- Concert pitch
Concert pitch refers to 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 musical history. This is also referred to as the reference frequency for "A" in an orchestra, the term "concert pitch" being used to indicate the difference between "written" and "sounding" notes in scores.
To avoid ambiguity when referring to pitches on transposing instruments, the term concert pitch is here used to refer to the pitch on a non-transposing instrument. In the literature this is also called international standard pitch. Music for transposing instruments is transposed into different keys from non-transposing instruments—for example, playing a written C on a B♭ clarinet or trumpet produces a non-transposing instrument's B♭. This pitch is referred to as "concert B♭".
Modern standard concert pitch
History of pitch standards in Western music
Historically, various standards have been used to fix the pitch of notes at certain frequencies. Various systems of musical tuning have also been used to determine the relative frequency of notes in a scale.
Until the 19th century there was no concerted effort to standardize musical pitch, and the levels across Europe varied widely. Pitches did not just vary from place to place, or over time—pitch levels could vary even within the same city. The pitch used for an English cathedral organ in the 17th century, for example, could be as much as five semitones lower than that used for a domestic keyboard instrument in the same city.
Even within one church, the pitch used could vary over time because of the way organs were tuned. Generally, the end of an organ pipe would be hammered inwards to a cone, or flared outwards, to raise or lower the pitch. When the pipe ends became frayed by this constant process they were all trimmed down, thus raising the overall pitch of the organ.
Some idea of the variance in pitches can be gained by examining old pitchpipes, organ pipes and other sources. For example, an English pitchpipe from 1720 plays the A above middle C at while the organs played by Johann Sebastian Bach in Hamburg, Leipzig and Weimar were pitched at A = a difference of around four semitones. In other words, the A produced by the 1720 pitchpipe would have been at the same frequency as the F on one of Bach's organs.
From the early 18th century, pitch could be also controlled with the use of tuning forks (invented in 1711), although again there was variation. For example, a tuning fork associated with Handel, dating from 1740, is pitched at A = while a later one from 1780 is pitched at A = almost a semitone lower.  Nonetheless, there was a tendency towards the end of the 18th century for the frequency of the A above middle C to be in the range of to
The frequencies quoted here are based on modern measurements and would not have been precisely known to musicians of the day. Although Mersenne had made a rough determination of sound frequencies as early as the 17th century, such measurements did not become scientifically accurate until the 19th century, beginning with the work of German physicist Johann Scheibler in the 1830s. The unit hertz (Hz), replacing cycles per second (cps), was not introduced until the 20th century.
During historical periods when instrumental music rose in prominence (relative to the voice), there was a continuous tendency for pitch levels to rise. This "pitch inflation" seemed largely a product of instrumentalists' competing with each other, each attempting to produce a brighter, more "brilliant", sound than that of their rivals. (In string instruments, this is not all acoustic illusion: when tuned up, they actually sound objectively brighter because the higher string tension results in larger amplitudes for the harmonics.) This tendency was also prevalent with wind instrument manufacturers, who crafted their instruments to play generally at a higher pitch than those made by the same craftsmen years earlier.
On at least two occasions, pitch inflation had become so severe that reform became needed. At the beginning of the 17th century, Michael Praetorius reported in his encyclopedic Syntagma musicum that pitch levels had become so high that singers were experiencing severe throat strain and lutenists and viol players were complaining of snapped strings. The standard voice ranges he cites show that the pitch level of his time, at least in the part of Germany where he lived, was at least a minor third higher than today's. Solutions to this problem were sporadic and local, but generally involved the establishment of separate standards for voice and organ ("Chorton") and for chamber ensembles ("Kammerton"). Where the two were combined, as for example in a cantata, the singers and instrumentalists might perform from music written in different keys. This system kept pitch inflation at bay for some two centuries.
The advent of the orchestra as an independent (as opposed to accompanying) ensemble brought pitch inflation to the fore again. The rise in pitch at this time can be seen reflected in tuning forks. An 1815 tuning fork from the Dresden opera house gives A = ,  while one of eleven years later from the same opera house gives A = . At La Scala in Milan, the A above middle C rose as high as . 
19th and 20th century standards
The most vocal opponents of the upward tendency in pitch were singers, who complained that it was putting a strain on their voices. Largely due to their protests, the French government passed a law on February 16, 1859 which set the A above middle C at 435 Hz. This was the first attempt to standardize pitch on such a scale, and was known as the diapason normal. It became quite a popular pitch standard outside France as well, and has also been known at various times as French pitch, continental pitch or international pitch (the last of these not to be confused with the 1939 "international standard pitch" described below).
The diapason normal resulted in middle C being tuned at approximately . An alternative pitch standard known as philosophical or scientific pitch, fixed middle C at (that is, 28 Hz), which resulted in the A above it being approximately . The appeal of this system was its mathematical idealism (the frequencies of all the Cs being powers of two).  This system never received the same official recognition as A = 435 Hz and was not widely used.
British attempts at standardisation in the 19th century gave rise to the old philharmonic pitch standard of about A = 452 Hz (different sources quote slightly different values), replaced in 1896 by the considerably "deflated" new philharmonic pitch at A = 439 Hz. The high pitch was maintained by Sir Michael Costa for the Crystal Palace Handel Festivals, causing the withdrawal of the principal tenor Sims Reeves in 1877, though at singers' insistence the Birmingham Festival pitch was lowered (and the organ retuned) at that time. At the Queen's Hall in London, the establishment of the diapason normal for the Promenade Concerts in 1895 (and retuning of the organ to A = 439 at 15 °C (59 °F), to be in tune with A = 435.5 in a heated hall) caused the Royal Philharmonic Society and others (including the Bach Choir, and the Felix Mottl and Artur Nikisch concerts) to adopt the continental pitch thereafter.
In 1939, an international conference recommended that the A above middle C be tuned to 440 Hz, now known as concert pitch. This standard was taken up by the International Organization for Standardization in 1955 and reaffirmed by them in 1975 as ISO 16. The difference between this and the diapason normal is due to confusion over the temperature at which the French standard should be measured. The initial standard was A = , but this was superseded by A = 440 Hz after complaints that 439 Hz was difficult to reproduce in a laboratory because 439 is a prime number.
Despite such confusion, A = 440 Hz is the only official standard and is widely used around the world. Many orchestras in the United Kingdom adhere to this standard as concert pitch. In the United States some orchestras use A = 440 Hz, while others, such as New York Philharmonic and the Boston Symphony Orchestra, use A = 442 Hz. Nearly all modern symphony orchestras in Germany and Austria and many in other countries in continental Europe (such as Russia, Sweden and Spain) play with tune to A = 443 Hz. A = 442 Hz is also often used as tuning frequency in Europe, especially in Denmark, France, Hungary, Italy, Norway and Switzerland.
In practice the orchestras tune to a note given out by the oboe, and many oboists use an electronic tuning device. When playing with fixed-pitch instruments such as the piano, the orchestra will generally tune to them—a piano will normally have been tuned to the orchestra's normal pitch. Overall, it is thought that the general trend since the middle of the 20th century has been for standard pitch to rise, though it has been rising far more slowly than it has in the past. Some orchestras like the Berliner Philharmoniker now use a slightly lower pitch (443 Hz) than their highest previous standard (445 Hz).
Many modern ensembles which specialize in the performance of Baroque music have agreed on a standard of A = 415 Hz. An exact equal-tempered semitone lower than A = 440 would be 440/21/12 = 415.3047 Hz; this is rounded to the nearest integer. In principle this allows for playing along with modern fixed-pitch instruments if their parts are transposed down a semitone. It is, however, common performance practice, especially in the German Baroque idiom, to tune certain works to Chorton, approximately a semitone higher than A-440 (460–470 Hz) (e.g., Pre-Leipzig period cantatas of Bach).
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