# 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

${\ displaystyle 1 \ \ mathrm {Savart} = {\ frac {1200} {1000 \ cdot \ log _ {10} (2)}} \ \ mathrm {Cent} \ approx 3 {,} 986 \ \ mathrm {Cent }}$ ${\ displaystyle 1 \ \ mathrm {Savart} = {\ frac {1} {\ log _ {10} (2)}} \ \ mathrm {Millioctaves} \ approx 3 {,} 3219 \ \ mathrm {Millioctaves}}$ ${\ displaystyle \ Leftrightarrow 1 \ \ mathrm {octave} \ approx 301 {,} 03 \ \ mathrm {Savart}}$ ## history

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