Two pulse trains at 3 against 2 are a groove. Speed them up past about 20 pulses a second and your ear stops counting and hears a perfect fifth. Press play, then accelerate.
Audio off. Press Play. Headphones or decent speakers help below 100 Hz.
| Voice | Per bar | Sound | Rate | What you hear | Remove |
|---|
Tap a voice to mute it. Change any count or sound, or add voices up to six, to build your own stack.
The scope always shows the same number of bars, so the pattern looks identical at 1 pulse a second and at 300. The signal keeps its shape. Somewhere around 16 to 30 Hz your hearing switches from counting events to reading a tone.
2:1 and 3:2 realign often, so as rhythm they lock in and as pitch they sound consonant. 16:15 or 7 against 11 take a long time to come back together. Slow, they feel disorienting. Fast, they sound rough.
The rate at which all voices realign is a pulse too. Sped up, it's the implied root your ear fills in under the chord. For 4:5:6 it sits two octaves below the lowest note.
A piano's fifth is 1.498:1, not 1.5:1. Switch to equal temperament at a slow speed and watch the voices slide against each other bar after bar. At pitch speed, that same slide is what you hear as beating. The dominant 7th shows it most, since its 7th is 31 cents off the 7:4 ratio. The harmonic seventh and septimal third sit about a third of a semitone from the nearest piano key, so in equal temperament they slide the fastest.
At rhythm speed you hear each pulse's shape: a click, a woodblock. At pitch speed that shape turns into the tone color. Voice runs the pulses through the resonances of "ah". Your vocal folds work the same way: a pulse train at 100 to 200 Hz, shaped by your throat.
Henry Cowell described this in New Musical Resources (1930). Stockhausen built on it in "…how time passes…" (1957).