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.

Background
Hermann von Helmholtz (born 1821 in Potsdam) was a 19th-century German physicist who contributed greatly to several areas of science. In the field of 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.

Helmholtz developed methods to investigate the acoustic differences between vowel sounds. Through his study of timbre, he showed that musical sounds are composed of not just their fundamental frequency but also their overtones according to the harmonic series. In an early experiment he depressed keys of a piano to act as a rudimentary analyser, singing vowels into the soundboard and picking out the pitches that resonated. He saw this sum of sine waves as being like a musical chord, so that a musical sound has no single pure 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.

Conception
To explore timbre further, Helmholtz realised he would need a method of synthesising unique timbres. After considering a design using organ pipes, he settled on using a set of electromagnetically-driven tuning forks to synthesise a fundamental pitch and its overtones. After delivering a popular lecture on combination tones in 1857, Helmholtz received the interest of King Maximilian II of Bavaria into his research. 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:

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 Sensations of Tone.

Later manufacturers
Building on Helmholtz's designs, In a catalogue produced c. 1911 by the Chemnitz-based firm Max Kohl AG, two synthesisers based on Helmholtz's work were advertised as "Vowel Apparatus after von Helmholtz [...] for demonstrating tones of different timbre, and more especially the vowels of the human voice". Models were available with eight or ten resonators, retailing for £60 and £70  respectively. One existing example of Max Kohl's synthesisers dates slightly earlier to c. 1905.

Design
Koenig's ten resonator version of the synthesiser measured around 105 x 60 x 40 cm. 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. The French physiologist Georges Rene Marie Marage likened Helmholtz's design to an electrical imitation of human anatomy, describing the tuning forks as "represent[ing] the larynx [and] the resonators [as] the supralaryngeal cavities". In general, Helmholtz synthesisers are made up of a large mahogany base which fits a master tuning fork along with several other forks (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,  with interrupters made of wire and liquid mercury providing frequency multiples to each electromagnet.

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 and  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, while another is needed to define a others. 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:

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. Alexander Graham Bell was familiar with the work of Helmholtz using the synthesiser; Bell's own experiments with electromagnetism began with an attempted recreation of Helmholtz's synthesiser.

Despite Helmholtz's progress made using the synthesiser, vowels produced by the synthesisers are of quite low quality. Due to this, Helmholtz's methods were criticised by some contemporaries such as Dayton Miller, who considered the vowels produced to be of little relation to actual speech. John William Strutt, 3rd Baron Rayleigh, thought the experiment was too hard to conduct.

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.

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