The fields
A field says what an essay is about. The order below is neither alphabetical nor a ranking — it is the order the subject builds itself, and each field leans on the ones above it. A vibrating thing produces a set of partials; the ratios between partials are what makes two notes consonant or rough; a selection of those intervals is a scale; chords built out of a scale move in a space with its own geometry. Rhythm is the same arithmetic in a slower register. Timbre is what the partials were doing all along, and what a room does to them.
The last two arrived after the rest and sit at opposite ends of the chain. Instruments asks where the sound came from before any of the above — almost always a boundary condition rather than a material, since a tube stopped at one end has only odd partials and would have them if it were made of glass. Form asks what happens when all of it is put in an order and left running for ten minutes, and it is the field where this site’s method is under the most strain: a ratio and a spectrum are objects with numbers in them, and a form is not. Every essay there computes from an encoding, and prints the encoding it computed from.
The listener is last for a reason rather than as an afterthought: it is the field every other one has been quietly assuming. The comma essays assume an ear that can hear twenty cents, the roughness essays assume a critical band, and the metre essays assume an inference nothing in the signal requires. That field puts numbers under those assumptions.
Two other axes cut across this one. Series gather the essays that argue about the same idea at increasing depth, whichever field they sit in. Threads say what an essay rhymes with — the motifs that keep turning up where they have no business being related.
Pitch and tuning
Frequency ratios, the comma that will not close, and every compromise ever made about it.
Intervals and chords
Two notes at once, why some of them beat, and the geometry of the ones that do not.
Scales and modes
Which seven of the twelve, and what changes when the same seven start somewhere else.
Harmony and voice leading
Chords as places, progressions as paths, and the smallest possible move between them.
Rhythm and metre
Time divided, subdivided and deliberately misaligned — drawn as a circle rather than a line.
Timbre and acoustics
What makes a clarinet a clarinet, and what a room does to it before it reaches an ear.
Perception and the listener
Loudness is not amplitude and a beat is not in the signal. What the ear adds, hides, merges and supplies — measured, with the numbers every other field has been assuming.
Instruments and their design
Where the sound came from before any of the above. A stopped tube has only odd partials, a hammer at one seventh silences the seventh, and a bass string is wound because a plain one would be longer than the room.
Form and structure
The shape a piece has in time, computed rather than labelled. A distance matrix finds the sections before anybody names them, a phrase turns out to be a number of seconds rather than of bars, and an ending is five separate signals that can each arrive without the others.