One note is a chord in disguise

Every note hides a ladder of quieter notes inside it: 1×, 2×, 3×, 4× the speed. Mix them and you build a sound from scratch.

the harmonic mixer — build a sound from its ingredients

fundamental — the bottom rung110 Hz ≈ A2

1 × 110 =110 Hz

2 × 110 =220 Hz

3 × 110 =330 Hz

4 × 110 =440 Hz

5 × 110 =550 Hz

6 × 110 =660 Hz

7 × 110 =770 Hz

8 × 110 =880 Hz

recipes:

all the sines, added together

Each slider is a smooth sine wiggle. Add them up and you get this shape — the sound's fingerprint.

A ladder of × tables

The hidden notes inside one note sit at 1×, 2×, 3×, 4× the fundamental's speed — nothing in between. It's the 110-times table, played out loud.

Why? Standing waves

A string (or the air in a tube) can only vibrate in whole loops — 1 loop, 2 loops, 3 loops. You can't have two and a half loops. Whole loops means whole-number multiples. That's the whole rule.

Brass players live here

A trombone or trumpet player picks notes off this exact ladder with their lips — same tube, higher rung. And the mix of rungs is why a trumpet and a clarinet playing the same note sound nothing alike.

For the classroom

Learning goals

Harmonics sit at whole-number multiples of the fundamental: fₙ = n × f — multiplication tables made audible.
Standing waves explain why only whole-number multiples exist (whole loops fit; fractions of a loop don't).
Timbre (tone colour) is a recipe: the same pitch with a different mix of harmonics is a different-sounding instrument.

Try this

1.Set the fundamental to 100 Hz and read the ladder aloud as a class: 100, 200, 300… Ask what harmonic 6 will be BEFORE revealing the slider row, then check.
2.Blind timbre test: one student switches between the Pure, Brassy and Hollow recipes while the class looks away — can they name the recipe by ear alone?