Harmonic analyzer

From Ccpi

In 1894, Olaus Henrici (1840-1918) of London devised a harmonic analyzer for finding the fundamental and harmonic components of complex sound waves. It consists of multiple glass spheres, called rolling-sphere integrators, connected to measuring dials. The image of a sound wave is placed under the device. The user moves a mechanical stylus along the curve's path, tracing out the wave form. The end result is an instrument capable of computing the first ten Fourier coefficients of the curve, the maximum often necessary in studying sound waves.

For its time, Henrici's analyzer was precise and easy to use. Dayton Miller of the Case School of Applied Sciences used it in his work in acoustics and the theory of music beginning in 1908, and would analyze thousands of sound waves with the device.

Rolling-sphere integrators work in essentially the same way as modern mechanical mice used in computing: the rolling motion of a ball on a two dimensional surface is broken down into rectangular coordinates for measurement. Two rollers at right angles to eachother touch the ball at its equator, while a third roller assists in pressing the ball against the other two. As the ball stylus traces the curve, the carriages holding the rollers physically rotate around the ball, in such a way that the rollers always remain at right angles to eachother. For the fundamental ball, its rollers rotate exactly one revolution around the ball over the entire length of the apparatus—one fundamental wavelength. Seen from above, the rollers trace out one wavelength of a sine and cosine curve. The next ball's rollers rotate around the ball exactly 2 revolutions. From above, this looks like a sine and cosine curve of twice the frequency. Subsequent rollers trace out sine and cosine curves of 3, 4, and 5 times the fundamental frequency; for this reason, they are called harmonics of the fundamental tone.

In the simplest terms, the entire device measures how much the motion along a complex curve coincides with motion along sines and cosines of various frequencies. If the sound wave was simply a sine function, the fundamental ball's rollers would always be in the right position to "collect" the motion of the stylus as it traces the curve.