MyWorld · reference samples

Math × Music Lab

Interactive samples where the math hiding inside music becomes something you can see and hear — from the spectrum of a sound to the group theory of chords. Made to explore, take apart, and build on.

交互小样,供参考探索:声音里的数学 — 频谱、傅立叶、几何、群论、节奏数论 — 都能看得见、听得见。全部浏览器直接打开,无需登录。

Start here

Playful and immediate — a good first look at “music is math.”

Go deeper

Rigorous, gifted / competition level — the real mathematics, made interactive and audible.

🌀Fourier Studio
Draw a curve and watch rotating circles (Fourier coefficients) re-trace it — then hear the same series as sound.
Fourier / DFTOpen →
🌈Constant-Q Spectrogram
A musical (log-frequency) spectrogram with a harmonic-stack overlay — see the overtone series land on the real partials.
spectra / CQTOpen →
🎛Synthesis Dojo
Stack harmonics into square/saw/triangle waves, or explore FM sidebands (Bessel functions) — and match a mystery timbre.
Fourier series / FMOpen →
🥁Hear the Shape of a Drum
Membrane vibration modes, Chladni nodal lines, and why drums sound un-pitched — with Kac's famous question.
spectral geometryOpen →
🔷Tonnetz & the P/L/R Group
Neo-Riemannian voice-leading on the hexagonal lattice — a dihedral group of order 24 that you can hear.
group theoryOpen →
♾️Voice-Leading Geometry
Chords live in orbifolds: the space of two notes is a Mobius strip. Drag, listen, and find the shortest voice-leading.
orbifold geometryOpen →
🕛The 12-Tone Clock
Pitch-class set theory (Forte, interval vectors, symmetry) plus Burnside/Polya counting of how many distinct scales exist.
set theory / countingOpen →
🦒Rhythm Necklace
Euclidean rhythms (the GCD algorithm in disguise), perfect balance via the DFT, maximally-even and well-formed scales.
rhythm number theoryOpen →
🎚Tuning Lab
Why 12 notes per octave? Continued fractions of log2(3/2) land on 12/41/53-EDO; hear just intonation lock vs equal temperament beat.
tuning / number theoryOpen →
🌸Harmonograph & Lissajous
Frequency ratios become curves: a 2:3 Lissajous is a perfect fifth you can see and hear; damped pendulums draw rosettes.
ratios / curvesOpen →

Each sample is a single self-contained page — it runs entirely in your browser, works offline, and loads no external code. Best on a laptop or tablet; the microphone samples need permission (they also work with built-in synthesized sounds if you decline). Clean-room originals built for MyWorld; concepts credit the open-source and academic work they learn from.