Acoustics & Music Theory
why it sounds like that
Generator

thirty-two-bar AABA, as a strip of time

thirty-two-bar AABA laid out one cell per bar, coloured by section, with the roman numeral in each bar. the A section's turnaround is the ii-V every variant keeps; the bridge is a chain of applied dominants. At 108 beats a minute in 4/4 the whole of it lasts 71 seconds.
thirty-two-bar AABA, as a strip of time. thirty-two-bar AABA laid out one cell per bar, coloured by section, with the roman numeral in each bar. the A section's turnaround is the ii-V every variant keeps; the bridge is a chain of applied dominants. At 108 beats a minute in 4/4 the whole of it lasts 71 seconds.

Drawn above with its standard settings, which is almost never how an essay draws it: an essay states the numbers it is arguing about, so the figure a reader meets there is about that argument rather than about the drawing in general. Every option a placement passes is checked against the ones this function actually reads, because an option it does not read is silently ignored and the figure quietly draws what is above instead.

It makes a noise. 16 of its 16 placements carry sound, built from the same numbers as the drawing, offering these buttons: The first eight bars, The last eight.

Called by 4 essays

the blast radius of changing it

thirty-two-bar AABA, every bar against every other bar. A self-similarity matrix of 32 bars of thirty-two-bar AABA. Each cell is the cosine similarity of two bars' pitch-class vectors, with the chord's own notes weighted 1 and the rest of the key 0.5. Similarity is quantised into four bands for drawing and anything under 0.35 is left as paper. Nothing in the computation knows what a section is; the blocks and stripes are what the arithmetic returns.

A piece is mostly itself again

Take a piece of music, encode each bar as the notes sounding in it, and compare every bar with every other bar. The picture that comes out has blocks and stripes in it, and those blocks and stripes are the form — arrived at by arithmetic that has never heard of an exposition, a chorus or a refrain.

form · Repetition Redundancy in bits, and why the number needs a length beside it. Left: the LZ78 cost of each scheme divided by the cost of sending the same symbols flat, against how many bars are sent, with each bar coded as its chord and key. Every scheme is above 1 at a single chorus — the coder loses — and every one falls under it as the piece runs. Right: new dictionary phrases per bar at one chorus, which is the statistic that survives at short lengths.

How much of this is new

Repetition can be counted rather than looked at. Feed a piece's bars to a compressor and the bits it needs are a measure of how much of the piece is a repeat of an earlier part of itself. The measurement works, the number is real, and it turns out to be a statement about the description rather than about the music — which is the most useful thing it has to say.

form · Repetition A phrase is a number of seconds, and the bars follow the tempo. Phrase durations for 1, 2, 4, 8, 16-bar phrases at seven tempos, on a logarithmic seconds axis, with the 2 to 8 second window shaded. The window is a property of the listener and does not move; which bar count falls inside it is decided entirely by the tempo.

A phrase is a number of seconds

Musical phrases are described in bars, and four is the number everybody names. But the constraint that fixes a phrase is a property of the listener and is measured in seconds, so the bar count is whatever the tempo makes it. Across seven ordinary tempos the bar count that lands inside the window moves by a factor of eight, while the window itself does not move at all.

form · Phrase thirty-two-bar AABA, as a strip of time. thirty-two-bar AABA laid out one cell per bar, coloured by section, with the roman numeral in each bar. the A section's turnaround is the ii-V every variant keeps; the bridge is a chain of applied dominants. At 108 beats a minute in 4/4 the whole of it lasts 71 seconds. Cut into 4 repeat units of 8 bars, 3 pairs of units agree on more than 50 per cent of their bars. 2 of them are not identical, and 2 of those 2 differ in a run of bars ending at the last bar of the unit; the changed bars are marked in orange.

Where a repeat is changed

Cut every scheme into its own repeat unit, compare each unit with every other, and ask where a repeat stops agreeing with what it repeats. The answer is that it stops at the end, in every case the corpus contains — and the number of cases the corpus contains depends entirely on where the threshold for "a repeat" is put. Moving it by nothing at all takes the count from two to twenty and the finding with it.

form · Repetition

All figures · What can be heard