About

This is a growing collection of illustrated essays about why music sounds the way it does. Each one takes a single idea and draws it until the argument is visible — and where the argument is about a sound, plays it.

What this is not

It is not a theory course, not an ear-training programme, and not a guide to composing anything. There is no syllabus and no obligation to cover the standard topics in the standard order. An essay exists because there is a figure that explains something better than a paragraph can — and if there is no such figure, there is no essay.

The figures are computed, not drawn

Every illustration is generated as SVG at build time by code in this repository. None are photographs, none are exported from a drawing program, and none are bitmaps. The consequence that matters is not that they are sharp or small, though they are both:

• They are correct by construction. The dissonance curve is evaluated from a roughness model over the partials of two real spectra, so its minima fall where the model puts them rather than where a caption would like them to. The comma is the actual ratio of twelve fifths to seven octaves. The Euclidean rhythms come out of Bjorklund's algorithm, not out of a transcription — which is why it is worth noticing that they match the ones people already play.
• They are parameterised. The same generator draws any scale as a necklace, any pair of tones as a beat pattern, any rhythm as a cycle, and the essay picks.
• They respond to the light and dark themes, because they reference colour roles rather than colours. Plum always means the note under discussion; orange always means the discrepancy.

The full set of generators is listed on the figure library page.

The sound is evidence, not decoration

Several figures carry buttons that synthesise what the picture describes. They exist because a number of claims on this site are not really checkable any other way: that two tones three hertz apart beat three times a second, that the seventh partial is genuinely flat of anything on a keyboard, that a progression in pure ratios comes home to a tonic that has moved.

The rules are strict, and they are the same rules a figure follows. Nothing plays until it is asked to. Nothing loops. The picture is complete and the essay's claim is true without ever pressing anything, so a reader on a train or without audio loses corroboration and never loses the argument. And the sound is synthesised from the same numbers the figure is drawn from — the same partial list, the same ratios — so the two cannot drift apart.

Nothing here is a rule

Music theory is often taught as legislation, and it is better read as description: an account of what a particular repertoire did often enough to be worth naming. Where this site says a progression is common, it means common somewhere, at some time, and it tries to say where. Where it says an interval is consonant, it means a specific measurable thing about roughness between partials, and that measurement is drawn.

Where the model stops

The subject is a stack of approximations, each excellent inside a range: that a string's partials are exact multiples of its fundamental, that the ear resolves frequency independently of level, that a room is a rectangular box, that pitch is what frequency is for. Every one of them fails somewhere, and several fail exactly where the interesting music is. Where a figure relies on one, the essay names it.

On being wrong

Corrections are welcome and will be made. A figure that is beautiful and wrong is worse than no figure, because it is more persuasive — and one with a play button on it is more persuasive still.