Definition
Nonlinear distortion occurs when the output of a system is not proportional to the input: y = f(x) with f nonlinear. Saturation is a gradual nonlinear distortion at low distortion levels, typical of tape, tubes and transformers; overdrive, distortion and fuzz indicate increasing levels up to hard clipping of the waveform.
Expanding the transfer function as a series: y = a1·x + a2·x² + a3·x³ + …. With x = A·cos(ωt):
- x² = (A²/2) · (1 + cos 2ωt): DC component and 2nd harmonic;
- x³ = (A³/4) · (3·cos ωt + cos 3ωt): 3rd harmonic (and a contribution to the fundamental).
Even-order terms produce even harmonics and come from asymmetric curves; odd-order terms produce odd harmonics and come from symmetric curves. For small signals the harmonic of order n grows by n dB for every dB of input increase: distortion increases rapidly with drive.
Total harmonic distortion is THD = √(V2² + V3² + … + Vn²) / V1, expressed in % or in dB (20·log10 THD): 10% = −20 dB, 1% = −40 dB, 0.1% = −60 dB. THD+N also includes noise. With two or more frequencies f1 and f2 the nonlinearity also produces intermodulation (IMD), with components at m·f1 ± n·f2 that are not harmonically related to the notes; the SMPTE test uses 60 Hz and 7 kHz in a 4:1 amplitude ratio. In digital, harmonics beyond fs/2 fold back into the band (aliasing) if the processor does not work with oversampling.
Parameters and units
- Drive / input: dB of gain before the nonlinearity.
- THD: light saturation 0.1–1%; obvious saturation 1–5%; overdrive 5–20%; distortion and fuzz above 20%.
- Bias / asymmetry: amount of even harmonics.
- Tone / pre and post filters: control which frequencies are distorted and which harmonics remain.
- Mix: 10–50% in parallel saturation.
- Oversampling: ×2–×16.
- Output: level compensation.
Character of the harmonics: the 2nd is the octave (consonant, density and warmth); the 3rd is the octave plus the fifth (more bite); the 5th, 7th and 9th are progressively harsher. For professional tape, the reference maximum operating level (MOL) is the level at which the 3rd harmonic reaches 3%.
Musical function
Saturation adds density and perceived loudness at the same peak level, makes bass audible on small speakers thanks to the harmonics (the missing fundamental is reconstructed by the ear), gives cohesion to buses and character to individual tracks. Distortion is a timbral choice for guitars, basses, drums and aggressive vocals. Intermodulation explains why heavy distortion sounds clean on power chords (fifth and octave, simple ratios) and dirty on chords with thirds and sevenths.
Practical example
- 808 at 45 Hz on a smartphone: the speaker reproduces from 150–200 Hz upward and the fundamental does not come through. A saturation with THD 5–10% generates harmonics at 90, 135, 180, 225, 270 Hz: the note becomes audible. In the analysis the Upper bass (120–250 Hz) and Low mids (250–500 Hz) bands of the track rise by 4–6 dB.
- Drive: raising the drive by 3 dB, the 3rd harmonic grows by 9 dB in absolute terms, that is 6 dB relative to the fundamental.
- Vocal with tape saturation: THD 1–2%; the crest factor drops by 1–2 dB and the vocal becomes denser at the same integrated loudness.
Common mistakes
- Saturating every track: small distortions add up and the mix becomes opaque and fatiguing.
- Judging saturation without compensating the level: the louder signal seems better.
- Saturating bright material without oversampling: aliasing produces inharmonic components.
- Heavily distorting complex chords or entire mixes: intermodulation makes the sound muddled.
- Adding strong odd harmonics to the sub: the harmonics in the low mids accumulate and produce mud.
- Forgetting that saturation lowers the crest factor and changes the work of subsequent compressors.
How to check it
- App analysis: compare the track before and after: the energy per band shows where the harmonics appear (for an 808, the Upper bass and Low mids bands); Crest factor (peak − RMS) and PLR drop; the Integrated loudness (BS.1770) must be brought back to the initial value with the output for a fair comparison.
- THD measurement: send a 100 Hz or 1 kHz sine wave to the saturator and read the harmonics with an analyzer at FFT ≥ 8192 (Voxengo SPAN, Plugin Doctor): THD = square root of the sum of the squares of the harmonics relative to the fundamental.
- Aliasing test: with a 5–8 kHz sine wave, components below the fundamental or between the harmonics indicate aliasing.
Starting settings
| Parameter | Value | Why |
|---|---|---|
| Light saturation (bus, vocal) | THD 0.1–1% | Density without perceptible distortion. |
| Saturation of 808s and basses | THD 3–10% | Harmonics audible on small speakers. |
| Parallel saturation | mix 10–50% | Controlled color while preserving transients. |
| Oversampling | ×4–×8 | Reduces aliasing of the high harmonics. |
| Asymmetry | low for neutrality, high for warmth | Even harmonics soften, odd ones add bite. |
| Level compensation | loudness unchanged within 0.5 LU | Fair comparison against bypass. |
How to check the result
- Integrated loudness of the track unchanged within 0.5 LU between saturation on and bypass during comparison.
- Crest factor of the saturated track reduced by no more than 3 dB.
- No inharmonic component in the spectrum with a 5–8 kHz test sine wave.
- Energy of the mix's Upper bass and Low mids bands within ±2 dB of the reference after saturating the basses.