User:Sintel/The mathematics of temperaments: Difference between revisions
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<h1>The mathematics of tuning and temperament (part 1)</h1> | <h1>The mathematics of tuning and temperament (part 1)</h1> | ||
<i><small>These articles are aimed at people with a good grasp of mathematics and not necessarily music theory.</small></i> | |||
<h2>Just intonation</h2> | <h2>Just intonation</h2> | ||
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<p> | <p> | ||
For example: 5-limit just intonation is | For example: 5-limit just intonation is the set of intervals generated by <math> \left\{ 2,3,5 \right\} </math>: | ||
$$ | $$ | ||
\forall q \in \mathbb{J}^{5} : \, q = 2^a \cdot 3^b \cdot 5^c \text{ with } a,b,c \in \mathbb{Z} | \forall q \in \mathbb{J}^{5} : \, q = 2^a \cdot 3^b \cdot 5^c \text{ with } a,b,c \in \mathbb{Z} | ||
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[[User:Sintel/The mathematics of temperaments part 2|Continued in part 2]] | [[User:Sintel/The mathematics of temperaments part 2|Continued in part 2]] | ||
</p> | </p> | ||