EXPERIMENT 001 · COMBINATORICS OF MUSIC

A universe in a single bar.

How many melodies fit into a fixed amount of time? Adjust the model, follow the growth, and listen to one of the possibilities.

NEW · Young diagrams, rhythmic inventories, and shape puzzles.Open the rhythm & shape lab →

THE PARAMETERS

Available pitches

048 PITCHES

p · The size of your pitch alphabet.

Total duration

064 UNITS

n · Measured in the smallest time unit.

A small rule. A vast universe.

Notes have pitch and duration. Rests have duration. Adjacent rests merge into a single silence.

a₀ = 1 · a₁ = p + 1
aₙ = (p + 2)aₙ₋₁ − aₙ₋₂

Unrestricted positive integer durations. Exact arithmetic, entirely in your browser.

EXACT COUNT

41,006,928,746,285,492,812,225

24 pitches · 16 time units · no adjacent rests

DURATION 0log₁₀(COUNT) · 22.61 AT n = 16

LISTEN & EXPLORE

C52

Rest3

F♯52

Rest2

F♯43

G♯52

Block width is duration. Violet is silence. These are illustrative legal examples, not uniformly sampled melodies.

Two consecutive notes remain distinct events. Consecutive rests are represented by one rest of their combined duration.

NRNallowedR R→Rmerge the silence