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

Acoustics

EP08: Shepard Tones and the Tritone Paradox

EP13: Polyrhythm and Rhythm-Pitch Duality

EP48: Spectral Orchestration — Grisey and the Roughness Curve

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