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.

Supporters of Soha Plu believe that the text was written in Schlaub before it was translated into Classical Windermere, and that Tsăhongtamdi is simply a Windermere pseudonym of a (probably) Hlou composer.

Contents

• 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.

Tsăhongtamdi's most influential recommendation was against using fixed-pitch instruments; he argued that they were expressively limited. This recommendation was lasting in influence - most instruments used in traditional Hlou-Shum music are flexible-pitch instruments.