Abstract
By mid-nineteenth century the climate of discussion had become optimum for undertaking the construction of keyboard instruments that are able to sound in just intonation. The technological expertise to realize this was readily available in the keyboard manufacturing sector. Helmholtz took the initiative for moving in this direction by transferring to the laboratory a problem that until then for the most part had been dealt with only in theory and in written works. The jumping-off point in our exploration of the construction of fixed tone keyboards in just intonation is Hermann Helmholtz.
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Notes
- 1.
Helmholtz, “Zur Theorie der Zungenpfeifen” (1861), Wissenschaftliche Abhandlungen 1 (1882) 388–394.
- 2.
Wilhelm Weber (1804–1891), professor of physics in Göttingen, is best known for his contributions to electrodynamics. His early interests in acoustics and wave phenomena were generated in large part by contacts with the physicist and acoustician E.F.F. Chladni (1756–1827) who for some years lived with Weber in the same house in Wittenberg. The Wellenlehre (Leipzig, 1825), a joint publication of Wilhelm and his older brother Ernst Weber (1795–1878), the Leipzig physiologist, was dedicated to “our admired friend Chladni, the founder of an acoustics based on experiments.” Wilhelm Weber’s doctoral dissertation of 1826 under Johann Schweigger, physicist and chemist at the University of Halle, was on the theory of reed organ pipes. A.E. Woodruff, “Wilhelm Weber,” DSB, 14 (1976) 203–209; “Wilhelm Weber,” Lexikon Geschichte der Physik A-Z, ed. Armin Hermann, Cologne, 1972, 397–400.
- 3.
Helmholtz, Wiss. Abh., Zungenpfeifen, 388.
- 4.
A number of works on the history and significance of the harmonium have been consulted. The earliest history was published anonymously in 1868 but is known to have been authored by W. Riehm, a Protestant pastor from Baden who was the owner of an harmonium with 12 registers and a percussion mechanism. Das Harmonium in seiner Construction und Behandlung, Basel & Ludwigsburg. In that volume the intention of the author is to explain, from his own experience with the harmonium, various aspects of the instrument that he believes will be of interest to the lay music learner: the instrument’s dynamic output, timbre, stability of tuning and flexibility, blending characteristics with other instruments, registers, deficiencies, and the names and addresses of the German and French harmonium builders. The most informative history of the harmonium, one that was published half a century after the Riehm volume, depicts the instrument in its final modern form. L. Hartmann, Das Harmonium umfassend die Geschichte, das Wesen, der Bau und die Behandlung des Druck- und Saugwindharmoniums nebst einer Abhandlung über das Harmoniumspiel, Leipzig, 1913. Author Hartmann remarks in the Preface that since the piano has pushed most musical instruments and their music, especially the string quartet, out of home and family, he hopes that the modern harmonium will be reappraised and reinstated as a Hausmusik instrument. A third volume, a compilation of essays on specialized topics dealing with the harmonium in Germany, brings the subject into the present and treats the instrument’s construction, economic significance, and utilization as an historic musical instrument. The general viewpoint expressed in this work is that “the great time of the instrument has long past…., that the harmonium today actually is, so to say, an historical instrument, appropriate and necessary at best for the performance of music of a bygone era.” (8–9) Christian Ahrens and Gregor Klinke (eds.), Das Harmonium in Deutschland. Bau, wirtschaftliche Bedeutung und musikalische Nutzung eines ‘historischen’ Musikinstruments, Frankfurt/Main, 1996. The volume on the harmonium that most directly relates to topics treated in this paper will be referred to as “Michaelstein” in what follows. Conference report, volume 62 of the Stiftung Michaelstein Kloster. Monika Lustig (ed.), Harmonium und Handharmonika, 20. Musikinstrumentenbau Symposium, Michaelstein, 19–21 Nov. 1999, Michaelstein/Blankenburg, 2002.
- 5.
The technical and financial arrangements for the Helmholtz- Schiedmayer transactions are spelled out in three letters (March 1861 to January 1862 with invoice for f 456), signed J. & P. Schiedmayer, Stuttgart, Piano, Harmonium, Harmonicorde. Nachlass Helmholtz, Item 426, Berlin-Brandenburgische Akademie der Wissenschaften. Akademiearchiv, Jägerstrasse 22/29, Berlin. The members of the Schiedmayer family were distinguished builders of clavichords, harpsichords, and pianos in eighteenth-century Bavaria. The modern branch of the firm was founded in 1809 in Stuttgart. In 1854 two Schiedmayer brothers, Julius (1822–1878) and Paul (1829–1890), opened the J. & P. Schiedmayer harmonium factory in Stuttgart. Julius, with training as a merchant, took charge of piano building. Paul, who had studied in Paris with A.F. Debain, the effective inventor of the harmonium, oversaw the construction of harmoniums. After 4 years in operation the harmonium factory had 40 workers and was building instruments that received worldwide recognition. At the exhibitions of 1862 in London and 1867 in Paris Schiedmayer instruments received the grand prize and the first silver prize. In the ‘70s and ‘80s the company carried on a prosperous and brisk business. The company was bombed in World War II. Exemplars of the various Schiedmayer keyboard instruments have survived mainly in German museums. Alexander Eisenmann, Schiedmayer and Soehne Hof-Pianofabrik, Vorgeschichte, Gründung und fernere Entwicklung der Firma, 1809–1909, Stuttgart, 1909. See esp. pp. 46–60.
- 6.
Helmholtz, Sensations of Tone, 1954 ed., 316. First Ger. ed. 1863, 485.
- 7.
Helmholtz, Sensations of Tone, 1954 ed., 319.
- 8.
Helmholtz, Sensations of Tone, 1954 ed., 319–320.
- 9.
Helmholtz, Sensations of Tone, 1954 ed., 320.
- 10.
Helmholtz, Sensations of Tone, 1954 ed., 320.
- 11.
Helmholtz, Sensations of Tone, 1954 ed., 321. In this context Helmholtz notably mentions composers such as Jean Philippe Rameau (1683–1764), Friedrich Marpurg (1718–1795), Johann Sebastian Bach (1685–1750), and the theorist and organist Andreas Werckmeister (1645–1706).
- 12.
Helmholtz, Sensations of Tone, 1954 ed., 321.
- 13.
Helmholtz, Sensations of Tone, 1954 ed., 322. The beats of the tempered fifth (9 beats in 10 seconds) are always quite audible. Beats of the combinational tones of the tempered fifth (5
per second) are audible for tones that are not too weak. The beats of the major third (10½ per second) are not audible unless the tones employed have high upper partials. Beats of the minor third (18 per second) are much weaker than those of the major third and only occur for high upper partials. All these beats occur twice as fast when the chord lies an octave higher and half as fast when the chord lies an octave lower. - 14.
Helmholtz, Sensations of Tone, 1954 ed., 323.
- 15.
Helmholtz, Sensations of Tone, 1954 ed., 323.
- 16.
Helmholtz, Sensations of Tone, 1954 ed., 324.
- 17.
The Austro-Hungarian violinist and composer Joseph Joachim was born in Köpcséy, Hungary, in 1821 and died in Berlin in 1907. With studies in Vienna and Budapest, and influenced by Mendelssohn in Leipzig, Joachim’s playing was in the French classical tradition. For most of his life he worked close to and in an advisory capacity with the Schumanns and Brahms. In spite of personal disputes with Brahms, he was a strong advocate of his music. From 1858 he taught in Berlin where he founded and led an influential string quartet.
- 18.
Helmholtz, Sensations of Tone, 1954 ed., 325.
- 19.
Helmholtz, Sensations of Tone, 1954 ed., 325.
- 20.
Helmholtz, Sensations of Tone, 1954 ed., 326.
- 21.
Helmholtz, Sensations of Tone, 1954 ed., 327.
- 22.
Helmholtz, Sensations of Tone, 1954 ed., 327.
- 23.
In a recent article Bradley Lehman claims to have solved a 250-year-old puzzle by unlocking the significance of what appeared at the top of one of J.S. Bach’s compositions as an arbitrarily scribbled design. The puzzle allegedly involves Bach’s views on a method of tuning the harpsichord. Bradley Lehman, Bach’s extraordinary temperament: Our Rosetta Stone – 1. Early Music, 33 (2005) 3–23. What Lehman’s puzzle-solving exercise shows about Bach is how he thought the harpsichord should be tuned in order to play the Well-Tempered Clavichord the way he wanted it to be played.
- 24.
Helmholtz, Sensations of Tone, 1954 ed., 327.
- 25.
Apologia ad Piet Hein, who was a sharp-witted, limerick-handy physicist at Niels Bohr’s Institute of Theoretical Physics in Copenhagen. He wrote in Grooks, Copenhagen, 1966, “Problems worthy of attack show their worth by striking back.”
- 26.
The Bosanquet Treatise of 1876 represents a revised and enlarged version of a number of papers published in the Proceedings of the Royal Musical Association (1874/5) entitled: On Temperament, of Division of the Octave. 1. Points of Historical Interest; 2. Formation of Scales and Properties of Systems; 3. Instrumental Means of Control. An edited version of the 1876 London Treatise was published in Utrecht in 1987 by Rudolf Rasch (b. 1945) who teaches music theory, music history, musical acoustics, and musical instrumentology at the Institute for Art History at the University of Utrecht. Rasch provides extensive biographical and bibliographical information about Bosanquet and offers a perceptive commentary on the historical importance of Bosanquet’s contributions to tuning and temperament. Rudolf Rasch, MGG, Personenteil 13 (2005), col. 1283–1284.
- 27.
John Tyndall, On Sound. Eight Lectures delivered at the Royal Institution, London 1867, 4th ed. 1883. Ger. transl., ed. by H. Helmholtz and G. Wiedemann, Braunschweig 1869; George Biddell Airy, On Sound and Atmospheric Vibrations, London, 1868, 1871; Sedley Taylor, Sound and Music. An Elementary Treatise on the Physical Constitution of Musical Sounds and Harmony, London, 1873, 1883, 1896; W.H. Stone, The Scientific Basis of Music, London, 1878, 1879; Lord Rayleigh (John William Strutt), The Theory of Sound, 2 volumes, Cambridge, 1877–1878, 1894.
- 28.
For example, Royal Society of London Catalogue of Scientific Papers; Poggendorff’s Biographisch-literarisches Handwörterbuch. Passim.
- 29.
The Musical Association included prominent scientists such as John Tyndall, Sedley Taylor, W.H. Stone, William Pole, Lord Rayleigh, Bosanquet, and A.J. Ellis.
- 30.
Rudolf Rasch, Biography in Bosanquet, An Elementary Treatise, Utrecht, 1987, 11–23.
- 31.
Helmholtz, Sensations of Tone, 1954 ed., 328–330 and Appendix XIX, 429–430. The sections on Bosanquet here described were first included in the 4th 1877 edition of Helmholtz’s Sensations of Tone, and published shortly after Bosanquet’s 1876 Treatise appeared. According to a footnote on p. 328 of the Dover ed. of Sensations of Tone, the Bosanquet harmonium was on display in 1876 in the Scientific Loan Exhibition at the Science Museum in South Kensington.
- 32.
R.H.M. Bosanquet, “On just intonation in music.” An Abstract. Proceedings of the Royal Society of London, 21 (1874–1875) 131–132.
- 33.
Bosanquet, An Elementary Treatise, London 1876, viii–ix.
- 34.
Rasch, Biography in Bosanquet, An Elementary Treatise, Utrecht, 1987, 24–25.
- 35.
The pre-Helmholtz history of this topic – the design and construction of enharmonic keyboards with more than 12-keys per octave – is extensive and merits an analysis that cannot be included here. An examination of the contributions of Ellis also would also take the reader beyond the scope of this analysis.
- 36.
Rasch, Biography in Bosanquet (1987), 30–31.
- 37.
Rasch, Biography in Bosanquet (1987), 51–52. In his various writings Bosanquet took note of the ideas of a number of other contemporary multi-tone keyboard proponents, and Rasch has discussed these matters.
- 38.
Rasch, Biography in Bosanquet (1987), 64–65.
- 39.
Iwan Rhys Morus, When Physics Became King, Chicago 2005, Section on “Berlin’s Imperial Institute.”
- 40.
David Cahan, An Institute for an Empire. The Physikalisch-Technische Reichsanstalt 1871–1918, Cambridge, 1989.
- 41.
These matters are examined in a forthcoming monograph entitled: Max Planck: Theoretical Physics with Caution, Music with Passion, Objective Laws of Nature as Stepping Stone to the Deity of Creation.
- 42.
Helmholtz, Vorlesungen über die mathematischen Principien der Akustik is vol. III in the X-volume Vorlesungen über die theoretische Physik, Leipzig, 1898.
- 43.
Helmholtz, Vorlesungen, 1.
- 44.
The Eitz harmonium is described in Max Planck, “Ein neues Harmonium in natürlicher Stimmung nach dem System von C. Eitz,” Verhandlungen der Physikalischen Gesellschaft, 12 (1893) 8–9, reproduced in Physikalische Abhandlungen und Vorträge 1 (1958) 435–436.
- 45.
Eitz to Helmholtz, Eisleben, 2 Sept. 1889. Nachlass Helmholtz, Akademiearchiv; Berlin, Item 30.
per second) are audible for tones that are not too weak. The beats of the major third (10½ per second) are not audible unless the tones employed have high upper partials. Beats of the minor third (18 per second) are much weaker than those of the major third and only occur for high upper partials. All these beats occur twice as fast when the chord lies an octave higher and half as fast when the chord lies an octave lower.References
Bosanquet, R.H.M. 1876. An elementary treatise, viii–ix. London.
Cahan, David. 1989. An Institute for an Empire. The Physikalisch-Technische Reichsanstalt 1871–1918. Cambridge: Cambridge University Press.
Helmholtz, H. 1954. Sensations of tone. New York: Dover Publications.
Morus, Iwan Rhys. 2005. When physics became king. Chicago: University of Chicago Press.
Rasch, Rudolf. 1987. Biography in Bosanquet. In An elementary treatise. Utrecht: Diapason Press.
Woodruff, A.E. 1976. Wilhelm Weber. DSB 14: 203–209.
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Hiebert, E. (2014). Just Intonation and the Harmonium. In: The Helmholtz Legacy in Physiological Acoustics. Archimedes, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-319-06602-8_8
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