Sound from Scratch

Watch a tone become a list of numbers, find the limit half the sample rate sets, and hear a tone above it fold into a slower one.

Store each sample in a handful of bits, watch the rounding error follow the tone, and hear dither turn distortion into hiss.

One phase accumulator drives every classic waveshape; watch it advance and wrap sample by sample, then hear the four shapes at 220 Hz.

A five-state machine draws a note's loudness tick by tick: attack, decay, sustain, release. Watch it run, break it with a zero, and hear the shape on a tone.

Add sines at multiples of a fundamental one at a time and watch a square, saw, or triangle emerge, corners, Gibbs ripple, and all.

Push a saw through a resonant low-pass biquad sample by sample, read the five numbers that make a filter, and hear the cutoff and resonance every synth bass is built on.

Let one oscillator push another's phase around, predict the sidebands with Bessel functions, and hear the bells and electric pianos that filled the 1980s.

Correlate one frame of samples with a probe cosine and sine for every bin, watch the sums grow and cancel, and read a wave's recipe back off it.

Cut a signal into overlapping frames, window each one, transform it, and watch the columns stand up into a picture of frequency against time.

Cut a signal into frames, turn each frame into cosine coefficients, keep the largest few and round them, then transform back: the idea under MP3, AAC, and Opus, one frame at a time.

Walk up the keyboard a semitone at a time, compute each frequency from A4 and a power of two, and see why equal steps come out equally spaced on a log axis.

Build a scale from a root and a pattern of semitones, stack thirds on every degree, and read each chord's quality off the gaps between its tones.

Run a sixteen-step pattern on two clocks: a jittery timer that looks ahead and a sample-accurate audio clock that plays, and watch a stall make a note late.

Three step patterns drive three synth voices through a mixer, one block at a time: every class from the earlier lessons running together as a tiny DAW.