"When Music Meets Mathematics" series + making music while typing + music version of Cursor.Turning the beauty of mathematics into audible sound with vibecoding.
1. Euclidean Rhythm (Series 1)
Conceptual origin
- Godfrey Howson in proposed in 2004(specifically introduced in the paper, with little direct relation to Euclid himself)
- A tight integration of mathematics × music
Core principle (16-step sequencer example)
Algorithm: Distribute N drum hits as evenly as possible across an M-step sequence.
| Number of drum hits | 16-step distribution | Result |
|---|---|---|
| 4 | 16 ÷ 4 = 4 | Perfectly even(1 drum hit every 4 steps) |
| 8 | 16 ÷ 8 = 2 | Perfectly even(1 drum hit every 2 steps) |
| 6 | 16 ÷ 6 ≠ integer | Maximally even(alternating 2-step + 3-step intervals, symmetric pattern) |
| 7 | 16 ÷ 7 ≠ integer | Mostly 2-step + 3-step intervals,no 4-step or 1-step gaps appear |
Core property: When division is not exact,avoid intervals that are too short or too long, and achieve maximally even distribution.
Practical application cases
| Tool | Use |
|---|---|
| Euclid Circles modular synthesizer | Physical hardware synthesizer module, strong Techno feel |
| Tidal Cycles programming language | Invoke the Euclidean rhythm algorithm with a short piece of code |
| Strudle live coding tool | Same as above, for music programming and creation |
| NI Circular (2024 plugin) | Native Instruments plugin with built-in Euclidean algorithm |
| Minimalism + Euclidean rhythm | Combined with circular visualization, displayed on a flat circle |
Creator's self-made tool
16-step sequencer based on open-source applications + self-development:
- Adjust the number of active points (number of drum hits)
- Adjust distribution positions
- Replaceable timbres (local sound library)
- 4 groups for comparison
- Adjust BPM + volume
2. Whitney Music Box (Series 2)
Concept
Visualization work by John Whitney (experimental animator) from the 1980s. An excellent trinity integration of music + mathematics + visualization.
Classic 48-count mode
48 个点 = 4 个八度(12 半音 × 4)
每个点代表一个半音
最外侧小球:速度最快(转 48 周)
最内侧小球:速度最慢(转 1 周)
Periodic visualization of mathematical ratios
As time progresses, the small balls form different fractional ratios (users can intuitively see):
- 1/8 → 1/7 → 1/5 → 1/4 → 1/3 → Half-period 1/2
- Also 2/7 and others
21 modes
| Mode | Description |
|---|---|
| Classic 48 mode | Semitone increments |
| Basic resonance mode | Fundamental tone 20 Hz → 2nd point 40 Hz → 48th point 960 Hz (by frequency ratio) |
| Microtonal mode | 12 semitones per octave → divided into 72 divisions(12 tones between Do and Re,extremely rich sonic layers) |
| Prime Numbers Only | Keep only tones at prime number positions(non-primes such as 4/6 are removed; tones are discontinuous, with mathematical beauty) |
| Stereo version | |
| Different timbre versions |
"The microtonal mode is my personal favorite; the sound under the 48-count setting is really particularly subtle."
Developer
Gem(developer of the Whitney Music Box) — web version with 21 modes available for online experience.
3. Making Music While Typing — Introduction to Strudle
Letters = timbre mapping
| Character | Timbre |
|---|---|
| K | Kick (bass drum) |
| R | Rimshot (snare rim) |
| -(hyphen) | Closed Hi-Hat |
| =(equals sign) | Open Hi-Hat |
| W | Woodblock (the creator's favorite) |
| T | Tom (tom drum) |
| Space | Pause |
| Copy and paste | Extend note length |
Pitch characters
钢琴符号映射:CDEFGAB = 哆来咪发嗦啦西
8 度感觉:C D E F G A B
和弦:CEF(三和弦)
颤音:用强调符号
Rhythmic freedom
"It doesn't have to strictly follow 8-beat, 6-beat, 16-beat; feels like 6-beat, 3-beat are all actually fine, the whole feel will be a bit different."
Special symbols
- Emphasis symbol: enhances the sound
- Parentheses: timbre change
- Tone symbol: removing it makes the sound duller
4. Music Version of Cursor — Strato live coding (see B1 for details)
See Xiaohongshu / Vibecoding Practical Collection (Games/Tools/Mini Programs) Case 9.Core features:
- Integrated with Codex Codex(adjustable ChatGPT 5.5 reasoning / fast mode)
- HONEST framework
- Code = NOTE blocks(C2/G2/EB3 scales + tracks + ADSR envelope)
- Library of 800+ code snippets(Disco / Rock / Space Ambient / Sense synthesizers)
5. Creating Music with Different Rhythmic Ratios
(Title information, content continues the themes of Euclidean rhythm + irregular meters)
Core: break out of the 4/4 time framework, and create using ratio theory (2:3 / 3:4 / 5:7).
6. If Music Is No Longer Twelve-Tone Equal Temperament
Possibilities beyond twelve-tone equal temperament:
- Microtonality(Whitney Music Box 72-division mode)
- Just intonation(based on integer frequency ratios)
- Non-Western tuning systems(Indian, Arabic, etc.)
- Just Intonation(Just intonation)
7. SuperCollider — Open-Source Synthesizer Project
SuperCollider: Classic open-source music programming language + synthesizer.
- Fully open source
- Server + client architecture
- Suitable for algorithmic composition / live coding / real-time synthesis
8. Core Mindset (running through this series)
"Mathematics and music have a very deep inner connection."
Through vibecoding, turn those "very niche and obscure" mathematical concepts (Euclidean rhythm, Whitney Music Box, microtones, Prime Numbers Only),into tools that can be directly heard, seen, and played with.
Shared design language across projects
| Element | Manifestation |
|---|---|
| Visualization first | Not just playback; let users see how mathematics changes(rotating light balls / flashing drum hits) |
| Adjustable | Number of drum hits / BPM / timbre / mode can all be adjusted |
| Cross-tool referencing | Community ecosystems such as NI plugins / Tidal / Strudle / SuperCollider |
| Open-source spirit | Creators are willing to share via direct message + deploy online for free experience |
See also
- Xiaohongshu / Vibecoding Practical Collection (Games/Tools/Mini Programs) — includes detailed explanation of the music version of Cursor (B1 Case 9)
- Xiaohongshu / AI Webpage + 3D Interaction + Pretext Design Collection — AI webpage design (the visualization tech stack for this series)
- Xiaohongshu / Data + History + Cultural Visualization Project Collection — same author's "Music Takes You Around the World" application
- Xiaohongshu / Creative + Healing + Nature Theme Collection — creative series
- Wang Kai RSI AI Investment Strategy and the "Good Asset, Good Price, Good Volatility" Framework — Wang Kai's investment strategy (corresponding to the analogous cross-discipline of "mathematics × decision-making")