Savart

Unit of measurement for musical pitch intervalsthe French physicist from whom the savart takes its name

The savart /s//ə/'/v//ɑr/ is a unit of measurement for musical pitch intervals One savart is equal to one thousandth of a decade (10/1: 3,986.313714 cents): 3.9863 cents. Musically, in just intonation, the interval of a decade is precisely a just major twenty fourth, or, in other words, three octaves and a just major third. Today, musical use of the savart has largely been replaced by the cent and the millioctave.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 One tenth of an heptameride is a decameride and a hundredth of an heptameride (thousandth of a decade) is approximately one jot .

The savart is named after the French physicist and doctor Félix Savart (1791–1841) who advocated the earlier similar interval of the French acoustician Joseph Sauveur (1653–1716). Sauveur proposed the méride, eptaméride (or heptaméride), and decaméride. In English these are meride, heptameride, and decameride respectively. The octave is divided into 43 merides, the meride is divided into seven heptamerides, and the heptameride is divided into ten decamerides. There are thus heptamerides in an octave. 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. The unit was given the name savart sometime in the 20th century. 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. There are approximately 100 jots in a savart. 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.

Name Steps per octave Cents Relative Interval Ratio Audio Decade 0.301030 3,986.313714 1,000 heptamérides 101/1 10.000000 Méride 43.004285 27.904196 7 heptamérides 107/1,000 1.016249 Heptaméride 301.029996 3.986314 1/1,000 decade, 1/7 méride, 10 decamérides, or 100 jots 101/1,000 1.002305 Demi heptaméride 602.059991 1.993157 1/2 heptaméride 101/2,000 1.001152 Decaméride 3,010.299957 0.398631 1/10 heptaméride 101/10,000 1.000230 Jot 30,103 0.0398631 1/30,103 octave 21/30,103 1.000023

The unit is used for acoustical engineering analysis, especially in underwater acoustics, where it is known as a millidecade.