Proof of concept — Max MSP → Web Audio · 3D

Subtractive Synth, Three-Axis View

Same patch as Fig 3.44 — two oscillators, resonant lowpass, twin ADSRs. The flat spectrum from before, now with a time axis. Each note's harmonic stack rings out into depth as it decays.

Spectrogram waterfall x · frequency y · magnitude z · time
20 Hz · low20 kHz · high
Scope (ground truth)— Hz
Hold & drag ↕ to morph waveform  ·  keys A S D F G H J K
oct 0
Oscillators
7 cents
Filter
800 Hz
6
2400 Hz
Filter envelope
0.05
0.60
0.50
1.50
Amp envelope
0.01
0.30
0.85
1.80

What the 3D adds

The flat spectrum is one slice of time — just now. The waterfall shows that slice and the previous ~1.3 seconds receding into depth. You can see the shape of an ADSR envelope drawn into the surface.

Hold a note. Watch the front edge bloom on the attack, settle into a sustained ridge while you hold, then fall away into a long release tail that recedes into depth. Let go: the colour-ridge keeps glowing for almost two seconds as the release rolls back through time.

Drag vertically while you hold — that morphs the timbre between Osc 1 (the slide-down target, sine by default) and Osc 2 (slide-up target, sawtooth by default). With the default pair, pulling down on a key collapses the stack to just the plum fundamental; pulling up grows the full saw harmonic ladder up into the orange/gold.

Lesson hook: set Osc 1 = sine and Osc 2 = sawtooth (defaults), hold a key, and drag from bottom to top of its travel. Students watch the harmonic stack literally appear one band of colour at a time — sine has none, the saw has them all. Try the same gesture with square or triangle on osc 2 to compare odd-only vs all-harmonic stacks.

Colour as a fourth axis

The surface is a 128 × 80 vertex grid. Height is FFT magnitude. Depth is time. And colour is frequency, on the thermal palette real audio software uses — deep indigo at the sub-bass end, plum and crimson through the bass, vermillion and burnt orange through the mids, gold at the top.

So bass energy reads as a heavy purple-red ridge on the left. The fundamental of a C3 note (130 Hz) sits in plum. The 2–4 kHz presence band glows orange. Brilliance above 8 kHz sparkles gold.

Magnitude also fades the saturation, so silent regions melt into the paper rather than colouring it — only where there's energy does the colour come up.