Literature:Elements of Harmony: Difference between revisions
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'''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. | '''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. | ||
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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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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
- 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