Draft:Helmholtz sound synthesiser

Helmholtz's Apparatus for the Artificial Construction of Vowels (Apparat zur künstlichen Zusammensetzung der Vocalklänge), better known as the Helmholtz sound synthesiser, is a scientific instrument created to reproduce certain vowels using a set of tuning forks as described in Helmholtz's Sensations of Tone.

History

Background

Hermann von Helmholtz (born 1821 in Potsdam) was a 19th-century German physicist who contributed greatly to several areas of science, including optics and acoustics. In acoustics, he published his foundational treatise On the Sensations of Tone as a Physiological Basis for the Theory of Music in 1863. While studying combination tones in 1855, he developed a type of resonator that could resonate at a specific frequency. He found that multiple of these resonators could be used to analyse the frequencies making up a sound, providing the basis for his later analysis of timbre.

Along with his work in various other areas of acoustics, Helmholtz developed methods to investigate the acoustic differences between vowel sounds. Through his study of timbre, Helmholtz showed that musical sounds are composed of not just their fundamental frequency but also their overtones according to the harmonic series. By using Fourier analysis, he saw this sum of sine waves as being like a musical chord, so that a musical sound has no single tone. The combinations of these overtones and their strength creates different timbres. By understanding the foundations of timbre and its applications to the human vocal tract, Helmholtz was able to investigate the frequency composition of vowels and their formants.

Rudolph Koenig (born 1832 in Königsberg) was a Prussian physicist who worked as a designer of scientific instruments, particularly involving acoustics. After completing his studies at the University of Königsberg, he undertook an apprenticeship to the Parisian luthier Jean-Baptiste Vuillaume in 1851. Seven years later, Koenig started his own firm of scientific instrument makers which he ran until his death in 1901. Koenig's instruments were made at his house in Paris.

First designs

To explore timbre further, Helmholtz realised he would need a set of tuning forks to synthesise additional overtones. After delivering a popular lecture on combination tones in 1857, Helmholtz received the interest of King Maximilian II of Bavaria. In the autumn of that year, Maximilian II provided Helmholtz with 400 gulden to create a new device capable of investigating timbre. Helmholtz completed his apparatus in the spring of 1858. In a letter to his friend Emil du Bois-Reymond on 15 April, Helmholtz wrote:

I have now put together a complicated apparatus at the King of Bavaria's expense, by which one is able to control the vibrations of a tuning-fork at will by an electro-magnet, with complete command of intensity and difference of phase. This is in order to regulate the production of timbre (Klangfarbe).

This first synthesiser's design was set to a fundamental frequency of 120 Hz (B♭2) and comprised eight tuning forks and resonators. This set of resonators produced a fundamental tone with its first seven overtones, ranging from B♭2 to B♭5. The apparatus allowed him to swiftly create sounds of different timbres using overtones of various intensities in a manner likened to his experiments with coloured lights. Although it became known as a synthesiser, Helmholtz named his creation "apparatus for the artificial construction of vowels" (Apparat zur künstlichen Zusammensetzung der Vocalklänge), as it was created to construct already existing vowels and not synthesise new sounds.

Helmholtz published the results of experiments made with the synthesiser in 1859, which was republished in a larger form in his 1863 work, Sensations of Tone.

Design

Koenig's ten resonator version of the synthesiser measured around 105 by 60 by 40 centimetres (41 in × 24 in × 16 in). Notes on Koenig's synthesisers are marked according to the French practice of labelling scale degrees, using Ut, Re, Mi, Fa, So, La and Ti to represent the seven notes of a C major scale. Koenig labelled the fundamental frequencies of his synthesisers differently from modern practice, using individual pulses instead of frequency as per 19th-century French practice. This makes Koenig's frequencies double their modern hertz equivalent: an example Koenig synthesiser built c. 1875 has its fundamental marked as Ut₂ = 256 but oscillates at 128 Hz.

Koenig's eight-resonator synthesiser, as depicted in his 1889 catalogue

Notes of an example eight-resonator Koenig synthesiser, c. 1875

Resonator number	French names	Scientific pitch	Interval from fundamental
1	Ut2	C3	Tonic
2	Ut3	C4	Octave
3	Sol3	G4	Perfect fifth
4	Ut4	C5	Octave
5	Mi4	E5	Major third
6	Sol4	G5	Perfect fifth
7	[unmarked]
8	Ut5	C6	Octave

The synthesiser is made up of a large mahogany base which fits a master tuning fork along with several others (usually eight or ten). Aside from the master, these forks are paired with brass Helmholtz resonators to amplify the sound continuously by their high Q factor. The tuning forks—chosen for their simple sinusoidal wave shape—resonate at a fixed fundamental frequency and its partials according to the harmonic series. Each resonator unit is made of its own wooden base, which is fixed to a tuning fork and a cylindrical resonator attached to the base by a stand. These units are connected to a keyboard with ivory plated wooden keys by a system of strings between each key and a corresponding resonator shutter. By pushing a key, a string removes the covering over a resonator's opening hole, allowing that tone to sound at a strength according to the pressure on the key. Releasing the key then lets the covering spring back into place. To avoid having to repeatedly strike them, all tuning forks are vibrated continuously using a system of copper wire coils that function as electromagnets. Although continuously active, the forks don't make a loud sound without activated resonators. Helmholtz acknowledged flaws in his original design, including the addition of other partials as a by-product of "strong activation". The distance between the forks and electromagnets can be altered using screws. An alternating electric current at the resonant frequency of the fundamental tuning fork is supplied to all forks via external connections on the main base.

Usage

Helmholtz originally intended for his synthesiser to synthesise different vowel sounds using various partial intensities in a form of additive synthesis. Using the synthesiser he was able to create realistic vowel sounds for those not requiring higher partials: vowels like /e/ and /i/ remained unconvincing. Through his experimentation with the synthesiser he discovered that different vowels have different harmonic content, realising that vowels like "Å", "Ä" and "E" have weaker fundamental frequencies that "U" and "O". He theorised that the unique harmonic content of each vowel was produced by the altering the resonances of the vocal tract. He identified these resonances as formants, proposing that some vowels can be identified with one formant (/a/, /o/, /u/), while another is needed to define a others (/ä/, /e/, /i/).

Ellis' table of vowel composition after Helmholtz's findings

Vowel	Resonator number (scientific pitch)								Audio
	1 (B♭2)	2 (B♭3)	3 (F4)	4 (B♭4)	5 (D5)	6 (F5)	7 (A♭5)	8 (B♭5)
U	forte	pianissimo	pianissimo
O	mezzo-forte	piano	piano	forte	piano
Å	piano	piano	piano	piano	fortissimo	fortissimo	fortissimo	fortissimo
Ä	piano	pianissimo	piano	forte	forte
E	piano	pianissimo	forte	piano	piano	piano	piano	piano

Later, Helmholtz began to synthesise instrument sounds. His approach was limited by the number of partials he could use, making his creations very crude. Helmholtz used his synthesiser to create clarinet and horn tones, which he commented were "given by using a series of unevenly numbered partials [and] by the full chorus of all the forks" respectively. By developing a relationship between partials and timbre, Helmholtz realised that the harmonic content of an instrument contributes directly to its perceived tonal quality:

If only the unevenly numbered partials are present [...] the quality of tone is hollow, and, when a large number of such upper partials are present, nasal. When the prime tone predominates the quality of tone is rich; but when the prime tone is not sufficiently superior in strength to the upper partials, the quality of tone is poor. [...] When partial tones higher than the sixth or seventh are very distinct, the quality of tone is cutting and rough.

The synthesizer was used as a teaching aid for 19th-century university physics courses at the University of Toronto, where it was introduced 1870–1880 by James Loudon.

Legacy

Helmholtz's work on vowel sounds was built on by Carl Stumpf, who built his own apparatus to study vowels out of 28 flue pipes. He used it to expand on Helmholtz's study of formants, showing that all vowels can be defined by a minimum of two formants.

Examples of the synthesiser are rare.

Synthesisers are held in the University of Toronto's Scientific Instruments Collection (Koenig: 1880s, ten resonators), Teylers Museum's Instrument Room (Koenig: 1865, eight resonators), Whipple Museum of the History of Science (Koenig: fourth-quarter 19th century, seven resonators), London Science Museum (Koenig: 19th century, ten resonators), Harvard Collection of Historical Scientific Instruments (Koenig: c. 1865, eight resonators),

Several auction houses have sold versions of the synthesiser. On 22 October 2014, Bonhams New York included a ten resonator model made c. 1905 by Kohl in their "History of Science" auction, which sold for $20,000. Sotheby's New York has auctioned two Kohl ten-resonator synthesisers: their offering during their 2017 "History Of Science And Technology" auction went unsold. In their 2018 edition of the same auction, a similar synthesiser was sold for $25,000.

Helmholtz's synthesiser is generally considered one of the first electronic sound synthesisers, a precursor to the development of modern synthesisers at large.

References

Sources

• Collins, Nick; Schedel, Margaret; Wilson, Scott (2013). "New sounds and new instruments: Electronic music up until 1948". Electronic Music. Cambridge Introductions to Music. Cambridge University Press. doi:10.1017/CBO9780511820540.003. ISBN 9781107010932.
• De Souza, Jonathan (2021). "Timbral Thievery: Synthesizers and Sonic Materiality". In Dolan, Emily I.; Rehding, Alexander (eds.). The Oxford Handbook of Timbre. Oxford Handbooks. New York: Oxford University Press. pp. 346–379. doi:10.1093/oxfordhb/9780190637224.013.8. ISBN 9780190637224.
• Greenslade, Thomas B. (1992). "The acoustical apparatus of Rudolph Koenig". The Physics Teacher. 30 (9). AIP Publishing: 518–524. Bibcode:1992PhTea..30..518G. doi:10.1119/1.2343629.
• Königsberger, Leo (1906). "Professor of Physiology and Anatomy at Bonn, 1855–1858". Hermann von Helmholtz. Translated by Welby, Frances A. Oxford University Press. pp. 147–175. OCLC 608727961. Retrieved 28 January 2024.
• Maor, Eli (2020). Music by the Numbers. Princeton University Press. doi:10.2307/j.ctvc77df7. ISBN 9780691202969. JSTOR j.ctvc77df7.
• Schroeder, Manfred R. (1999). "A Brief History of Speech". Computer Speech. Springer Series in Information Sciences. Berlin/Heidelberg: Springer. pp. 23–40. doi:10.1007/978-3-662-03861-1_2. ISBN 9783662038635.
• Steege, Benjamin (2015). "Voices of reform". Helmholtz and the Modern Listener. Cambridge University Press. doi:10.1017/CBO9781139057745.007. ISBN 9781107504332.
• Turner, Gerard L'Estrange (1983). "Sound". Nineteenth-century scientific instruments. London: Sotheby Publications. pp. 129–146. ISBN 9780520051607. Retrieved 24 January 2024.

To add

• Helmholtz, Hermann von (1863). On the Sensations of Tone as a Physiological Basis for the Theory of Music. Translated by Ellis, Alexander John (3rd ed.). New York: Cambridge University Press (published 2009). doi:10.1017/CBO9780511701801. hdl:2027/mdp.39015000592603. ISBN 9781108001779.
• Pisko, Franz Josef (1865). Die neueren apparate der akustik. Für freunde der naturwissenschaft und der tonkunst [The latest devices of acoustics. For friends of natural science and the art of sound] (in German). Vienna: Carl Gerold's Sohn. OCLC 1014820137. Retrieved 28 January 2024.
• Kursell, Julia (January 2013). "Experiments on Tone Color in Music and Acoustics: Helmholtz, Schoenberg, and Klangfarbenmelodie". Osiris. 28 (1). University of Chicago Press: 191–211. doi:10.1086/671377. JSTOR 10.1086/671377. S2CID 143772378.
• Physical Apparatus (PDF). Vol. II and III. Chemnitz: Max Kohl Aktiengesellschaft. c. 1911. OCLC 83026752. Retrieved 24 January 2024. p 460
• Pantalony, David (2005). "Rudolph Koenig's Workshop of Sound: Instruments, Theories, and the Debate over Combination Tones". Annals of Science. 62 (1). Taylor & Francis: 57–82. doi:10.1080/00033790410001712183. S2CID 143791144.
• Hankins, Thomas L.; Silverman, Robert J. (1999). "Vox Mechanica: The History of Speaking Machines". Instruments and the Imagination. Princeton University Press. pp. 178–220. ISBN 9780691635200. JSTOR j.ctt7ztvhb.12.
• Lenoir, Timothy (1994). "Helmholtz and the Materialities of Communication". Osiris. 9 (1). University of Chicago Press: 184–207. doi:10.1086/368736. JSTOR 302005. S2CID 27790157.
• Fuller, Matthew (2007). Media Ecologies. Leonardo. Cambridge, Massachusetts: MIT Press. ISBN 9780262562263.
• Cahan, David (1994). Hermann von Helmholtz and the Foundations of Nineteenth-Century Science. California Studies in the History of Science. Berkeley: University of California Press. ISBN 9780520083349. JSTOR 10.1525/j.ctt1pnwfn.
• Buchwald, Jed; Fox, Robert, eds. (2013). The Oxford Handbook of the History of Physics (1st ed.). Oxford University Press. doi:10.1093/oxfordhb/9780199696253.001.0001. ISBN 9780199696253.
• Honisch, Erika Supria; Schedel, Margaret (August 2018). "Editorial: New Wor(l)ds for Old Sounds". Organised Sound. 23 (2). Cambridge University Press: 133–143. doi:10.1017/S1355771818000018.
• Wittje, Roland (January 2013). "The Electrical Imagination: Sound Analogies, Equivalent Circuits, and the Rise of Electroacoustics, 1863–1939". Osiris. 28 (1). University of Chicago Press: 40–63. doi:10.1086/671362. JSTOR 10.1086/671362. S2CID 144251012.
• Pantalony, David (Autumn 2004). "Seeing a Voice: Rudolph Koenig's Instruments for Studying Vowel Sounds". American Journal of Psychology. 117 (3). University of Illinois Press: 425–442. doi:10.2307/4149009. JSTOR 4149009.
• Blamey, Peter John (2008). Sine Waves and Simple Acoustic Phenomena in Experimental Music: with Special Reference to the Work of La Monte Young and Alvin Lucier (PhD thesis). University of Western Sydney. Retrieved 26 January 2024.
• Vallee, Mickey (2019). Sounding Bodies Sounding Worlds. Palgrave Studies in Sound. Berlin/Heidelberg: Springer. doi:10.1007/978-981-32-9327-4. ISBN 9789813293267.
• Wittje, Roland (2016). The Age of Electroacoustics. Transformations: Studies in the History of Science and Technology. Cambridge, Massachusetts: MIT Press. doi:10.7551/mitpress/10989.001.0001. ISBN 9780262035262.
• Pantalony, David (2009). Altered Sensations. Archimedes. Vol. 24. Dordrecht: Springer. doi:10.1007/978-90-481-2816-7. ISBN 9789048128150.
• Kursell, Julia (June 2005). Shaping Differences: Hermann von Helmholtz's Experiments on Tone Colour (PDF). The Shape of Experiment (Preprint 318). pp. 215–223. Retrieved 26 January 2024.
• Sluijter, Rob (2005). The development of speech coding and the first standard coder for public mobile telephony (PhD thesis). Eindhoven University of Technology. doi:10.6100/IR596759. OCLC 1359155292.
• Pantalony, David (2002). Rudolph Koenig (1832-1901), Hermann von Helmholtz (1821-1894) and the Birth of Modern Acoustics (PhD thesis). University of Toronto. hdl:1807/121611. OCLC 53180988. Retrieved 26 January 2024.
• Bader, Rolf (2021). How Music Works: A Physical Culture Theory. Cham, Germany: Springer. doi:10.1007/978-3-030-67155-6. ISBN 9783030671556.
• van Eck, Cathy (2017). Between Air and Electricity. New York: Bloomsbury Academic. doi:10.5040/9781501327636. hdl:1887/22868. ISBN 9781501327605. Retrieved 26 January 2024.
• Lazzarini, Victor (2021). Spectral Music Design: A Computational Approach. New York: Oxford University Press. doi:10.1093/oso/9780197524015.001.0001. ISBN 9780197524015.
• Koenig, Rudolph (1865). Catalogue des Appareils D'Acoustique Construits par Rudolph Koenig [Catalog of Acoustic Devices Built by Rudolph Koenig] (in French). Paris: Simon Raçon Et Compagnie. OCLC 793549922. p10
• Koenig, Rudolph (1889). Catalogue des Appareils D'Acoustique Construits par Rudolph Koenig [Catalog of Acoustic Devices Built by Rudolph Koenig] (in French). Paris: P. Mouillot. OCLC 903989196. p 25

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