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Artificial Intelligence for Musicians

  1. Introduction
  2. Emergent Harmonic Structures | Software 1.0
  3. Pythagoras and the Music of the Spheres
  4. Building the Modes from Ancient Theory
  5. Harmonic Ratios in Nature and Music
  6. Musical Mathematics
  7. Exploring Chance and Randomness
  8. Statistics of Sound
  9. Software 2.0 | Deep Learning: Teaching Computers to See
  10. Software 2.0 | Deep Learning: Teaching Computers to Hear
  11. Software 3.0 | Generative AI: Teaching Computers to Read & Write
  12. Software 3.0 | NotebookLM as RAG

Chapter 4: Harmonic Ratios in Nature and Music

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4.1 Universal Harmony: Ratios in Nature

Harmony shows up everywhere: in spiral leaf growth, ocean resonances, even atomic vibrations. Early philosophers saw these patterns as proof of an ordered universe, the same order that makes musical intervals sound right.

4.2 Harmonic and Overtone Series

A vibrating string produces a harmonic series: integer multiples of a base frequency. These overtones create the natural template for musical intervals.

# Base frequency
base_frequency = 440  # A4

# First 10 harmonics
harmonics = [base_frequency * (n + 1) for n in range(10)]
harmonics

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