Literature:Elements of Harmony

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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.


  • Book 1 discusses mathematical results:
    • Prime factorization
    • Continued fractions and mediants
  • 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 just intonation scales built from notes taken from overtone and undertone series.
    • odd- and prime-limit
    • chord voicings
    • The tonality diamond is described as a way to "connect" overtone chords/scales over different fundamentals.

Full text (Classical Windermere)

Full text (English)