The Tuning Fork

Wayne Staab
April 1, 2012

The tuning fork has a long history in hearing differential diagnosis, but what do we know about its origin?

Tuning fork with resonating box.

The table fork is supposedly the precursor of the tuning fork.  However, my investigation shows that the table fork, as a kitchen utensil, was known to the Greeks and Romans and to the Germanic Tribes of the Great Migration.  For eating purposes it was first used at Italian Courts around 1,000 AD, but even until the end of the 16th century, it was still considered a luxury item.  The table fork itself did not become generally accepted until the 18th century.  Interestingly, primitive peoples are not known to have ever used forks.  However, Fiji islanders used wooden forks when eating human flesh, since superstition did not permit them to touch such flesh with their bare hands.  An old German wives tale warns against making a fork produce sounds by beating it with another tool.  This was to invoke the devil and was therefore expressly forbidden {{1}}[[1]] Handbook of Germanic Superstitions, 1930-31.[[1]] Is this possibly the source of the item eventually known as the tuning fork?  This reference to sound is the closest this blogger found to the fork as a source of sound, but it does seem to be a stretch.

John Shore and his Pitch Fork

John Shore was a famous trumpeter to the English king who is credited with the invention of the tuning fork in 1711 {{2}}[[2]] Feldmann, H (1997). “History of the tuning fork. I: Invention of the tuning fork, its course in music and natural sciences. Pictures from the history of otorhinolaryngology, presented by instruments from the collection of the Ingolstadt German Medical History Museum”. Laryngo- rhino- otologie 76 (2): 116–22.[[2]]  Handel, who was then the court composer, wrote many of the florid trumpet parts for him.  As fate would have it, during one of his concerts he split his lip and was never again able to perform with the trumpet at the level required.  But, being a musician at heart, he turned his attention to playing the lute, and it was for this instrument that he devised the tuning fork for tuning his lute.  Being somewhat of a humorous character, he often remarked at the start of his performances that he never went anywhere without his pitch fork.

Shore shared his tuning method with Handel, giving him one of his tuning forks.  It produced a pitch C at 512 Hz.  This method of tuning instruments allowed musicologists to place the exact pitch at which Handel, Mozart, Beethoven, and their contemporaries intended their works to be heard.

However, the first published description of the tuning fork seems to be that in a book by William Trans’ur 35 years after its invention in 1772{{3}}[[3]] Tans’ur W.  A new musical grammar. London, 1746.[[3]]  It was named an intonator or retonator and described as:

‘An elastic sounding instrument of one tone, of late invention and used to set other instruments to concert pitch.  It is made of good steel, very sound of spring temper and well polished; and its resonant parts vibrate in unison when put in motion.  It is first put in tone by lightly holding it between the forefinger and thumb and smartly striking one of its branches on a board or table and bearing it upright while it resounds a stronger tone or if you hear it below your ear or tooth or on your head you will hear it more distinct.  If the whole length of an intonator be made about eight inches and the double branches thereof be 1/2 of an inch square each, and the stem double that magnitude, it will sound very near the tone of English concert.  But as no true determinate size can be given because of the temper and different tones of metal, it is best to form them long enough at first, seeing they must be ground shorter afterwards to raise them to the tone you desire.’


What Pitch Should be Pitched?

During the 19th century the standard pitch rose a little more than a semi-tone, from A at 422.5 to 452 Hz, came to be known as the Philharmonic Pitch, and by the end of the century an official European Standard was set by the French Government at 435 Hz.  This was also known as the International Pitch in France and the Philharmonic Pitch in England.  This difference made it difficult for military bands from the two countries to play together until 1929 when a British Colonel Somerville accepted the International Standard.  But, for clinical use rather than musical performance, today’s tuning forks are based on the so-called “philosophical” or “scientific” pitch stated in terms of C at 512 Hz.

Interestingly, Handel’s tuning fork, which he donated to the Foundling Hospital, where he had given performances of the Messiah, was located among possessions removed from the hospital when it was demolished in 1926.

The utilization of the tuning fork expanded in music to the point where individuals attempted to construct complete musical instruments based on sets of tuning forks, but they were not widely accepted.

The Physics of the Tuning Fork

The German physicist E. Chladni in Wittenberg around 1800 was the first to systematically investigate the mode of tuning fork vibration, with particular attention to its nodal points.

It was another German living in Paris, physicist K.R. Koenig who invented a tuning fork that was kept in continuous vibration by a clockwork, and H. Helmholtz, a physiologist in Heidelberg in 1863 used sets of electromagnetically powered tuning forks for his famous experiments on the sensations of tone.  Until the invention of the vacuum tube, tuning forks remained indispensable instruments for producing defined sinusoidal vibrations.  Even watches used the principle of the tuning fork to keep time.

Quartz crystal resonator from a quartz watch, formed in the shape of a tuning fork.

The tuning fork shape, unlike many other types of resonators, produces a very pure tone, with most of the vibrational energy at the fundamental frequency, and little at the overtones (harmonics).  The reason for this is that the frequency of the first overtone is about 52/22 = 25/4 = 61/4 times the fundamental (about 21/2 octaves above it).  By comparison, the first overtone of a vibrating string or metal bar is only one octave above the fundamental {{4}}[[4]] Tyndall, John (1915). Sound. New York: D. Appleton & Co. p. 156.[[4]]  So, when a tuning fork is struck, little of the energy goes into the overtone modes.  They also dampen correspondingly faster, leaving the fundamental.  With musical instruments, this makes it easier to tune them.

Another reason for the fork shape is that, when it vibrates in its principal mode, the handle vibrates up and down as the prongs move apart and together.  There is a node (point of no vibration) at the base of each prong.  Because the handle motion is small, it allows the fork to be held by the handle without damping the vibration, but it still allows the handle to transmit the vibration to a resonator, which is sometimes used, that amplifies the sound of the fork {{5}}[[5]] Journal of the Society of Arts, Vol. 28,  p. 297.[[5]]   Without the resonator (such as pressing the handle to a table) the sound is very faint. This is because the sound waves produced by each fork prong are 180° out of phase with the other, so at a distance from the fork they interfere and largely cancel each other.  If a sound-absorbing sheet is slid in between the prongs of a vibrating fork, reducing the waves reaching the ear from one prong, the volume heard will actually increase, due to a reduction of this cancellation.  Weathering and temperature can vary the pitch of a tuning fork slightly.  A decrease in frequency of one vibration in 21,000 for each degree Fahrenheit change is typical for a steel tuning fork {{6}}[[6]] Journal of the Society of Arts, Vol. 28, p. 297.[[6]]  The standard temperature is now 68 °F (20 °C).

For those more interested in how the frequency of a tuning fork is determined, the following formula should suffice {{7}}[[7]] Han, Seon M.; Benaroya, Haym; Wei, Timothy (1999). “Dynamics of Transversely Vibrating Beams Using Four Engineering Theories”. Journal of Sound and Vibration 225 (5): 935.[[7]]

A future blog will discuss how the tuning fork was/is used in differential diagnosis – something that was not readily apparent when the concept of bone-conduction hearing was first identified.

Leave a Reply