Literature:Elements of Harmony

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Elements of Harmony (Classical Windermere: Yămyămał clisăybäl) 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/monzos by unique factorization
  • Book 3 discusses harmonic properties of various scales.
    • odd- and prime-limit
    • chord voicings
    • otonal and utonal chords
    • tonality diamond

Full text (Varrkkún)

Full text (English)

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