Literature:Elements of Harmony: Difference between revisions

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'''Elements of Harmony''' (~~Netagin: letter~~/~~[TRANSFIX~~]~~-PL.CONST harmony~~) is a ~~collection of~~ [[~~Netagin~~]]~~-language textbooks~~ by physicist, mathematician and composer ~~Tsâhoŋ-Tamdi~~ covering elementary number theory, acoustics, and just intonation music theory.

'''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.

Supporters of [[Verse:Tricin/Plud Schrog-Hahn|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:

**~~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)

**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

**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

**chord voicings

**~~otonal and utonal~~ chords

**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.

==Full text (Schlaub)==

==Full text (~~Netagin~~)==

==Full text (Classical Windermere)==

==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 $|x| < 1$.

-->

[[Category:Tricin]]

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-'''Elements of Harmony''' (Netagin: letter/[TRANSFIX]-PL.CONST harmony) is a collection of [[Netagin]]-language textbooks by physicist, mathematician and composer Tsâhoŋ-Tamdi covering elementary number theory, acoustics, and just intonation music theory.
+'''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.
+Supporters of [[Verse:Tricin/Plud Schrog-Hahn|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:
-**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)
 **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
+**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
 **chord voicings
-**otonal and utonal chords
+**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.
+==Full text (Schlaub)==
-==Full text (Netagin)==
+==Full text (Classical Windermere)==
 ==Full text (English)==
@@ Line 35: / Line 39: @@
 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 $|x| < 1$.
 -->
+[[Category:Tricin]]