Savart

The savart /səˈvɑːr/ is a unit of measurement for musical pitch intervals (playⓘ).

Today, musical use of the savart has largely been replaced by the cent and the millioctave.

The savart is practically the same as the earlier heptameride (eptameride), one seventh of a meride (playⓘ).

is the ratio of frequencies of a given interval, the corresponding measure in savarts is given by:

Like the more common cent, the savart is a logarithmic measure, and thus intervals can be added by simply adding their savart values, instead of multiplying them as you would frequencies.

Sometimes this is rounded to 300, which makes the unit more useful for equal temperament.

[1] The conversion from savarts into cents, millioctaves or millidecades is:

Sauveur proposed the méride, eptaméride (or heptaméride), and decaméride.

[3] The attraction of this scheme to Sauveur was that log10(2) is very close to .301, and thus the number of heptamerides in a given ratio is found to a high degree of accuracy from simply its log times 1000.

This is equivalent to assuming 1000 heptamerides in a decade rather than 301 in an octave, the same as Savart's definition.

[1] A disadvantage of this scheme is that there are not an exact number of heptamerides/savarts in an equal tempered semitone.

[4] A related unit is the jot, of which there are 30103 in an octave, or approximately 100,000 in a decade.

The jot is defined in a similar way to the savart, but has a more accurate rounding of log10(2) because more digits are used.

The jot was first described by Augustus De Morgan (1806-1871) which he called an atom.

The name jot was coined by John Curwen (1816-1880) at the suggestion of Hermann von Helmholtz.