AMATH 390
数学与音乐
数学基础篇
01 Chord Space and the Torus 02 String Vibration and the Wave Equation 03 Bach and Graph Connectivity 04 All-Interval Rows and ℤ₁₂ 05 Turán's Theorem and Counterpoint 06 Graph Coloring and Voice Assignment 07 Information Entropy and All-Interval Rows 08 Shepard Tones and the Tritone Paradox 09 Combination Tones and Nonlinear Acoustics
Jacob Collier 系列
10 Negative Harmony and the Dihedral Group D₁₂ 11 Comma Drift and the Impossibility of Perfect Tuning 12 The Circle of Fifths as a Folded Spiral 13 Polyrhythm and Rhythm-Pitch Duality
拓扑数学专篇
14 Tonnetz Hodge Duality
歌剧系列
15 Opera Acoustics and the Singer's Formant 16 Rossini's Code — Budden, Gossett, and the Convention System 17 Leitmotif Networks — Wagner's Ring Cycle 18 Game Theory in Operatic Duets 19 Vibrato as FM Synthesis 20 Character Interaction Networks in Opera
AI 音乐三部曲
21 From Markov to Diffusion — Sixty Years of AI Composition 22 How AI Writes Music — EnCodec and RVQ 23 Can AI Understand Music? Latent Space and Information Bottleneck
流行音乐 × 数学
24 The Information Code of Pop Music 25 Why Music Gives You Goosebumps — Prediction Error and Frisson 26 The 1/f Law of Music 27 Answering Viral Critics with Mathematics
音乐技术系列
28 Your Microphone Is a Damped Oscillator 29 Primes in the Studio — Standing Waves and QRD Diffusers 30 The Sampling Theorem Is Not What You Think 31 The Warmth of Moog Has an Equation 32 Chebyshev Waveshaping — Buchla and West Coast Synthesis 33 One Delay Line, One String — Physical Modeling 34 The Bessel Secret of the DX7 — FM Synthesis Mathematics 35 The Phase Vocoder — Mathematics of Pitch Shifting 36 Quanta of Sound — Gabor and the Uncertainty Principle 37 Your EQ Moves Poles — Biquad Filters 38 Reverberation Is Matrix Multiplication 39 How Spotify Knows You Are Too Loud — The LUFS Algorithm 40 What MP3 Deletes — Psychoacoustics and MDCT
分离与识别
41 The Mathematics of Source Separation — NMF to Demucs 42 Chord Recognition — From Chroma Vectors to Viterbi Decoding
节奏数学篇
43 Euclidean Rhythms 44 Microtiming & Groove 45 Minimalism & Phase Patterns 46 Rhythmic Canons & Tiling
算法作曲篇
47 Counterpoint as Constraint Satisfaction 48 Spectral Orchestration — Grisey and the Roughness Curve 49 L-Systems & Algorithmic Composition 50 Stochastic Composition — Xenakis and Probabilistic Music 51 Why Twelve Notes? — Continued Fractions and Tuning Optimization 52 Optimal Transport & Melody
定理索引 数学领域 关于

Combinatorics

EP05: Turán's Theorem and Counterpoint
EP06: Graph Coloring and Voice Assignment
EP07: Information Entropy and All-Interval Rows
EP16: Rossini's Code — Budden, Gossett, and the Convention System
EP43: Euclidean Rhythms
EP45: Minimalism & Phase Patterns
EP46: Rhythmic Canons & Tiling
EP47: Counterpoint as Constraint Satisfaction
EP49: L-Systems & Algorithmic Composition
Sibelius P.
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