Intervals

Harmonics · Exhibit

Open a note.
See what is inside.

Each bar is a pure tone at 1×, 2×, 3× the lowest pitch. Silence one partial and the colour of the note changes.

Harmonics · One note is already a chord.

Listen for the pitch to stay recognizable while its colour changes.

Keyboard tuned to the fundamentalA2 = 110 Hz

Ear test

Which note do you hear after partial 1 fades?

Run the test and follow the low pitch while the first bar fades. All six partials sound first; then only partials 2 through 6 remain. Their equal frequency spacing still points to the missing fundamental, so your ear may supply A2 even though 110 Hz is silent. Perceived pitch can come from the pattern that the partials make together.
Six consecutive partials are ready.
fₙ = n · f₁

Whole numbers
all the way up.

The first four shapes that fit. The marked points never move.

Both ends of the string are tied down and cannot move. Only a shape that stands still at both ends fits, so the string holds a whole number of half waves and nothing between them. The two fixed ends are where the whole numbers come from.

With a 110 Hz fundamental the partials run 110, 220, 330, 440 and up.

Moving Brightness tilts the whole row, where each bar’s height shows how loud one partial sounds. Which partials sound and how loud they are decide much of a tone’s timbre. Much of the rest comes from a note’s start and fade. Your ear hears one note and may supply a fundamental that never sounded.

Which of those partials a culture lifts into its scale, and how far it stretches or shrinks each one when it tunes an instrument, is a cultural choice.

Explore

Your ear supplied a note that never sounded.

Hear what else partials decide in Temperament →Return to the exhibit directory →

Harmonics · The partials inside one tone

Build a tone out of transparent parts.

Turn partials on and off, play the spectrum, then remove the fundamental. Listen for the tone’s colour to change and test whether its low pitch remains. Each ribbon is a pure whole-number multiple of that fundamental; their spacing can still point to it when partial 1 is silent. The experiment separates a note’s perceived pitch from any single sounding component.

Turn partials on and off, play the spectrum, then remove partial 1. Hear the colour change and test whether the low pitch remains. Whole-number spacing can still point to the silent fundamental. The test shows how a note’s pitch can come from that pattern.

Compose the spectrum6 active partials