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Intervals

Story

How did one finding
open the next?

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

Step 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. Every note of the added line keeps one fraction against the chant, which turned a measured interval into a rule for two voices singing at once. This practice was called organum.

Play the chant alone, then add each shadow voice. Listen for the second line to hold a fixed fifth or fourth below the melody all the way through.

Turn intervals into chords in Harmony ↗

Harmony · Chord architecture

Turn remembered distances into a place.

Add or remove ratio points, then play the constellation together and one note at a time. Watch its geometry change as you listen for the chord to grow richer or emptier, and for how settled it sounds. Every point fixes one frequency relationship above the root, so changing the shape changes the sound. The constellation makes a chord’s musical identity visible as a set of intervals.

Add or remove ratio points, then play the constellation together and one note at a time. Watch the shape change and hear the chord’s colour shift. Each point sets one interval above the root, so changing the geometry changes the sound and the chord’s identity.

Build the constellation3-point constellation