Harmonic Analyzers and Synthesizers

Fourier analysis has widespread applications in physics – tidal motion, sound, and light signals can all be divided into harmonics. Surviving harmonic analyzers and synthesizers reflect this wide range of applications. Sometimes, as with tide predictors, the output was designed to be easily recorded on paper. At other times, the output was a light signal or sound.

In 1872, the British physicist William Thomson (later Lord Kelvin) devised a machine to simulate mechanically the combination of periodic motions that produce tides. Inspired by this example, William Ferrel of the U.S.
Description
In 1872, the British physicist William Thomson (later Lord Kelvin) devised a machine to simulate mechanically the combination of periodic motions that produce tides. Inspired by this example, William Ferrel of the U.S. Coast and Geodetic Survey designed a tide predictor and had it built by the Washington, D.C., firm of Fauth and Company. This elegant machine was more compact than that of Thomson, and gave maxima and minima rather than a continuous curve as output. It was designed in 1880, went into service in 1883 and remained in use until 1910. The success of Ferrel's tide predictor suggested the feasibility of replacing calculations performed by people with computation by machines.
Location
Currently not on view
Date made
1883
1880
used during
1883-1910
maker
Fauth & Co.
designer
Ferrel, William
ID Number
MA.315917
catalog number
315917
accession number
223203
Barus Harmonic Synthesizer. Designed by physicist Carl Barus (1856-1935) to study various wave forms.
Description (Brief)
Barus Harmonic Synthesizer. Designed by physicist Carl Barus (1856-1935) to study various wave forms. Barus wrote that this wave machine was, "sufficiently comprehensive in design to embody in a single mechanism the types of harmonic motion met with in acoustics, light, electricity and elsewhere, with a clear bearing on their kinematic analysis. ... I [believe] the apparatus to be more complete than any similar machine which I have seen, and having, after considerable experience, become assured of its usefulness in class work." Carl Barus, "The Objective Presentation of Harmonic Motion," Science, New Series, 9, no. 220 (17 March 1899): 385-405.
This unit was disassembled for shipping and is stored in sections: one main section with the discs (13.75" h x 33" w x 24" d) and a bundle of connecting rods (8" h x 48" w x 13" d). There is a frame with indicating tines for showing compressional effects with the bundle. The latter is noted as "with coil springs and wires on ends. "y" and perpendicular".
Location
Currently not on view
date made
ca 1898
ID Number
EM.330649
catalog number
330649
accession number
271855
collector/donor number
30.670
This is a large acoustic instrument with 14 universal resonators. The “Max Kohl A.G. / Fabrikphysikalischer Apparate / Chemnitz 1 SA.” indicates a date of 1908 or later.Ref: Max Kohl A.G., Physical Apparatus (Chemnitz, [1912]), vol. 2, pp. 458-459.Currently not on view
Description
This is a large acoustic instrument with 14 universal resonators. The “Max Kohl A.G. / Fabrikphysikalischer Apparate / Chemnitz 1 SA.” indicates a date of 1908 or later.
Ref: Max Kohl A.G., Physical Apparatus (Chemnitz, [1912]), vol. 2, pp. 458-459.
Location
Currently not on view
maker
Max Kohl
ID Number
PH.327653
catalog number
327653
accession number
268279
In the early nineteenth century, the French mathematical physicist Joseph Fourier showed that many mathematical functions can be represented as the weighted sum of a series of sines and cosines of differing period (e.g.
Description
In the early nineteenth century, the French mathematical physicist Joseph Fourier showed that many mathematical functions can be represented as the weighted sum of a series of sines and cosines of differing period (e.g. as the sum of harmonic functions with different coefficients). An apparatus arranged to mechanically derive the Fourier equation of a curve is called a harmonic analyzer. The first account of such an instrument, was published in 1876 by the British physicist William Thomson (Lord Kelvin). His device, which occupied considerable space, was used especially for tide prediction. In 1889 the German-born British mathematician and physicist Olaus Henrici developed a new, more compact, form of harmonic analyzer. He showed his model, as improved by Archibald Sharp, to G. Coradi of Zurich, who already was known as a maker of planimeters and integrators. Coradi made further improvements, and began manufacture. This harmonic analyzer has a single glass sphere. It is in a wooden case. To find different terms in the Fourier expansion of a function, one uses different discs in the machine. These are stored in a separate case that has catalog number 323827. Documentation that describes the two Coradi harmonic analyzers in the NMAH collection is stamped "James W. Glover (/) 620 Oxford Rd. (/) Ann Arbor, Michigan." Correspondence received relating to Glover's 1928 attempt to purchase a harmonic analyzer came with the object (see 1987.0705.005 & 1987.0705.06). Hence it seems likely that the harmonic analyzers were purchased for James Waterman Glover (1868-1941), a member of the faculty of the Department of Mathematics at the University of Michigan from 1895 to 1937. Glover offered the first courses in actuarial science taught at the university.
References:
O. Henrici, "On a new Harmonic Analyser," London, Edinburgh & Dublin Philosophical Magazine, 5th Series, #38, July-December, 1894, pp. 110-121.
G. Coradi, "Instructions for the use of the Harmonic Analyser Gear Wheel Type."
Location
Currently not on view
date made
ca 1928
maker
Coradi, Gottlieb
ID Number
1987.0705.01
accession number
1987.0705
catalog number
323826
These fifteen wheels are for use with harmonic analyzer 323826 (#60 - record number 1987.0705.01). They are marked as follows:1. n = 2 - 202. n = 3 - 6- 303. n = 4 - 8 - 404. n = 5 - 10- 505. n = 7 - 356. n = 9 - 457. n = 118. n = 129. n = 1310. n = 1411. n = 1512. n = 1613.
Description
These fifteen wheels are for use with harmonic analyzer 323826 (#60 - record number 1987.0705.01). They are marked as follows:
1. n = 2 - 20
2. n = 3 - 6- 30
3. n = 4 - 8 - 40
4. n = 5 - 10- 50
5. n = 7 - 35
6. n = 9 - 45
7. n = 11
8. n = 12
9. n = 13
10. n = 14
11. n = 15
12. n = 16
13. n = 17
14. n = 18
15. n = 19
The wheels are in a wooden case. A paper sticker attached to the front of the case reads: Pinons For (/) Harmonic Analyser (/) #60.
Location
Currently not on view
date made
ca 1928
maker
Coradi, Gottlieb
ID Number
1987.0705.02
catalog number
323827
accession number
1987.0705
In the early nineteenth century, the French mathematical physicist Joseph Fourier showed that many mathematical functions can be represented as the weighted sum of a series of sines and cosines of differing period (e.g.
Description
In the early nineteenth century, the French mathematical physicist Joseph Fourier showed that many mathematical functions can be represented as the weighted sum of a series of sines and cosines of differing period (e.g. as the sum of harmonic functions with differing coefficients). An apparatus arranged to mechanically derive the Fourier equation of a curve is called a harmonic analyzer. The first account of such an instrument was published in 1876 by the British physicist William Thomson (Lord Kelvin). His device, which occupied considerable space, was used especially for tide prediction. In 1889 the German-born British mathematician and physicist Olaus Henrici developed a new, more compact, form of harmonic analyzer. He showed his model, as improved by Archibald Sharp, to G. Coradi of Zurich, who already was known as a maker of planimeters and integrators. Coradi made further improvements and began manufacture.
This harmonic analyzer has a five glass spheres. It is in a wooden case. To find different terms in the Fourier expansion of a function, one uses different discs in the machine. These are stored in a separate case that has catalog number 323829. Documentation that describes the two Coradi harmonic analyzers in the NMAH collection is stamped “James W. Glover (/) 620 Oxford Rd. (/) Ann Arbor, Michigan." Correspondence received with the object relating to Glover's 1928 attempt to purchase a harmonic analyzer has museum numbers 1987.0705.005 and 1987.0705.06. Hence it seems likely that the harmonic analyzers were purchased for James Waterman Glover (1868-1941), a member of the faculty of the Department of Mathematics at the University of Michigan from 1895 to 1937. Glover offered the first courses in actuarial science taught at the university.
References:
O. Henrici, "On a new Harmonic Analyser," London, Edinburgh & Dublin Philosophical Magazine, 5th Series, #38, July-December 1894, pp. 110-121.
G. Coradi, "Instructions for the use of the Harmonic Analyser Gear Wheel Type."
Location
Currently not on view
date made
ca 1930?
maker
Coradi, Gottlieb
ID Number
1987.0705.03
accession number
1987.0705
catalog number
323828
These are the 28 wheels for use with harmonic analyzer 323828 (1987.0705.03). They are marked as follows:1. n = 7 - 352. n = 9 - 453. n = 114. n = 125. n = 136. n = 147. n = 158. n = 169. n = 1710. n = 1811. n = 1912. n = 2113. n = 2214. n = 2315. n = 2416. n = 2517. n = 2618.
Description
These are the 28 wheels for use with harmonic analyzer 323828 (1987.0705.03). They are marked as follows:
1. n = 7 - 35
2. n = 9 - 45
3. n = 11
4. n = 12
5. n = 13
6. n = 14
7. n = 15
8. n = 16
9. n = 17
10. n = 18
11. n = 19
12. n = 21
13. n = 22
14. n = 23
15. n = 24
16. n = 25
17. n = 26
18. n = 27
19. n = 28
20. n = 29
21. n = 31
22. n = 32
23. n = 33
24. n = 34
25. n = 36
26. n = 37
27. n = 38
28. n = 39
The wheels are in a wooden case.
Location
Currently not on view
date made
ca 1930?
maker
Coradi, Gottlieb
ID Number
1987.0705.04
catalog number
1987.0705.04
accession number
1987.0705
catalog number
323829
This is a letter from James Glover to Gaertner Scientific Corporation dated April 3, 1928. It requests information about harmonic analyzers.Currently not on view
Description
This is a letter from James Glover to Gaertner Scientific Corporation dated April 3, 1928. It requests information about harmonic analyzers.
Location
Currently not on view
date made
1928
ID Number
1987.0705.05
accession number
1987.0705
This letter , written Apriil 7, 1928, is in response to one from Prof. James W. Glover of the University of Michigan requesting information about the Michelson harmonic analyzer.Currently not on view
Description
This letter , written Apriil 7, 1928, is in response to one from Prof. James W. Glover of the University of Michigan requesting information about the Michelson harmonic analyzer.
Location
Currently not on view
date made
1928
maker
Gaertner, William
ID Number
1987.0705.06
accession number
1987.0705
catalog number
1987.0705.06
A harmonic analyzer is a mechanical instrument for reducing a curve to its expression as a Fourier expansion. It calculates the coefficients to be used when the curve is expressed as the sum of a series of sines and cosines.
Description
A harmonic analyzer is a mechanical instrument for reducing a curve to its expression as a Fourier expansion. It calculates the coefficients to be used when the curve is expressed as the sum of a series of sines and cosines. In 1909, the German engineer Otto Mader introduced this form of harmonic analyzer, which used a set of wheels to find successive coefficients for the expansion of a plotted curve. This version of Mader’s invention was made the firm of A. Ott in Kempten, Germany.
The wooden box, 34 ¾” wide x 27” deep x 3 ¼” high contains the following components:
1. A triangular carriage, measuring 18” x 12” with three wheels. This contains a smaller triangular carriage with a rack as well as a plate with holes for inserting gear wheels. A mark on the gear wheel plate reads: A. Ott, Kempten, no. 2253. A mark on the bottom reads: 5650A. A mark on the bottom of the smaller carriage reads “2”. Another mark there reads: A. Ott Kempten.
2. Some 108 brass gear wheels (two sets of 54), the smallest 5/8” in diameter and the largest 3 1/8” in diameter.
3. A tracer arm, 26 ½” long, graduated in tenths from 2 to 73. A pivot is at one end and a guide knob controlling the height at the other. Attached are a moveable tracer pin as well as a rotating lever. The lever is 7 ¾” long with a pivot at the other end.
4. A guide rail, 28 3/8” x 1 ¾”, graduated from 0 to 36. It has one groove, two notches, and two holes for fastening pins.
5. A lever 15” x 8 ¼” x 16 ½”. The first side is a tracer arm graduated from 2 to 37 in tenths that contains a moveable tracer pin, ball pivot, and guide knob like (3).
6. A triangle, 11 ½” x 11 ½” x 5 ¾”. It has one wheel, two ball pivots, and one hole; and is stamped “2” on the bottom.
7. A guide rule, 17 ¼” long, with a grooved piece 5 ½” long attached at the left end. It is stamped on the bottom: 29. The grooved piece is graduated in tenths with the zero-point at the center, and runs from 0 to 37 in both directions. A second set of readings runs from 0 to 36 using the same scale reading from +36 to -36 of first set.
8.Two brass and steel compensating polar planimeters, both marked: A. Ott Kempten. One is also marked with a serial number “No. 49475”, the other “No. 49476”. Each consists of a tracer arm, 7” long, attached to a plate containing a measuring roller and counter, and a pole arm, 8 ¾” long with pole.] Each planimeter has a pole plate and a control rule 4” long. Each planimeter also has a screwdriver (a metal piece ¾” x ¾”) for replacing the pivot point. Both planimeters are in black wooden cases that measure 10 ½” x 3 5/8” x 1 ¾”. A listing of constants in German is pasted inside the case.
9. A wooden base, 19 ¾” x 10 ¼” x 1 ¾”.
Unless indicated otherwise, the components are made of steel with chrome and aluminum finish.
References:
NMAH Accession file 254098.
Detlef Zerfowski, “Calculating Waves Not only on the Beach, Mechanical Calculation of Harmonic Waves by Harmonic Analyzers,” Proceedings of the 25th International Meeting of Collectors of Historical Calculating Instruments, September 20th to 22nd, 2019, The Hague & Scheveningen, The Netherlands, pp. 191-210. See https://www.zerfowski.com/Papers/Zer2019-1_Calculating_Waves.pdf , accessed September 1, 2020.
Compare the example at the Science Museum, London – see https://collection.sciencemuseumgroup.org.uk/objects/co60186/harmonic-analyser-maders-form-in-fitted-case-harmonic-analyser-planimeter, accessed September 2, 2020.
Location
Currently not on view
date made
1931
maker
Ott, Albert
ID Number
MA.324276
catalog number
324276
accession number
254098
Currently not on view
Location
Currently not on view
maker
Ott
ID Number
1994.0397.01
accession number
1994.0397
catalog number
1994.0397.01

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