Concert pitch, or how we came to tune (mostly) to A=440 Hz

Yesterday I stumbled onto another of these “A=432 Hz” advocacy pages: it got me thinking that “how did we get to A=440 Hz?” would be a good subject for a post. So here goes. TL;DR summary: there is neither conspiracy nor deep ‘harmony with the cosmos’: the standard came about for purely pragmatic reasons. Let me explain.

In antiquity and the Middle Ages, there were no absolute pitch standards. Sure, theoretical math about the construction of scales goes back all the way to the School of Pythagoras, but that concerns itself with relative pitch (intervals), not with an absolute reference pitch. Whichever fixed-pitch instrument was part of the ensemble would have dictated the reference pitch for the others — and since this was long before the era of mass manufacturing, those were all one-of-a-kind instruments.

The German composer and theoretician Michael Praetorius (1571-1621)
did mention that in his day, there was “chamber tuning” (Kammerton) and there was “choir tuning” (Chorton, which followed the church organ) and that those were a whole tone apart. So historical organs would give us a clue as to historical pitch, right?

Well… it was indeed so that the pipes for the lowest note of an organ “principal” stop were by convention made eight foot long. (Hence the practice of labeling organ stops, or later drawbars on a Hammond organ, by “foot”: 16’ will sound one octave below, 4’ one octave above, 5 1/3’ a fifth above,… the notes played on the keyboard.) So that would seem to impose standardization at least for church music, right?

Not quite. Whose foot are we talking? Each principality in those days had its own set of customary units. We do know that German Baroque organs that have been preserved are almost invariably sharp of modern concert pitch, typically by about a semitone, but sometimes as much as a whole tone. An even-tempered semitone, 2^(1/12)≈1.05946, up from A=440 Hz would be about 466 Hz, two semitones about A=494 Hz. A whole tone down from A=466 Hz would imply a chamber pitch somewhere around A=415 Hz, as favored today by many ‘historically informed performance’ ensembles — but this would not have been universal, and actual concert pitch may have been higher.

The first tuning fork wasn’t invented until 1711, by an English court musician (trumpeter) named John Shore. Tuning forks (or “pitchforks”, as Shore punningly called them) are small and portable, drift very little with temperature and over time, and yield a nearly pure sinusoidal sound (i.e. devoid of overtones).

One of Shore’s London customers was the great expat German composer Handel. Händel’s tuning fork has actually been preserved

handels-tuning-fork

and sounds at A=422.5 Hz. A number of other historical tuning forks have been preserved, e.g., those used by fortepiano (and later piano) manufacturers for initial setup and tuning. The record shows that pitch kept drifting up and up, as orchestras kept pursuing an ever brighter sound. (This is not mere psycho-suggestion, particularly for the string section: tuning string instruments higher means increasing the tension on the strings, leading to more overtones in the sound.) Two other developments took place in parallel: the opera genre became a mainstay of classical music throughout Europe, and as long-distance travel became more practical and affordable thanks to the Industrial Revolution, star opera singers would travel widely.

What this also meant, however, is that an opera diva could be traveling to a new city, and suddenly would be unable to hit the highest notes as the orchestra was tuning higher. The resulting protests led to a pushback against “pitch inflation”, and hence to efforts to arrive at a standard.

[[[sidebar: scientific tuning, a.k.a. Sauveur pitch, philosophical tuning, Verdi tuning.

The French courtier and physicist Joseph_Sauveur, who first coined the term “acoustics” for that subfield of physics, in 1713 proposed an absolute pitch standard based on the frequencies of all C’s being powers of two: middle C=256 Hz, C’=512 Hz, and so forth. In Pythagorean tuning, that implies A=256 x (27/16) = 432 Hz. [in 5-limit just intonation, that would be A=256 x (5/3) = 426.666… Hz; in 12-tone equal temperament A=256 x 2^(9/12)= 430.54 Hz.] This was considerably sharp of French Baroque practice and was hence not adopted by performers. A century and a half later, the composer Giuseppe Verdi tried to revive this proposal, at a time when orchestras routinely turned way sharp of this. In recent years, various mystical and numerological ideas have been attached to Sauveur pitch, which has led to some (usually nonclassical) musicians adopting it.]]]

In 1834, a German industrialist, inventor, and amateur acoustician named J. H. Scheibler  devised an array of tuning forks pitched at multiples of 4 Hz, permitting pitch measurements at 4 Hz resolution. (As Heinrich Hertz yet had to be born, the unit was of course not named “Hz.” but cycles per second, or Schwingungen pro Sekunde.) At an 1834 meeting in Stuttgart of the German Society of Natural Scientists and Physicians , Scheibler demonstrated the device, and a motion was adopted to use A=440 Hz as standard concert pitch (the first time that this proposal was made). As Scheibler had many contacts in the German-speaking music world, a number of musicians informally adopted his standard.

The trailblazer for standardization of measurement units in Europe was, of course, France, with its 1799 adoption of the metric system, which eventually became the standard for nearly the entire industrialized world as well as of the worldwide scientific community. (In 1875, seventeen countries would sign a metric system convention, which led to the creation of the International Bureau for Weights and Measures outside Paris.) In the same vein, the French government issued a ministerial decree in 1859 that mandated a “diapason normal” (standard tuning fork) throughout France at A=435 Hz: this compromise value had been recommended by an ad hoc commission advised by the likes of the composers Halévy, Meyerbeer, Auber, Ambroise Thomas and Rossini. A number of continental European countries adopted the French standard.

In Britain, on the other hand, attempts had been made to standardize to an A=452 Hz concert pitch (almost a quarter-tone sharp of modern concert pitch). Protests by singers led to the adoption of a modified French standard: concert hall organs were tuned at A=435 at about 15 degrees centigrade: assuming a thermal expansion coefficient of about 0.1% per degree Fahrenheit (actually, closer to 0.067%) of the air column in the  organ pipes, it was argued that pitch would drift up to about 439 Hz in a heated concert hall, and hence in 1896, A=439 Hz was adopted by the Royal Philharmonic as the “new philharmonic pitch”. The older standard was then being referred to as “old pitch” or “high pitch”.

Recording and broadcast technology gave a new impetus to international standardization. On June 11, 1925, the US recording industry adopted A=440 as a standard. and eventually, this revived “Stuttgart value” was agreed upon at the 1939 London meeting of the International Standards Association (the predecessor of today’s ISO). What tipped the scales for 440 Hz rather than 439 Hz was again a practical argument: the BBC’s engineers could generate a stable, invariant A=440 Hz from a 1 MHz quartz crystal oscillator through a combination of frequency division and multiplication circuits (divide by 1000, then by 25, then multiply by 11).  This was an impractical approach for 439, which is a prime number. Eventually, A=440±0.5 Hz would be enshrined as ISO standard 16.

Many symphony orchestras actually tune slightly higher, A=442 or 443 Hz: a list of reference pitches for orchestras worldwide can be found here (in German). The Berlin Philharmonic, in the halcyon days of Karajan, actually tuned to A=445, to revert to the more common 443 Hz under later conductors.

In the “historically informed performance” community, A=415 Hz is commonly used for Baroque music. Why that specific number? Again, a practical compromise: more or less in the ballpark of what was (German) Baroque practice, and exactly an even-tempered semitone down from A=440 Hz. This means that modern fixed-pitch instruments can still perform in an ensemble with period instruments: all that is required is transposing the former’s part down by a half-step.

 

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