Scientific pitch
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Scientific pitch, also known as philosophical pitch, Sauveur pitch or Verdi tuning, is an absolute
concert pitch Concert pitch is the pitch (music), pitch reference to which a group of musical instruments are musical tuning, tuned for a performance. Concert pitch may vary from musical ensemble, ensemble to ensemble, and has varied widely over music history. ...
standard which is based on
middle C C or Do is the first note and semitone of the C major scale, the third note of the A minor scale (the relative minor of C major), and the fourth note (G, A, B, C) of the Guidonian hand, commonly pitched around 261.63  Hz. The actual frequen ...
( C4) being set to 256 Hz rather than 261.62 Hz, making it approximately 37.6 cents lower than the common A440 pitch standard. It was first proposed in 1713 by French physicist
Joseph Sauveur Joseph Sauveur (24 March 1653 – 9 July 1716) was a French mathematician and physicist. He was a professor of mathematics and in 1696 became a member of the French Academy of Sciences. Life Joseph Sauveur was born in La Flèche, the son of a ...
, promoted briefly by Italian composer
Giuseppe Verdi Giuseppe Fortunino Francesco Verdi (; 9 or 10 October 1813 – 27 January 1901) was an Italian composer best known for his operas. He was born near Busseto to a provincial family of moderate means, receiving a musical education with the h ...
in the 19th century, then advocated by the
Schiller Institute The Schiller Institute is a German based political and economic think tank founded by Helga Zepp-LaRouche, with stated members in 50 countries. It is among the principal organizations of the LaRouche movement. The institute's stated aim is to app ...
beginning in the 1980s with reference to the composer, but naming a pitch slightly lower than Verdi's preferred 432 Hz for A, and making controversial claims regarding the effects of this pitch. Scientific pitch is not used by concert orchestras but is still sometimes favored in scientific writings for the convenience of all the octaves of C being an exact round number in the
binary system A binary system is a system of two astronomical bodies which are close enough that their gravitational attraction causes them to orbit each other around a barycenter ''(also see animated examples)''. More restrictive definitions require that th ...
when expressed in
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
(symbol Hz). The octaves of C remain a whole number in Hz all the way down to 1 Hz in both binary and
decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
counting systems. Instead of A above middle C (A4) being set to the widely used standard of 440 Hz, scientific pitch assigns it a frequency of 430.54 Hz. Since 256 is a power of 2, only
octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
s (factor 2:1) and, in
just tuning In music, just intonation or pure intonation is the Musical tuning, tuning of musical Interval (music), intervals as Natural number, whole number ratios (such as 3:2 or 4:3) of Frequency, frequencies. An interval (music), interval tuned in this ...
, higher-pitched
perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval fro ...
s (factor 3:2) of the scientific pitch standard will have a frequency of a convenient integer value. With a Verdi pitch standard of A4 = 432 Hz = 24 × 33, in just tuning all octaves (factor 2),
perfect fourth A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to ...
s (factor 4:3) and fifths (factor 3:2) will have pitch frequencies of integer numbers, but not the
major third In classical music, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third () is a third spanning four semitones. Forte, Allen (1979). ''Tonal Harmony in Concept and P ...
s (factor 5:4) nor
major sixth In music from Western culture, a sixth is a musical interval encompassing six note letter names or staff positions (see Interval number for more details), and the major sixth is one of two commonly occurring sixths. It is qualified as ''major ...
s (factor 5:3) which have a prime factor 5 in their ratios. However scientific tuning implies an
equal temperament An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...
tuning where the frequency ratio between each half tone in the scale is the same, being the 12th root of 2 (a factor of approximately 1.059463), which is not a rational number: therefore in scientific pitch only the octaves of C have a frequency of a whole number in hertz.


History

Concert tuning pitches tended to vary from group to group, and by the 17th century the pitches had been generally creeping upward (i.e. becoming "
sharper A sharper is an older term, common since the seventeenth-century, for thieves who use trickery to part an owner with his or her money or other possessions. Sharpers vary from what are now known as con-men by virtue of the simplicity of their co ...
"). The French acoustic physicist
Joseph Sauveur Joseph Sauveur (24 March 1653 – 9 July 1716) was a French mathematician and physicist. He was a professor of mathematics and in 1696 became a member of the French Academy of Sciences. Life Joseph Sauveur was born in La Flèche, the son of a ...
, a non-musician, researched musical pitches and determined their
frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
. He found several frequency values for A4 as presented to him by musicians and their instruments, with A4 ranging from 405 to 421 Hz. (Other contemporary researchers such as
Christiaan Huygens Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists of ...
, Vittorio Francesco Stancari and
Brook Taylor Brook Taylor (18 August 1685 – 29 December 1731) was an English mathematician best known for creating Taylor's theorem and the Taylor series, which are important for their use in mathematical analysis. Life and work Brook Taylor w ...
were finding similar and lower values for A4, as low as 383 Hz.) In 1701, Sauveur proposed that all musical pitches should be based on a ''son fixe'' (fixed sound), that is, one unspecified note set to 100 Hz, from which all others would be derived. In 1713, Sauveur changed his proposal to one based on C4 set to 256 Hz; this was later called "philosophical pitch" or "Sauveur pitch". Sauveur's push to standardize a concert pitch was strongly resisted by the musicians with whom he was working, and the proposed standard was not adopted. The notion was revived periodically, including by mathematician Sir
John Herschel Sir John Frederick William Herschel, 1st Baronet (; 7 March 1792 – 11 May 1871) was an English polymath active as a mathematician, astronomer, chemist, inventor, experimental photographer who invented the blueprint and did botanical wor ...
and composer
John Pyke Hullah John Pyke Hullah (27 June 1812 – 21 February 1884) was an English composer and teacher of music, whose promotion of vocal training is associated with the singing-class movement. Life and career Hullah was born at Worcester. He was a pupil ...
in the mid-19th century, but never established as a standard. In the 19th century, Italian composer
Giuseppe Verdi Giuseppe Fortunino Francesco Verdi (; 9 or 10 October 1813 – 27 January 1901) was an Italian composer best known for his operas. He was born near Busseto to a provincial family of moderate means, receiving a musical education with the h ...
tried to stop the increase in pitch to which orchestras were tuned. In 1874 he wrote his ''Requiem'' using the official French standard ''diapason normal'' pitch of A4 tuned to 435 Hz. Later, he indicated that 432 Hz would be slightly better for orchestras.Rosen, David, ''Verdi, Requiem''
/ref> One solution he proposed was scientific pitch. He had little success. In 1988,
Lyndon LaRouche Lyndon Hermyle LaRouche Jr. (September 8, 1922 – February 12, 2019) was an American political activist who founded the LaRouche movement and its main organization the National Caucus of Labor Committees (NCLC). He was a prominent conspiracy ...
's
Schiller Institute The Schiller Institute is a German based political and economic think tank founded by Helga Zepp-LaRouche, with stated members in 50 countries. It is among the principal organizations of the LaRouche movement. The institute's stated aim is to app ...
initiated a campaign to establish scientific pitch as the
classical music Classical music generally refers to the art music of the Western world, considered to be distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical music, as the term "classical music" also ...
concert pitch standard. The Institute called this pitch "Verdi tuning" because of the connection to the famous composer. Even though Verdi tuning uses 432 Hz for A4 and not 430.54, it is said by the Schiller Institute to be derived from the same mathematical basis: 256 Hz for middle C. The Institute's arguments for the notation included points about historical accuracy and references to
Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
's treatise on the movement of planetary masses. The Schiller Institute initiative was opposed by opera singer
Stefan Zucker Stefan Zucker (born 1949) is an American singer, expert on Italian opera and self-described "opera fanatic." He was listed in the 1980 Guinness Book of Records as the "world's highest tenor" for having hit and sustained an A above high C for 3.8 ...
. According to Zucker, the Institute offered a bill in Italy to impose scientific notation on state-sponsored musicians that included provisions for fines and confiscation of all other tuning forks. Zucker has written that he believes the Schiller Institute claims about Verdi tuning are historically inaccurate. Institute followers are reported by Tim Page of ''Newsday'' to have stood outside concert halls with petitions to ban the music of
Antonio Vivaldi Antonio Lucio Vivaldi (4 March 1678 – 28 July 1741) was an Italian composer, virtuoso violinist and impresario of Baroque music. Regarded as one of the greatest Baroque composers, Vivaldi's influence during his lifetime was widespread a ...
and even to have disrupted a concert conducted by
Leonard Slatkin Leonard Edward Slatkin (born September 1, 1944) is an American conductor, author and composer. Early life and education Slatkin was born in Los Angeles to a Jewish musical family that came from areas of the Russian Empire now in Ukraine. His fat ...
in order to pass out pamphlets titled "Leonard Slatkin Serves Satan".


See also

*
History of pitch standards in Western music Concert pitch is the pitch reference to which a group of musical instruments are tuned for a performance. Concert pitch may vary from ensemble to ensemble, and has varied widely over music history. The most common modern tuning standard uses ...


References

{{reflist Musical tuning