Waveforms and Timbre
Timbre lets you distinguish sounds with similar pitch and loudness. A waveform's spectrum contributes to that identity, while attack, decay, noise and resonance describe how the spectrum changes through time.
- spectrum plus time
- 4 ideal waveforms
- same pitch, different partials
Where you run into this
- Synthesis
- Production
- Orchestration
- Mixing
The four ideal spectra
| Waveform | Ideal harmonic content | Approximate amplitude rule |
|---|---|---|
| sine | fundamental only | one component |
| triangle | odd harmonics | 1/n squared |
| square | odd harmonics | 1/n |
| sawtooth | all integer harmonics | 1/n |
These are mathematical ideals. Digital oscillators often use bandlimited versions to prevent high harmonics from folding back as aliasing.
Hear each recipe
Sine. With no harmonic partials above the fundamental, it sounds spectrally simple and is useful for sub-bass and testing.
Triangle. Odd harmonics fall rapidly, adding a soft edge while remaining close to sine.
Square. Stronger odd harmonics produce a hollow, reedy character.
Sawtooth. Even and odd harmonics create a bright starting spectrum with substantial material for filtering.
Match levels before comparing. A louder waveform can appear brighter or fuller even when spectrum is the intended variable.
Timbre changes during a note
A piano begins with a short hammer transient and a bright spectrum, then upper partials decay at different rates. A bowed string can sustain energy. A flute includes breath noise around its periodic tone.
An ADSR envelope controls amplitude over time, but real timbre also involves spectral envelopes that change independently. A filter envelope can brighten an attack and darken the sustain.
Attack carries identity
Remove the first 50 to 100 milliseconds from an instrument recording and recognition may become harder. The onset contains noise, pitch instability and mechanical cues such as pick, hammer, tongue or bow contact.
Reverse a sound and its long-term spectrum can remain similar while its temporal envelope changes completely. The result demonstrates that spectrum alone does not define timbre.
Filter one waveform
Start with sawtooth and close a low-pass filter. Upper harmonics weaken, reducing brightness while the fundamental may remain.
Raise resonance near the cutoff and one frequency region is emphasised. The source spectrum, filter response and envelope now work together.
Compare correctly
- Fix pitchuse one MIDI note.
- Match perceived levelreduce loudness bias.
- Sustain each waveformcompare steady spectra.
- Apply the same envelopeisolate waveform differences.
- Change only attackhear temporal timbre.
- Add the same low-pass filtercompare how rich sources respond.
Real instruments are more complex
A clarinet can emphasise odd harmonics in part of its range, but it is not an ideal square wave. Playing level, register and fingering alter its spectrum. The same caution applies to flute-sine and string-saw comparisons: they are useful starting analogies, not complete acoustic models.