For the French physicist from whom the savart takes its name, see Félix Savart.
The savart/səˈvɑːr/ is a unit of measurement for musical pitch intervals (playⓘ). 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 Today, musical use of the savart has largely been replaced by the cent and the millioctave.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 (playⓘ). One tenth of an heptameride is a decameride (playⓘ) and a hundredth of an heptameride (thousandth of a decade) is approximately one jot (playⓘ).
If is the ratio of frequencies of a given interval, the corresponding measure in savarts is given by:
or
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.[1]
Conversionedit
The conversion from savarts into cents, millioctaves or millidecades is:
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 43 × 7 = 301 heptamerides in an octave.[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. The unit was given the name savart sometime in the 20th century.[1] A disadvantage of this scheme is that there are not an exact number of heptamerides/savarts in an equal tempered semitone. For this reason Alexander Wood used a modified definition of the savart, with 300 savarts in an octave, and hence 25 savarts in a 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.[5] 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.[6]
^Martin, S. B., Gaudet, B. J., Klinck, H., Dugan, P. J., Miksis-Olds, J. L., Mellinger, D. K., ... & Moors-Murphy, H. (2021). Hybrid millidecade spectra: A practical format for exchange of long-term ambient sound data. JASA Express Letters, 1(1), 011203.
^Hermann von Helmholtz (1912). On the sensations of tone as a physiological basis for the theory of music, p.437. Longmans, Green.
^Alexander Wood, The Physics of Music, pages 53-54, Read Books, 2007 ISBN140674493X (first published Methuen, 1944 OCLC 220112916.
^Joe Monzo, "Heptaméride" and "Jot", Tonalsoft Encyclopedia of Microtonal Music Theory, retrieved and 11 October 2012.
^Hermann von Helmholtz, (trans. A. J. Ellis), On the Sensations of Tone as a Physiological Basis for the Theory of Music, page 654, Longmans, 1875 OCLC 8101251.
January 11, 2024
savart, french, physicist, from, whom, savart, takes, name, félix, savart, ɑːr, unit, measurement, musical, pitch, intervals, play, savart, equal, thousandth, decade, 313714, cents, 9863, cents, musically, just, intonation, interval, decade, precisely, just, m. For the French physicist from whom the savart takes its name see Felix Savart The savart s e ˈ v ɑːr is a unit of measurement for musical pitch intervals play 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 play One tenth of an heptameride is a decameride play and a hundredth of an heptameride thousandth of a decade is approximately one jot play 1 100 heptameride jot 1 10 heptameride decameride 1 heptamerides 10 heptamerides 100 heptamerides 1 000 heptamerides decade Contents 1 Definition 2 Conversion 3 History 4 Comparison 5 Other uses 6 See also 7 NotesDefinition editIf f 1 f 2 displaystyle frac f 1 f 2 nbsp is the ratio of frequencies of a given interval the corresponding measure in savarts is given by s 1000 log 10 f 1 f 2 displaystyle s 1000 log 10 frac f 1 f 2 nbsp orf 1 f 2 10 s 1000 displaystyle frac f 1 f 2 10 s 1000 nbsp 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 1 Conversion editThe conversion from savarts into cents millioctaves or millidecades is 1 s a v a r t 1 2 log 10 2 c e n t 3 9863 c e n t 1 mathrm savart frac 1 2 log 10 2 mathrm cent approx 3 9863 mathrm cent nbsp 1 s a v a r t 1 log 10 2 m i l l i o c t a v e 3 3219 m i l l i o c t a v e 1 mathrm savart frac 1 log 10 2 mathrm millioctave approx 3 3219 mathrm millioctave nbsp 1 savart 0 001 decade 1 millidecade 2 History editThe savart is named after the French physicist and doctor Felix Savart 1791 1841 who advocated the earlier similar interval of the French acoustician Joseph Sauveur 1653 1716 Sauveur proposed the meride eptameride or heptameride and decameride 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 43 7 301 heptamerides in an octave 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 The unit was given the name savart sometime in the 20th century 1 A disadvantage of this scheme is that there are not an exact number of heptamerides savarts in an equal tempered semitone For this reason Alexander Wood used a modified definition of the savart with 300 savarts in an octave and hence 25 savarts in a 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 5 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 6 Comparison editName Steps per octave Cents Relative Interval Ratio AudioDecade 0 301030 3 986 313714 1 000 heptamerides 101 1 10 000000 Play Meride 43 004285 27 904196 7 heptamerides 107 1 000 1 016249 Play Heptameride 301 029996 3 986314 1 1 000 decade 1 7 meride 10 decamerides or 100 jots 101 1 000 1 002305 Play Demi heptameride 602 059991 1 993157 1 2 heptameride 101 2 000 1 001152 Play Decameride 3 010 299957 0 398631 1 10 heptameride 101 10 000 1 000230 Play Jot 30 103 0 0398631 1 30 103 octave 21 30 103 1 000023 Play Other uses editThe unit is used for acoustical engineering analysis especially in underwater acoustics where it is known as a millidecade See also edit nbsp Music portalDecidecade Musical tuningNotes edit a b Huygens Fokker Foundation Logarithmic Interval Measures Retrieved 2007 06 13 Martin S B Gaudet B J Klinck H Dugan P J Miksis Olds J L Mellinger D K amp Moors Murphy H 2021 Hybrid millidecade spectra A practical format for exchange of long term ambient sound data JASA Express Letters 1 1 011203 Hermann von Helmholtz 1912 On the sensations of tone as a physiological basis for the theory of music p 437 Longmans Green Alexander Wood The Physics of Music pages 53 54 Read Books 2007 ISBN 140674493X first published Methuen 1944 OCLC 220112916 Joe Monzo Heptameride and Jot Tonalsoft Encyclopedia of Microtonal Music Theory retrieved and archived 1 11 October 2012 Hermann von Helmholtz trans A J Ellis On the Sensations of Tone as a Physiological Basis for the Theory of Music page 654 Longmans 1875 OCLC 8101251 Retrieved from https en wikipedia org w index php title Savart amp oldid 1180350158, wikipedia, wiki, book, books, library,
