Music Theory

Build pitch from frequency: why the octave is a doubling, where the consonances come from, and why the octave ends up cut into twelve equal steps of $2^{1/12}$.

How a printed dot becomes a named frequency: five lines, two clefs, octave numbering, ledger lines, and the five accidentals.

Duration written by repeated halving, with dots and ties patching what halving cannot reach, and a tempo mark turning the fractions into seconds.

Where the strong beats are: what the two numbers of a time signature mean, simple against compound, beaming, tuplets, and syncopation measured against the pattern it contradicts.

The distance between two notes, named by a number counted in letters and a quality counted in semitones, with inversion halving the work and the ratios from the first lesson explaining consonance.

Which seven of the twelve, and in what order: the major scale as a step pattern, why the degrees are not equal, the three minor scales, and the modes as rotations.

Why the sharps and flats appear in that order, how to read a key off a signature in two moves, and why the circle of fifths closes at all.

Stacking thirds gives four triad qualities and seven chords per key, named by roman numeral, rearranged by inversion and extended by one more third.

Why one chord follows another: the three functions, the tritone inside V7 and its resolution, the four cadences, voice leading, and modulation by pivot chord.

Everything on the page that is not a chord tone: non-chord notes, dynamics, articulation, transposing instruments, and an eight-bar excerpt analysed from scratch.