Savart

The savart /IPA|saˈvaːr/ (Audio|Savart on C.mid|play) is a unit of measurement for musical intervals. Today the savart has largely been replaced by the cent and the millioctave. Another name for the savart is the eptaméride.

Definition

If $frac\{f\_2\}\{f\_1\}$ is the ratio of frequencies of a given interval, the corresponding measure in savarts is given by:

$s\; =\; 1000\; log\_\{10\}\{frac\{f\_2\}\{f\_1$

or

$frac\{f\_2\}\{f\_1\}\; =\; 10^\{frac\{s\}\{1000$

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. The number of savarts in an octave is 1000 times the base-10 logarithm of 2, or nearly 301.03. Sometimes this is rounded to 300, which makes the unit more useful for equal temperament.cite web|url=http://www.xs4all.nl/~huygensf/doc/measures.html|title=Logarithmic Interval Measures|author=Huygens-Fokker Foundation|access-date=2007-06-13]

Conversion

The conversion from savarts into cents or millioctaves is rather simple:

$1\; mathrm\{savart\}\; =\; frac\{1200\}\{1000log\_\{10\}\{2\; mathrm\{cent\}\; approx\; 3.986\; mathrm\{cent\}$

$1\; mathrm\{savart\}\; =\; frac\{1\}\{log\_\{10\}\{2\; mathrm\{millioctave\}\; approx\; 3.3219\; mathrm\{millioctave\}$

History

The savart is named after the French physicist and doctor Félix Savart (1791-1841), but it was devised earlier by the French acoustician Joseph Sauveur (1653-1716), who named it the "eptaméride" or "heptaméride", as one seventh of a "méride", the earliest logarithmic interval measure. The name was changed to savart in the 20th century.

See also

*Cent (music)
*Musical tuning
*Logarithm

Notes

External links

* [http://www.xs4all.nl/~huygensf/doc/measures.html Logarithmic Interval Measures]