Why can distortion make bass perception seem deeper on small speakers?

Small speakers often can’t reproduce true sub-bass. Distortion introduces harmonics (like the 2nd, 3rd, etc.) that fill in the bass region perceptually, fooling the brain into hearing deeper bass even when the fundamental is weak. The video discusses this psychoacoustic effect and demonstrates it with harmonic content.

What happens when you square a signal in these examples?

Squaring a signal creates new frequency components, notably a strong second harmonic around twice the fundamental. The video shows how squaring moves energy to higher frequencies and can introduce a second, third, or fourth harmonic depending on how you combine powers of the input. This is demonstrated with the harmonic analyzer.

What is asymmetrical distortion vs symmetrical distortion?

Asymmetrical distortion emphasizes even harmonics (2nd, 4th, 6th), often altering the waveform's symmetry, while odd harmonics (3rd, 5th, etc.) tend to preserve the original waveform more. The video explains this distinction and shows a technique to preserve symmetry by manipulating the sign of the input.

What does the sign-preserving distortion technique do?

The sign-preserving approach keeps the original waveform's sign while applying a distortion operation, then re-applies the sign to the distorted output. This helps control which harmonics are emphasized and can shift a distortion from asymmetrical toward symmetrical behavior.

What is clipping distortion, and when is it used?

Clipping distortion simply cuts the waveform at the top and bottom when it exceeds a threshold, producing a square-like waveform and a strong set of harmonics. The video presents clipping as a classic, straightforward method and compares it to other nonlinear operations.

How many lines of code are used to create the simple distortion example, and what does it do?

The video notes that the distortion example can be implemented in a small amount of code—often just a handful of lines—plus some optional components like gate and delay. The speaker even points out a six- to seven-line snippet, illustrating how compact DSP routines can be for audio effects.

Coding a Guitar Sound in C - Computerphile

Computerphile

Education3 min read15 min video

Mar 5, 2026|38,364 views|2,539|214

computers computerphile computer science

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Key Moments

TL;DR

Nonlinear distortion shapes harmonics to color sound in code.

Key Insights

Distortion arises from nonlinear behavior in audio processing, creating harmonics that alter timbre and perceived bass.

Simple mathematical operations (e.g., squaring, cubing) generate specific harmonic patterns: even harmonics (2f, 4f) and odd harmonics (3f, 5f) in distinct ways.

Symmetry and sign handling affect the harmonic content: asymmetrical operations tend to push certain harmonics differently, while preserving or manipulating sign can reshape the spectrum.

Distortion can trick the brain to perceive bass on small speakers by adding harmonics that imply lower frequencies even when the fundamental is weak or absent.

Practical DSP techniques—clipping, squaring, square-rooting, and alternative power laws—paired with gates, delays, and EQ can build compact, musical effects with few lines of code.

LINEAR VS NONLINEAR BEHAVIOR IN AUDIO

The speaker illustrates a fundamental distinction in audio processing: linear systems respond predictably to changes in input, while nonlinear systems introduce distortions that generate new frequency content. The discussion leans on a real-world example using Formula VST, emphasizing that distortion—not just volume increase—changes how signals are molded as they pass through a device. Nonlinearities produce harmonics, which can color sound from pleasant warmth to aggressive grit. This concept underpins much of audio engineering and digital sound design.

HOW NONLINEARITIES CREATE HARMONICS

By demonstrating operations like input times input (squaring) and higher powers, the speaker shows how new frequencies emerge. Squaring a 1000 Hz tone yields a strong 2000 Hz component (the second harmonic) and, with further operations, introduces 3000 Hz (the third harmonic) and beyond. The visual aid of a harmonic analyzer helps explain why even powers tend to suppress the original fundamental while adding higher multiples. This wave shaping is the essence of many distortion effects.

EVEN VS ODD HARMONICS AND SYMMETRY

The talk distinguishes how even and odd harmonics behave under distortion. Squaring tends to generate even harmonics and can push energy away from the fundamental, sometimes creating an asymmetrical waveform. Conversely, manipulations that preserve symmetry or reintroduce the sign can alter which harmonics dominate. The speaker further demonstrates how manipulating sign can transform an asymmetrical distortion into a more symmetrical one, revealing how subtle coding choices shape the resulting timbre.

WAVE SHAPING EXPERIMENTS AND PRACTICAL OPERATIONS

Beyond squaring, the speaker experiments with other operations such as cubing and taking higher nth powers, showing how different mathematical manipulations craft distinct harmonic patterns. Additional techniques like clipping (hard-limiting the peaks) and even sqrt-based distortions yield very different tonal flavors. The demonstration connects these operations to practical outcomes: creating perceived bass, enhancing transients, or making drums and guitars sound more aggressive or polished depending on the chosen curve.

BUILDING A SIMPLE DISTORTION CHAIN IN CODE

The tutorial showcases a compact plugin chain implemented with a few lines of C code: distortion, a dry/wet mix, and a basic signal path, augmented by a gate, delay, and a bit of EQ. This serves as a concrete example of how developers can experiment locally to sculpt tone, push transients, and shape the spectral content. The speaker emphasizes that such minimal code can still yield surprisingly musical results, especially when paired with practical processing like gating and subtle EQ adjustments.

REAL-WORLD APPLICATIONS: DRUMS, GUITAR, AND PERCEPTION

The discussion applies these concepts to a guitar and a drum track, illustrating how distortion interacts with transients, harmonics, and room/frequency response. Drums with subtle distortion can gain punch, while guitars benefit from controlled clipping and delay. The speaker notes that real-world devices often rely on a mix of harmonic enrichment and transient control to achieve perceived loudness and bass response, sometimes leveraging harmonic content to compensate for speaker limitations on smaller systems.

Mentioned in This Episode

●Tools & Products

Distortion Quick Reference Card

Practical takeaways from this episode

Do This

Start with a clean signal to observe how nonlinearity changes the spectrum.

Use a dry/wet mix to control the amount of distortion you hear.

Experiment with squaring, cubing, and higher powers to shape harmonic content.

Clipping is a simple, classic distortion; compare it with soft/clipped variants.

Add transient-focused processing (e.g., gentle delay or gate) to accompany distortion without overwhelming the signal.

Avoid This

Don’t over-distort; excessive distortion can mask the original signal and reduce intelligibility.

Don’t neglect transients and dynamic content when applying distortion.

Don’t rely on distortion to create real bass content on devices that can’t reproduce sub-bass.

Don’t assume the same harmonic effect will translate identically across all playback systems.

Common Questions

Nonlinear distortion occurs when the input-output relationship is not proportional, which generates new frequencies called harmonics. The video explains that nonlinearities in audio produce distortion and harmonics, which can be used creatively or sound unpleasant depending on how they’re applied. This is demonstrated through examples with simple signal manipulations in a plugin like Formula VST.