accounted for (e.g., instead of A-Aeolian, B-Locrian, C-Ionian, etc, you might have Bb-Aeolian, C-Locrian, Db Ionian, etc).
As an example, rotating the polygon above so that the point currently marked ‘2’ is situated at D#/Eb instead of D gives the Key-Mode combinations D#/Eb-Dorian, F-Phrygian, F#/Gb-Lydian, G#/Ab-Mixolydian, A#/Bb-Aeolian, C-Locrian, and C#/D-Ionian (the set of notes becomes D#, E#, F#, G#, A#, B#, C# or equivalently Eb, F, Gb, Ab, Bb, C, Db)
Now, more generally, if we separate the polygon itself from the labeled note names, each point on the polygon (no matter its rotation) can be thought of as representing one of the seven diatonic modes (Aeolian, Locrian, Ionian, Dorian, Phrygian, Lydian, Mixolydian).
Starting on a particular point in the shape (and moving forward along the shape and back to that point), is equivalent to being in the mode represented by that point. In other words, ignoring note names, to start on the point marked 1 on the polygon is to be in the Ionian mode, regardless of rotation. To start on the point marked 2 is to be in the Dorian mode, regardless of rotation. To start on the point marked 3 is to be in the Phrygian mode, on 4 is the Lydian mode, on 5 is the Mixolydian mode, on 6 is the Aeolian mode, and on 7 is the Locrian mode.
The diatonic polygon in the upright orientation is what you would consider its Dorian orientation, and whatever that “top” point on the polygon (marked 2 in the second image) is pointing to is in the Dorian mode.
If the polygon is upright, and that top point is pointing at the note label C, then C is in Dorian mode.
If the polygon is rotated, and that point is then pointing at C#/Db, then C#/ Db is now what’s in Dorian mode.
The symmetry of the diatonic polygon in this “upright” position is also reflected by the interval sequence for the Dorian mode, which is also symmetric (T, S, T, T, T, S, T), and its sequence pattern reflects onto itself (T, S, T, T, T, S, T backward is T, S, T, T, T, S, T).
The other modes’ pattern sequences, on the other hand, reflect across the Dorian pattern. For example, the Mixolydian pattern (T, T, S, T, T, S, T) is a reflection of the Aeolian pattern (T, S, T, T, S, T, T). In other words, the Mixolydian pattern is the Aeolian pattern backward (and vice versa). Likewise, the Lydian pattern (T, T, T, S, T, T, S) is a reflection of the Locrian pattern (S, T, T, S, T, T, T), and the Phrygian pattern (S, T, T, T, S, T, T) is a reflection of the Ionian pattern (T, T, S, T, T, T S).