savart

The savart was originally identical to the heptameride. 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 heptameride.

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 is:

savarts = log₁₀(ratio) * [300 / log₁₀(2)]

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.

The potential defect of using heptamerides 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.)

REFERENCES

Ellis, Alexander. 1885.
Appendix XX, in his translation of
Helmholtz, On the Sensations of Tone, p 437.
Dover reprint 1954.

[from Joe Monzo, JustMusic: A New Harmony]

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