Savart

Physical unit
Unit name	Savart
Unit symbol	${\displaystyle \mathrm {Savart} }$, ${\displaystyle \mathrm {savart} }$
Physical quantity (s)	musical interval
Formula symbol	${\displaystyle \Delta }$
dimension	${\displaystyle {\mathsf {{\frac {T^{-1}}{T^{-1}}}=1}}}$
In SI units	${\displaystyle 1}$
Named after	Félix Savart
Derived from	Frequency ratio
See also: cent , millioctave , neper , octave

Diatonic intervals
Prime second third fourth fifth sixth seventh octave none decime undezime duodecime tredezime semitone / whole tone
Special intervals
Microinterval Comma Diësis Limma Apotome Ditone Tritone Wolf fifth Natural septime
units
Cent Millioctave Octave Savart

The Savart / saˈvaːr / (after Félix Savart ; older name of the unit: Eptaméride ) is an auxiliary unit of measurement for musical intervals . 1000 Savart corresponds to a frequency ratio of 10: 1.

Today, instead of the Savart, the cent measure is usually used, and occasionally the millioctave .

definition

If the frequency ratio that determines a given interval, then the associated Savart value is: ${\displaystyle {\frac {f_{2}}{f_{1}}}}$

${\displaystyle s=1000\cdot \log _{10}\left({\frac {f_{2}}{f_{1}}}\right)}$

${\displaystyle {\begin{aligned}\Leftrightarrow {\frac {f_{2}}{f_{1}}}&=10^{\frac {s}{1000}}\\&=({\sqrt[{1000}]{10}})^{s}\\&\approx 1{,}0023^{s}\end{aligned}}}$

Like the more common cent measure , the savart is a logarithmic measure for intervals. Therefore one can add interval sizes in Savart instead of having to multiply them as with frequency ratios.

Example:

interval	Frequency ratio	in Savart	In cents
1 octave	2: 1	301	1200
2 octaves	4: 1	602	2400
3 octaves	8: 1	903	3600
Fifth	3: 2	176	702
Fourth	4: 3	125	498
major third	5: 4	97	386

Conversions

${\displaystyle 1\ \mathrm {Savart} ={\frac {1200}{1000\cdot \log _{10}(2)}}\ \mathrm {Cent} \approx 3{,}986\ \mathrm {Cent} }$

${\displaystyle 1\ \mathrm {Savart} ={\frac {1}{\log _{10}(2)}}\ \mathrm {Millioktaven} \approx 3{,}3219\ \mathrm {Millioktaven} }$

${\displaystyle \Leftrightarrow 1\ \mathrm {Oktave} \approx 301{,}03\ \mathrm {Savart} }$

history

The Savart was invented in 1701 by the French acoustician Joseph Sauveur and named by him as Eptaméride or Heptaméride .

See also

• Mood

Web links

• Compilation of logarithmic units of measurement for interval sizes ( Memento from June 28, 2001 in the Internet Archive )