Harmonic Stack Synthesizer
Run the Harmonic Stack Synthesizer MicroSim Fullscreen
You can include this MicroSim on your website using the following iframe:
1 2 | |
About This MicroSim
A flute and a violin playing the same written note sound completely different, yet a tuner reports the same pitch for both. This sim shows why.
The fundamental is pinned at 440 Hz. The four sliders above it add overtones at exact integer multiples — 880, 1320, 1760, and 2200 Hz. As you raise them, the combined waveform's shape changes dramatically. What does not change is the dashed red spacing: the whole pattern still repeats every 1/440 second.
Press Play Sound and you hear the same thing you are looking at: five sine oscillators, one per harmonic, at the amplitudes the sliders are set to. The mix is normalized to its own peak, so adding overtones changes the character of the sound without making it louder — the change you hear is timbre alone.
That is the separation you are meant to see:
- Pitch is the repetition rate of the pattern. It is set by the fundamental.
- Timbre is the shape of the pattern within one repetition. It is set by the overtone mixture.
This matters for the rest of the course because an FFT of any of these waveforms puts a spike at 440 Hz and additional spikes at each active overtone. The overtone mixture is the spectrum.
How to Use
- Start at the default pure tone: only the fundamental is on, and the wave is a plain sine. Note where the dashed cycle markers fall.
- Raise the 2nd slider to about 75%. The waveform develops a lopsided shape — but check the dashed markers. They have not moved.
- Press Violin, then Clarinet. Compare the two shapes and the two slider patterns. The clarinet's near-empty even harmonics are why it sounds hollow.
- Check Show individual harmonics overlay to see the component sine waves that are being summed. Count how many peaks the 3rd harmonic fits into one fundamental cycle. (Three.)
- Press Play Sound, then step through the presets again with the sound on. The character changes; the note does not. Leave the sound running while you drag a single overtone slider to hear that one partial fade in and out.
- Return to Pure tone and confirm the shape resets while the period never budged through any of it. Press Stop Sound when you are done.
Presets
| Preset | 1st | 2nd | 3rd | 4th | 5th | Character |
|---|---|---|---|---|---|---|
| Flute | 100% | 20% | 5% | 0% | 0% | Nearly pure, breathy |
| Violin | 100% | 75% | 55% | 30% | 20% | Rich, many strong overtones |
| Clarinet | 100% | 5% | 70% | 5% | 45% | Hollow — odd harmonics dominate |
| Pure tone | 100% | 0% | 0% | 0% | 0% | A plain sine wave |
Lesson Plan
Grade Level
Undergraduate (college junior/senior)
Duration
12-15 minutes
Prerequisites
- A sine wave has an amplitude and a frequency
- Waves can be added together point by point
Learning Objective
Students will be able to examine how the combined waveform's shape changes with overtone mixture, and differentiate the role of the fundamental frequency (pitch) from the role of the overtone mixture (timbre).
Activities
- Move one overtone (4 min): Students raise the 2nd harmonic alone and describe what changed and what stayed fixed, citing the cycle markers.
- Compare instruments (6 min): Students record the slider patterns for violin and clarinet and articulate what distinguishes them.
- Predict the spectrum (4 min): For the clarinet preset, students sketch where they expect spikes to appear in a frequency plot.
Assessment
Ask: "Two waveforms have identical repetition periods but different shapes. What is the same about them and what is different, in both musical and signal-processing terms?"
Related Resources
References
- Harmonic series (music) — integer-multiple overtones above a fundamental.
- Timbre — why instruments differ at identical pitch.
- Fourier series — the formal statement that periodic waves decompose into harmonics.