Cancelled Harmonics (ASA 1)

This tool demonstrates Fourier analysis by letting you build and deconstruct complex tones from their harmonic components. It is an interactive example of the ASA Cancelled Harmonics demo.

A key insight from psychoacoustics is that our perception of complex sounds depends on whether their components change independently. When all harmonics maintain constant relative amplitudes, we perceive a unified timbre. But the moment a single harmonic is removed or added, it becomes distinctly audible—even if we couldn't hear it as a separate tone before.

This phenomenon reveals that our auditory system can switch between two modes: perceiving the whole sound as a single entity, or attending to its individual frequency components. The spectrogram visualizes these components in real time, making it easier to connect what you hear with what you see.

Four waveform presets control the harmonic structure: sawtooth (all harmonics at 1/n amplitude), square (odd harmonics at 1/n), triangle (odd harmonics at 1/n²), and sine (fundamental only). The fundamental frequency is adjustable from 50-500 Hz.

Try the following exercises to develop your analytical listening skills:

1. Click Auto Demo and listen carefully. Pay attention to how each harmonic separates from the complex tone when it is removed, then merges back into the unified timbre when restored. Can you follow each harmonic as it "pops out" and returns?
2. Enable all harmonics and toggle individual ones manually. Notice how a harmonic becomes distinctly audible when it changes state, even though you couldn't hear it as a separate tone before.
3. Start with all harmonics disabled and add them one by one from the fundamental up. Notice how the timbre builds as you add higher harmonics.
4. Try isolating specific harmonics: Disable all except one or two adjacent harmonics. Can you hear them as separate tones?
5. Experiment with waveform presets and notice how different harmonic structures create different timbres (sawtooth vs. square vs. triangle).