Tier 1+ Pass-1. 5 paper 34 of 45. ITU-derived music + arts on pitch + rhythm + timbre + harmony + form. Pythagoras + AI music + Suno/Udio + RIAA 2024. 6. 24. Defines Kₘusic = -log ρₘusic as the operator-algebraic modular Hamiltonian on Hₚitch ⊗ Hᵣhythm ⊗ Hₜimbre ⊗ Hₕarmony ⊗ Hform. Kₘusic inherits from KQG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Pythagorean / Just / 12-TET intervals: perfect 5th 3: 2 vs 12-TET +1. 955 cents, major 3rd 5: 4 -13. 686 cents, Pythagorean comma 23. 460 cents; Krumhansl-Kessler C major H=2. 42 nats; diffusion descent T=1000 reverse generation recovers ~86 nats Kₘusic structure (Suno/Udio-style). Topics covered. Pythagoras 6c BCE 2: 1/3: 2/4: 3/5: 4, Bach 1722 Well-Tempered, Schoenberg 1908 atonality + 1923 12-tone, Krumhansl 1990 probe-tone, Zatorre 2007 dopamine, Mehr-Sapolsky 2019 Science universality, Suno v3 2024. 3 + v4 2024. 11 + Udio 2024. 4, RIAA 2024. 6. 24 lawsuit, Spotify 626M users 2024. 10, DALL-E 2021->3 + Midjourney v6 + SD 2022. 8 + SDXL + Flux, Beeple 69. 3M Christie's 2021. 3. 11, Taylor Swift Eras Tour 2. 2B 2023-24, Refik Anadol MoMA 2022. 11, Vesuvius Challenge 2024. 2. 45-vertex polytope #34 top couplings: #2 AI (0. 92), #28 Neuro (0. 92), #33 Lang (0. 85), #36 Edu (0. 85), #37 History (0. 85), #43 Sports (0. 85). Ten falsifiable predictions: Pₐvg=0. 62, S/M/W=1/6/3: arXiv 2026 (0. 90 S), RIAA Suno/Udio settlement 2025 (0. 70 M), Diffusion = ITU descent formalized 2027 (0. 60 M), Vesuvius complete decoding 2027 (0. 70 M). Pass-2 roadmap: ~1. 5M: Music analytics (500K) + Lean Mathlib (150K) + Suno/Udio/Stability partnership (850K). Copyright © 2026 Munehiro Terada / Roboken. Licensed under CC-BY-4. 0.
Munehiro Terada (Tue,) studied this question.