Literature:Elements of Harmony: Difference between revisions

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'''Elements of Harmony''' ([[Windermere/Classical|Classical Windermere]]: ''Yămyămał clisăyfäl'') is a textbook on just intonation authored in [[Windermere/Classical|Classical Windermere]] by physicist, mathematician and composer Tsăhongtamdi covering elementary number theory, acoustics, and just intonation music theory.
'''Elements of Harmony''' (Windermere: ___) is a collection of [[Windermere]]-language textbooks by physicist, mathematician and composer Tsăhong-Tamdi covering elementary number theory, acoustics, and just intonation music theory.


==Contents==
==Contents==
*Book 1 discusses mathematical results:
*Book 1 discusses mathematical results:
**Basically the number theory results in Euclid's Elements plus...
**Prime factorization
**Continued fractions<!--
**Continued fractions and mediants
**Calculus
**log(x)-->
*Book 2 discusses basic acoustics (don't mention frequencies)
*Book 2 discusses basic acoustics (don't mention frequencies)
**monochord; building it
**monochord; building it
**Mersenne's Laws?
**Mersenne's Laws?
**harmonic series
**harmonic series
**intervals as rational string length ratios (given equal thickness and tension); these can be written as tuples/monzos by unique factorization
**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.
*Book 3 discusses just intonation scales built from notes taken from overtone and undertone series.
**odd- and prime-limit
**odd- and prime-limit
**chord voicings
**chord voicings
**otonal and utonal chords
**The tonality diamond is described as a way to "connect" overtone chords/scales over different fundamentals.
**tonality diamond


==Full text (Varrkkún)==
==Full text (Classical Windermere)==


==Full text (English)==
==Full text (English)==
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Ts-T derives using calculus that the desired function is well-approximated by Taylor polynomials: namely, $log(x+1) = A(x+1) ≈ \sum_{n=1}^{N} (-1)^n \frac{x^n}/{n}$, when $|x| < 1$.
Ts-T derives using calculus that the desired function is well-approximated by Taylor polynomials: namely, $log(x+1) = A(x+1) ≈ \sum_{n=1}^{N} (-1)^n \frac{x^n}/{n}$, when $|x| < 1$.
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[[Category:Translation exercises]]

Latest revision as of 12:52, 9 December 2019

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:
    • 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)

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