Dayton C. Miller was Professor of Physics at Case School of Applied Sciences at the beginning of the twentieth century whose life's work has outlived him by many decades. He designed the Rockefeller building and, with such brilliant colleagues as Albert Michelson, Edward Morley, and Robert Shankland, began a continuing tradition of excellence in teaching and research at the then very young institution. He left behind not only a building and tradition, but also hundreds of pages of writing and large quantities of research equipment. At his time, he was one of the foremost researchers in the science of sound. He is also survived by a body knowledge represented by several books, including The Science of Musical Sounds and Sound Waves: Their Shape and Speed.

The last fifty years of Miller's life was devoted to Case. He was Professor of Physics, holding the first endowed chair in the field at Case School of Applied Sciences (though Michelson was the first Professor of Physics) from 1890 to 1941. He did not teach after 1927, when his chair was endowed with $100,000 by Ambrose Swasey and he spent the rest of his days researching acoustics and continuing work on the Michelson-Morley ether drift experiment. Miller's life work was tainted somewhat by his refusal to accept the results of Michelson and Morley's Nobel Prize-winning efforts. He spent three decades, using better and better equipment, in failed attempts to show that the ether did exist. At Miller's death, a colleague said that he "might have been wiser to have concentrated on his valuable research in acoustics...."

Miller also made lantern slides to document his work during his long tenure at Case. There are at least a thousand of them, covering every imaginable aspect of Miller's professional life from beginning to end. These include pictures of his early work with X-rays, drawers of slides showing the history of the Case School of Applied Sciences and contemporary shots of Cleveland and University Circle, dozens of slides showing interferometers and apparatus used in the Michelson-Morley experiments and Miller's successors to it, tourist pictures of landmarks in Paris (which Miller had occasion to visit while shopping for equipment), his facilities and equipment at Case and other locations, and hundreds of demonstrative slides for lectures on acoustics. The slides were most informative, and all of the pictures used here come from that collection, via the pair of Miller's books previously mentioned.

Tuning Forks and Driven Tuning Forks

The most important means for producing a pure tone has been the tuning fork since its invention in 1711 by John Shore, Handel's trumpeter. Case School of Applied Sciences had a collection of tuning forks that once numbered in the hundreds. Dayton C. Miller bought the forks, along with a huge collection of other acoustic and musical equipment, some highlights of which appear elsewhere in this paper. The highest quality tuning forks came from the workshop of Rudolf Koenig, who made the very best acoustic instrumentation according to Miller. All of the pieces that Koenig made (he had a handful of employees in his shop, which was located below his home in Paris, but he either crafted himself or at least had a hand in making all of the products) are stamped either with an "RK" digraph character or the legend "RUDOLPH KOENIG Á PARIS."

A significant portion of the instruments and equipment, especially tuning forks, were produced in Chemnitz, Germany, by Max Kohl, A.G. According to literature, there were a number of competing companies in Western Europe which made items for acoustic research. Miller said that all competitors were simply copiers of Koenig, who Miller regarded highly enough to include in the stonework roll of great physicists atop Case Western Reserve University's Rockefeller building, which he designed. To the author's modern eyes, the Max Kohl pieces are equal to those of Koenig in fit and finish, if not in function when that can be compared. Inventory cards from the Department of Physics indicate that many of the Max Kohl pieces were purchased in 1929, after Koenig's death.

A tuning fork is simply a piece of steel carefully shaped so that the two tines vibrate with a specific frequency. Koenig's forks were made in two shapes, as shown in figure 1. Each type of fork has a rectangular cross section. The yoke of the fork, where the tines meet the base, is thicker for forks of higher frequency. The slimmer yoke and tines of the other fork shape allow a lower elasticity so that the tines vibrate more slowly.

Figure 1: Shapes of tuning forks by Koenig

All of the antique tuning forks in the CWRU collection are labeled in the unit Vs, or vibrations per second, rather then Hertz. The Hertz was not recognized as a unit until well into the twentieth century (a Vs is equivalent to 1/2 Hz). The name for the tone of each fork is also stamped into the yoke. The names are German so a tuning fork that is a "C" is labeled "Ut" as opposed to "Do."

Almost all of the CWRU collection of tuning forks are mounted on hollow wooden boxes. The boxes have mahogany sides and pine tops and bottoms. The boxes for forks with tones below about C3, 256 Hz, have one closed end. The boxes act as resonance chambers for the tuning forks, with the same purpose as the body of a guitar or violin. Figure 2 shows a selection of tuning forks mounted on boxes. The lowest half inches of the forks are threaded and there is a nut on the inside of the box to fasten them tightly to the boxes. The lowest tone of this set of forks is Ut1 or 64Hz, and the highest is Mi5, 4096 Hz. Their lengths range from about one foot to about four inches.

Figure 2: Tuning forks with wooden resonance boxes.

At one time there were several tuning forks that were paired with hollow, cylindrical brass resonating chambers, as in figure 3. These beautiful forks seem to have been the reference standards for the musical scale. The only surviving member of the collection of such forks is a "middle" C 256 Hz fork, though there is another such chamber that is meant specifically for a 64 Hz driven fork. Figure 3 shows the standard A of 440 Hz. The tuning fork is mounted by its threaded end to the stand so that the tines are very close to but do not touch the end of the chamber. The chamber has a vertical rectangular opening in its end which is about 20% wider than the distance between the tines of the tuning fork. The author found that if the fork is mounted so that the one can see into the brass chamber (as in figure 3), the tone when the fork is struck has a higher volume, while if the fork is turned 90°, the tone will be audible for a longer time because the standing wave that the fork generates inside the resonance chamber will act to preserve the fork's motion.

Figure 3: Standard A = 440 Hz fork with brass resonator

The workings of a driven tuning fork are simple by modern standards. Figure 4 shows a schematic. There is a coil of wire between the tines of the fork (the tines are shaded in the diagram), with the axis of the coil in the plane of the tines and perpendicular to them, so that if the fork is vertical the axis of the coil of wire is horizontal. A short piece of wire is attached to one tine of the fork and bent so that it nearly touches an adjustable pad that is connected to one end of the coil. The other end of the coil is wired to one terminal of a battery or DC power source of about 3V and 500 mA. The other terminal of the battery is connected either directly to the fork or to some convenient connector that is wired to the fork. When the fork is struck, the outward motion of the tines will bring the short wire into contact with the brass pad, allowing current to flow from the power source through the coil, through the short wire, then through the fork and to the other terminal of the power source. This current in the coil creates a magnetic field along the axis of the coil, drawing the tines of the fork toward each other. When the tines swing inward sufficiently far, the short wire loses contact with the brass pad and the current in the coil vanishes, allowing the tines of the fork to swing outward again.

Figure 4: Driven tuning fork schematic.

The CWRU Department of Physics has perhaps a dozen driven tuning forks. There are a few that are mounted more or less permanently with their coils, and a few others that are free (three forks are in a wooden box as a set with frequencies of 50, 30, and 25 Hertz) and can be mounted on an adjustable frame that includes a coil. There is a 64 Hz fork on display that was probably used as a reference fork, as it is better made (it bears Koenig's mark) and mounted solidly on a stand along with a large brass resonance chamber. There is a mirrored surface mounted atop one tine (and a brass piece of similar size and weight for balance on the other) so that the vibrations can be observed with a beam of light. This fork runs nicely on a pair of C sized batteries, consuming about 500 mA of current at roughly 3 volts.

Clock Fork

The Physics Department's clock fork was constructed by Max Kohl A.G., Chemnitz, Germany, probably in about 1928. There is no way to be sure exactly when it was made, as there is no longer a bill of sale or indicative marking on the piece. According to Robert Prochko it was Professor Albert Michelson's instrument, but most likely it was used mainly by Professor Dayton C. Miller, who may have purchased it on a trip to Europe in 1896 or on a second trip in 1902, but likely was acquired later. Department of Physics inventory records from 1942 (shortly after Miller's death in 1941) indicate that a Max Kohl clock fork was purchased for $70 in 1929. It is not known whether that is the same clock fork still in the CWRU Physics Department's collection, or how the 1929 purchase date was determined by the inventory taker.

The tuning fork itself was made by Max Kohl's shop. It is labeled Ut1 128 Vs which is 64 Hertz. There is a brass weight near the top of each tine which is threaded and can be adjusted up and down an inch or two. The effect of this is to shift the center of gravity of the tines and adjust the frequency of the fork over a range of about 62 to 68 Hz, a musical semi-tone. The weights can be locked in place with clamping screws.

The clock mechanism is driven by an enclosed spring, typical of clockworks of the time. It is a hat box-shaped brass enclosure about 4" in diameter and 1.5" thick. It has a large gear as one end, which drives the works, and a winding post that is exposed on the rear of the clock. The spring is a helix of stout steel band with one end atatched to the winding post and the other to the outside of the enclosure. There is a ratchet mounted on the frame of the works so that the spring may be wound.

Except for the escapement, the whole works, even the chassis, is made of polished brass. The escapement, which is very small, is made of stainless steel. Brass would be too soft to endure the strains of manufacture and use in such small, high tolerance moving parts. Indeed, the stainless steel escapement ratchet had snapped at its smallest point and a crude replacement had to be fashioned in order to make the device function.

The spring provides the potential energy for the system, which bleeds off at a rate controlled by the fork. There is a tiny escapement atop one tine of the fork, attached to the last gear of the clockwork. An escapement works by a ratchet and sprocket. The spring, through the works' system of gears, puts tension on the sprocket, which is not allowed to turn because of the position of the ratchet. The ratchet is shifted periodically by some activator which has a controlled to and fro motion (in the case of the clock- fork, the vibrating tine of the tuning fork supplies this motion), allowing the sprocket to advance until the next tooth is engaged by the ratchet. The ticking sound that a mechanical clock or watch makes is due to its ratchet and sprocket hitting one another.

The purpose of the clock fork is not to keep good time. Though it can be set to keep very good time with proper adjustment of the weights on each tine of the fork, generally the clock is used to indicate the frequency for which the fork is currently adjusted. When compared with an accurate clock over a period of days (the works was designed so that the back swing of the ratchet in the escapement would impart a small impulse on the fork so as to maintain its vibration), one can read how many seconds the clock fork loses or gains. When that number of seconds is divided into the number of seconds actually elapsed and multiplied by 64, the frequency of the fork in the clock fork is obtained, to precision of easily 0.0001 Hertz, according to Miller.

The idea, then, is to look through the microscope on the clock fork at another fork set up horizontally so that its vibrations are at right angle to those of the clock fork, as in figure 5.

Figure 5: Clock-fork set up for verifying another fork.

If one fixes one's view on a light spot on the second fork, one can see a lissajous figure with the aid of the microscope. The figure changes shape periodically, with a period in seconds equal to the frequency of the second fork divided by that of the first fork. So if the first fork, the one in the clock fork, is set to 64.000 Hz and the second fork, the test fork, is 256.00 Hz, then the lissajous figure's changes will have a period of 4 seconds. If the period is timed and found to have a duration of 4.05 seconds, then the test fork has a frequency of Hz. Then a small amount of material can be filed from the test fork and it can be tested again to see if it has reached the desired frequency. In this way it is possible to fashion very accurate tuning forks. If the test fork is found to vibrate at too high a frequency (to be sure one sticks, say, a small blob of wax to the end of one tine to slow the fork), it can be filed or ground near its yoke.

Manometric Flames

A manometer measures pressure. The flame manometer, or manometric flame, is a device that uses variations in the height of a flame to show changes in the pressure of the flame's gas supply, due to whatever quantity is being measured. In the case of acoustic instruments (the term "instruments" is here used very loosely as no reliable quantitative measure can be made with this method), the supply gas is on one side of a diaphragm in a little chamber, while vibrations in the air on the other side cause the changes in the flame. A small amount of gas (commercially available propane works well, but the natural gas from city lines burns more brightly) flows into the chamber from a small supply line and out through another opening into a tiny line that has a minute hole, perhaps .5 mm, in it. The gas coming out of this hole is what supports the flame. Flames should be less than one inch high, depending somewhat on the size of the flame hole.

Rudolph Koenig produced the first commercially available manometric flame device in 1862 at his shop in Paris. The technology was in use for at least 40 years in research and for decades after as a teaching tool. Its demise as a useful scientific technique was brought about by the advent of photographic and electronic means of collecting more quantitative acoustic data.

The CWRU Department of Physics has perhaps two dozen manometric flame devices. The diaphragms were all natural rubber or sometimes a waxy tissue paper, and were all decayed beyond use. All but two of the manometric flame devices were wooden "organ pipes" meant to be sounded with compressed air. The pipes are long boxes with square cross-sections, with a tapered input at one end that connects with an air line by friction. The vibrating part of the pipe is near the input and is usually just a tapered section of the wall of the box with a narrow opening below to make a reed. The far end of the pipe is sometimes open but usually stopped. The manometric pipes are completely made of mahogany wood. Figure 6 shows a collection of organ pipes that do not have the diaphragm attachment. The diaphragm would be mounted in the front of the pipes, over a hole drilled right into the body. The outer half of the capsule (made of wood this time) would be attached to the pipe's body covering the diaphragm, with input and output lines as before.

Figure 6: A set of organ pipes of uniform loudness.

One of the other two manometric flame devices is a portable unit, shown in a 1909 photograph in figure 7. It is a simple gas input mounted on a base. The input line curls up in an 'S' to the back of the diaphragm chamber c, which is two spherical sections butted together and sealed around the edge, held by three small screws. The original diaphragm (or rather the remnants of it which were found in the unit) seemed to be red, pure rubber glued to a cardboard ring. The free area of the diaphragm would have been about 1" in diameter. The old diaphragm had long since solidified and disintegrated into small pieces. The gas output is a narrow line which curves to the vertical and tapers to its opening j, which is about .5 mm in diameter and can support a flame about 4 cm tall. The other half of the chamber has the sound input, which is a short brass line about 1 cm in diameter.

Figure 7: Portable manometric flame unit with viewing mirror.

A new diaphragm for the portable unit was fashioned from a piece of a synthetic vinyl laboratory glove and glued with rubber cement to an "O" shaped piece of manila card stock. The capsule was sealed with vacuum grease to prevent gas leakage and the unit was attached by rubber laboratory hose to a small tank of propane gas. Originally, a small horn t would have been attached by rubber hose to the sound input of the device. The Physics Department no longer has any such horn but for purposes of demonstrating the technology, a brass resonator works well.

Figure 8: Manometric flame records of speech by Nichols and Merritt

Figure 8 shows photographs of manometric flame oscillations. If one were to use the apparatus shown in figure 5 to view the motion of the flame, one would be able to see this effect. The method is to look at the flame's reflection in the hand-cranked rotating mirror, which acts to sweep the image of the oscillating flame. The photographs in figure 8 were made by Professors Nichols and Merritt, contemporaries of Miller, using acetylene flames.

The best way to use manometric flames to show harmonics in music and other sounds is to couple the diaphragm and flame with a resonating chamber to pick a certain frequency from the background. Today there are a number of Helmholtz resonators in the department's collection. They are spherical, hollow brass balls of different diameters, smaller for higher tones and larger for lower tones. There are about ten left from the original collection--there is no information as to how many of these varnished pieces were in the department's collection; it may be that every one has survived--all but one is stamped with Koenig's mark. The resonators have an opening which admits incoming sound, and a smaller, tapered neck at their opposite side to emit the resonance frequency of the chamber. The necks of the spherical resonators are designed both to attach to laboratory hose and to be inserted into the researcher's ear. The latter has an effect reminiscent of the sound heard at the opening of a sea shell, but rather than a broad frequency range of random, "white" noise, one hears a narrow frequency range of random noise.

The manometric flame method reached its peak with a device known only as the harmonic analyzer. This sixty pound behemoth, made by Rudolph Koenig's shop, has fourteen adjustable cylindrical resonators, spanning over four octaves, from 64 Hz to 4096 Hz. It has seven manometric capsules and a large four-sided rotating mirror built in. There is also a manifold built in which divides gas input from a single line into seven feeders for the individual capsules, with tiny brass ball valves for each feeder line. The harmonic analyzer has been restored to working condition and placed on display in the Rockefeller building. This author cannot recommend actually using the analyzer because of the large amounts of gas required to operate it.

The Phonodiek

The Phonodiek was a device used to make photographic records of the shapes of sound waves. It is an optical, rather than mechanical or electronic instrument. The principle is that sound causes a diaphragm to vibrate. The diaphragm is connected to a tiny mirror which shakes along with the diaphragm and reflects a beam of light in different directions and to different degrees depending on the nature of the sound. The reflected beam of light is captured on film. Figure 9 shows a schematic of the phonodiek.

Figure 9: Principle of the Phonodiek.

Sound enters through the horn, H, and strikes the diaphragm, D. A few untwisted fibers of silk or a steel monofilament is wrapped around a tiny axle to which is fixed a minute mirror, M. The (usually) silk thread is kept under small tension by a tiny leaf spring, S. In some versions of the phonodiek the spring, prone to breakage, is replaced by a pulley and a 1 gram mass is tied to the end of the thread, its weight supplying the needed tension. A pencil-beam of light is supplied by a source, P, and focused by a lens, L. The beam is reflected by the mirror onto the film. In this diagram the reflected beam would scan perpendicularly with the plane of this page, the light source being out of the plane of the page. The film is a long strip, drawn vertically in the plane of the page by a motor, so that the beam of light makes a trace along the length of the film.

The name "phonodiek" is a fictitious Greek word (in the vein of "phonograph," "telephone," and "gramophone") from roots meaning "to show sound," coined at the American Physical Society's Boston meeting in December, 1909 by Professor Edward W. Morley of Case School of Applied Sciences. The phonodiek was conceived because the three devices just mentioned could be used to preserve shapes of sound waves but were prone to distortion of the waves in their primitive electronics or loose mechanical parts, and by 1913 (five years after the prototype was built) had been improved to surpass its competing instruments in quality of sound preservation.

Figure 10: The phonodiek used for photographing sounds.

The phonodiek is an instrument of amazing delicacy and high tolerance. The specimen now in the CWRU Department of Physics' possession is made of brass. The detail of the mirror shown in figure 11 gives some indication of the scale. The pivots and cap jewels, made of sapphire "in the manner of the balance-wheel staff of a fine watch," are shown in the diagram with a mottled pattern in the cross section. The block and cap, shown by fine diagonal lines, were bronze. The staff, on which the mirror (facing to the right) was cleverly mounted so that the whole assembly has one axis of inertia, was only 0.1 millimeter in diameter at the pivots. The whole mirror and staff assembly, pulley included, was 3.3 mm high and 1.6 mm wide overall, and had a mass of 2.72 mg. The scale and precision of craftsmanship displayed here are nothing if not amazing.

Figure 11: Mirrored staff and jewel mounting.

Professor Miller used the phonodiek to capture a huge variety of sounds on film. There are a few dozen pieces of phonodiek film in the CWRU collection, each about a foot long and five inches wide, mostly showing shapes of waves from musical instruments. Miller was able to use a planimeter to find the center line for a periodic wave as drawn by his phonodiek and then to discover the fundamental and overtones. The phonodiek could also be used to display the amount of pressure caused by a sound. He took his portable phonodiek and many barometers to Sandy Hook proving ground during the first World War and measured the durations and pressures of shock waves from guns of many sizes, including service rifles, mortars, and artillery pieces, to discover their physiological effects.

Figure 12: Flute, Clarinet, Oboe, Saxophone

Figure 12 shows four wave traces made using the phonodiek c. 1916. Miller photographed the wave forms of each of four instruments as they produced a 256 Hz note--C3, "middle" C. Note how the phonodiek shows the differences between the tone quality of the four woodwinds. The flute, which does not have a reed, produces a note with fewer overtones and a simpler wave form in the photograph.

Note the time stamps on the curves F, G, and H. in figure 12. Miller used a 100 Hz tuning fork with another beam of light set up so that a "T" shaped flash hit the film every .01 second. The timing flashes were most useful when recording non-periodic sounds such as rifle reports and speech.