Literature:Elements of Harmony

Elements of Harmony (Classical Windermere: Yămyămał clisăyfäl) is a textbook on just intonation authored in Classical Windermere by physicist, mathematician and composer Tsăhongtamdi covering elementary number theory, acoustics, and just intonation music theory.

Contents

• Book 1 discusses mathematical results:
  • Basically the number theory results in Euclid's Elements plus...
  • Continued fractions
• Book 2 discusses basic acoustics (don't mention frequencies)
  • monochord; building it
  • Mersenne's Laws?
  • harmonic series
  • intervals as rational string length ratios (given equal thickness and tension); these can be written as tuples by unique factorization
• Book 3 discusses harmonic properties of various scales.
  • odd- and prime-limit
  • chord voicings
  • The tonality diamond is described as a way to "connect" overtone chords/scales over different fundamentals.