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Encyclopedia of Microtonal Music Theory

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[Joe Monzo]

The savart was originally identical to the heptaméride. Later, it was "rationalized" to be a logarithmically equal 1/300 of an octave. This latter will concern us here; for the earlier definition see heptaméride.

A savart is calculated as the 300th root of 2, or 2(1/300), with a ratio of approximately 1:1.002313162. It is an irrational number. A savart has an interval size of exactly 4 cents.

The formula for calculating the savart-value of any ratio r is: savarts = log10(r) * [300 / log10(2)] or savarts = log2(r) * 300.

This interval therefore divides the octave, which is assumed to have the ratio 2:1, into 300 equal parts. Thus a savart represents one degree in 300-edo tuning.

One potential defect of using heptamérides or the related jots, namely that the familiar 12-edo semitone does not come out with an integer number of the smaller division, is here avoided, since 300 divides evenly by 12. Thus, the 12-EDO semitone is exactly 25 savarts.

(Many thanks to John Chalmers for clarifying the history of savarts.)

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savarts calculator

Ratio may be entered as fraction or floating-point decimal number.
(value must be greater than 1)

For EDOs (equal-temperaments), type: "a/b" (without quotes)
where "a" = EDO degree and "b" = EDO cardinality.
(value must be less than 1)

Enter ratio: = savarts

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Ellis, Alexander. 1885.
Appendix XX, in his translation of

Helmholtz, On the Sensations of Tone, p 437.
Dover reprint 1954.

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