Intervals

Story · Guided tour

How did one finding
open the next?

Start with one stretched string. Seven pages each add one finding and one sound experiment.

Discovery 3 of 7
about 900 CE

Voices split apart

Two lines at once.

For centuries European church music moved as a single line that everyone sang together. Around 900 CE, Frankish writers set down something new in a treatise called Musica enchiriadis: let a second group sing the same chant shape a fourth or a fifth below, in step with the first. These are the earliest surviving written rules for polyphony in the West.

The choice of distances came straight from the old fractions. Fourths and fifths were the blends singers trusted for a long hold, so the added voice shadowed the chant at exactly those intervals. This practice was called organum.

Play the chant alone, then add each shadow voice. Follow the upper melody while the second line moves with it at a fixed fifth or fourth below. Every note in the added line keeps the same small-number relationship to the chant. Hearing that constant spacing shows how measured intervals became a rule for two simultaneous voices in early Western polyphony.

Turn intervals into chords in Harmony

Phonology · The vibrating string

This is a monochord.

One string is stretched over a sounding box between two fixed ends. The rule beneath it measures the string, and the movable bridge stops it wherever you set it. Musicians and early students of nature both worked with this instrument, because it turns a length you can measure into a pitch you can hear. Set the equal parts, watch the bridge slide, then pluck. The shorter the sounding length, the higher the pitch.

One string over a sounding box, a rule that measures it, and a bridge that stops it. Musicians and early students of nature both used this instrument to turn a measured length into a pitch. Set the equal parts, watch the bridge slide, then pluck. The shorter the sounding length, the higher the pitch.

Move the bridgewhole string · 110 Hz
Sounding length1