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Lissajous tuning forks with attached mirrors for projecting Lissajous figures

Tuning forks of this design were used as part of the French attempt to create an international standard for concert performance pitch in 1858.

Invention and use

Invented in 1855 by the French physicist Jules Antoine Lissajous (1822-1880), these tuning forks (above) are part of an apparatus for the visualization and analysis of sound vibrations. This particular set was manufactured by the Parisian scientific instrument maker Rudolph Koenig (1832-1901) for educational demonstrations and also for the fine calibration of new tuning forks.

Sketch of Jules Lissajous observing Lissajous figures through a microscope
Image 1: Jules Lissajous observing Lissajous figures through a microscope. Image from Wikimedia Commons.

Musical figures

Each tuning fork has a small mirror mounted at the end of one prong, counterbalanced at the other by a small mass of equal weight. To perform a demonstration experiment, the forks are arranged at right angles in a frame so that one vibrates in the North-South direction and the other in the East-West direction. A narrow light beam is reflected from one mirror to the next and projected onto a screen (or observed through a microscope, as in image 1). When the forks are vibrating the beam is thus periodically deflected in two dimensions and will trace on the screen a curve whose geometric properties depend on the ratio of frequencies of the forks. 'Lissajous figures' of great beauty and complexity can be produced in this way and the most stable and perfect only appear when the two forks vibrate at frequencies of simple ratios, such as 2:1 or 3:2 (e.g. 500Hz:250Hz or 600Hz:400Hz). These frequency ratios correspond to the musical intervals of the octave and perfect fifth respectively (see image 2).

Illustration of Lissajous figures
Image 2: Lissajous figures as illustrated in Rudolph Koenig's 1885 acoustical catalogue.

Optical calibration

Lissajous figures were used to calibrate tuning forks during manufacture. By pairing an unfinished fork with a fork of a known standard frequency and by viewing the resultant figures it is possible to make tuning adjustments to an accuracy much greater than can be achieved by ear. Such fine-tuning was made using a simple metal file: to increase the frequency of the fork one files the top of the prongs, and to decrease one files inside the bottom of the U shaped 'yoke' of the fork.

Lissajous also invented the vibration microscope (a tuning fork with microscope lens attached to one prong), which became a key tool in the acoustical researches of Herman von Helmholtz and Rudolph Koenig. An image viewed through this microscope will vibrate with the tuning fork and if one views an object that is itself vibrating at right angles to the vibration of the microscope then Lissajous figures may be produced. These figures can be used to deduce the nature of the vibrations in question. Helmholtz, for example, used this device to understand the vibrations of a violin string.

Calibrating music

Lissajous performed his work on tuning forks during the second half of the 19th century. This was a period of great enthusiasm for standardization in science, and the science of acoustics was no exception. However, the world of music was also crying out for standardization and in particular musicians and musical instrument makers desired a standard for pitch. In 1858, and in response to the recently established German standard of A=440Hz the French government set up a commission charged with setting such a standard. Lissajous was a member of this committee, which also featured great composers such as Hector Berlioz (1803-1869) and Gioachino Rossini (1792-1868).

Torben Rees

Torben Rees, 'Lissajous tuning forks: the standardization of musical sound', Explore Whipple Collections, Whipple Museum of the History of Science, University of Cambridge, 2010

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