Harmony & Melody
What you build once the grid exists. Chords, keys, the routes between them, and the lines people play over the top, for anyone who would rather see the circle of fifths derived than be told to memorise it.
The happy surprise of this subject is how much of it is arithmetic wearing a costume. The circle of fifths falls out of seven and twelve having no common factor. The major scale is the most evenly spread seven notes you can choose from twelve. Nobody decided which chords in a key come out minor. Standard teaching hides all of that, and this course does not.
The derivation
Lesson 1 spends the last of the physics. After that the arguments are structural, and where something is genuinely a stylistic choice rather than a consequence, the lesson says so plainly.
- 01TriadsThe last thing in this course that acoustics can hand you, and why minor is not the mirror image of major.Establishes: A major triad is 4:5:6 from the harmonic series. Minor is a rearrangement, not a reflection.
- 02Scales as subsetsThere are 792 ways to pick seven notes from twelve. What makes one of them the one everybody uses.Establishes: The diatonic set is maximally even and generated by fifths, and those two facts are the same fact.
- 03The circle, derivedNot a mnemonic to memorise. A consequence of seven and twelve sharing no common factor.Establishes: The fifth generates all twelve notes, so keys are rotations and neighbours differ by one accidental.
- 04Chords in a keyThree major, three minor, one diminished. Nobody decided that; it is forced by where the semitones sit.Establishes: The quality of every chord in a key is a consequence of the scale's interval pattern.
- 05Voice leadingChords as points in a space, and the moves between them measured rather than described.Establishes: Smoothness is minimal motion plus held common tones, and it does not predict which progressions get used.
- 06MelodyThe least derivable part of the subject, treated honestly: what people do, and where the reason runs out.Establishes: Streaming is perceptual, gap-fill is mostly a statistical artefact, and the rest is style. All three are labelled.
Where the physics stops
It stops in lesson 1, and that is not a hedge. Acoustics gives you the major triad, sitting in the harmonic series as partials four, five and six, and after that it is close to silent. It does not tell you which seven notes to use, why chords follow one another, or what makes a melody good.
What replaces it is not taste, though. It is combinatorics, symmetry and a little group theory, and those give real answers to real questions. Where they run out, in the last lesson especially, the honest word is convention, and it gets used.