If you were Benedetto Bergonzi you would invent a horn with keys something like this
Corno da Caccia con Chiavi


Please note: The horn shown below is a modern functional reconstruction of the Corno da Caccia con Chiavi invented by Benedetto Bergonzi in 1822. It is NOT a true copy of Sr. Bergonzi's invention since there are no known extant exemplars, models, drawings, or detailed descriptions of the construction of the original instrument.
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(click on photos for larger view)


The horn shown above is a modern functional reconstruction of the Corno da Caccia con Chiavi (literally "hunting horn with keys") invented by Sr. Benedetto Bergonzi in 1822. It is a single horn in F to which have been added four keys. These keys have the effect of shortening the vibrating air column such that the pitch is raised in half steps, thus giving harmonic series for F♯, G, G♯, and A.1  In the left photo they are located approximately at the 6 o'clock, 4 o'clock, 2 o'clock, and 12 o'clock positions, respectively. The finger plates of the key levers have been placed in the modern positions for the left hand. A removable hand rest (clearly visible in the photo at right) has been added for the modern player accustomed to placing the right hand in the bell. Although he was an accomplished natural horn player, Sr. Bergonzi, probably gripped the corpus with his right hand leaving the bell open, since hand technique has little effect on the keyed notes. This is suggested in a letter Bergonzi submitted  on August 30, 1822 to the Imperial Royal Institute of Sciences, Letters and Arts of Milan to participate in the Institute's competition that year. In describing the innovations he has made to the ordinary hunting horn and listing the facilities it could offer instrumentalists, Bergonzi states specifically that one advantage is that the right hand in the bell is no longer necessary to produce the notes notes. 2

Bergonzi wrote out the fingering chart shown below as a Scala Cromatica por il Corno da Caccia colle Chiavi, ascending in sharps and descending in flats. At right is a modern transcription for the the reconstructed Corno da Caccia con Chiavi shown above. Bergonzi consistently designates notes probably played using the ring finger (G concert harmonic series) as 1 and those played with the index finger (A harmonics) as 3. (They have been reversed in the above figure to correspond to the modern convention.) Open notes (F series) are not always indicated in Bergonzi's Scala and several of the lower notes must be played by lipping down ("factitious" notes) to complete the scale. Interestingly notes fingered with a given key are not always playable in tune an octave higher as they are on a valved horn. For example one might expect that pitches sounding in half step increments above open notes would always be played as 4, 3, 2, 1 which is true in the first three octaves where the harmonics are widely spaced. Above the eighth harmonic (written third-space C), however, the second key (G#) provides better half-step intervals than the fourth key between the open harmonics. This is shown in Bergonzi's Scala and in practice on the reconstructed horn (see also the fingering chart on the right).



(click for a larger printable image)
* Fingerings in parentheses not indicated in Bergonzi's finger chart.
** Bergonzi consistenly designates notes probably played using the ring finger as 1 and those played with the index finger as 3.
*** factitious notes must be lipped down


James Hampson
Play the video to hear the talented Boston free-lance horn player James Hampson play an excerpt from Bergonzi's Capricci  on  the reconstructed corno da caccia con chiavi.
The Trombini
In his description of the corno da caccia con chiavi, Bergonzi mentions the addition of trombini to the key holes to enhance the sound and make it more like the true horn tone coming from he bell of the horn. These are understood to mean small bell-shaped cones perhaps similar to the one shown below. (Note that the actual key has been removed only to illustrate how the trombino might have appeared. Imagine what four of them would have looked like!) The sound is not changed appreciably on the reconstructed model horn and the problem of how to configure the lever and key inside the trombino has not been pursued.


Benedetto Bergonzi (1790 - 1839) was born on February 28, 1790 in Cremona, Italy into the family of of great violin makers. His father was Nicola Bergonzi, a professional merchant, who was the eldest son of Zozimus and the grandson of Carlo Bergonzi, who had apprenticed in the workshop of Girolamo Amati, and later in those of Guiseppe Guarneri and Antonio Stradivari. Benedetto was a registered shopkeeper, but also an accomplished horn player. After his educational years he studied the horn with Luigi Belloli.3 

Bergonzi's innovation of 1822 consisted of adding keys similar to those already in use on keyed trumpets, cornets, and bugles.4

Gabriele Rocchetti has written the following summary of his excellent article about Bergonzi published in Recercare  in 1990:

Benedetto Bergonzi: hornplayer, composer and inventor from Cremona

    Until now the scant and nebulous information we have had concerning Benedetto Bergonzi has made it impossible  to make a proper assessment of this versatile figure.
    Bergonzi was born into the celebrated Bergonzi family of luthiers, and though he was principally a merchant, he also seems to have been an accomplished instrument reparier.
    After his schooling he studied the corno da caccia in Milan with one of the most famous Italian instrumentalists, Luigi Belloi, and on his return to Cremona was offered the position of first horn in the orchestra of the Teatro della Concordia (today called the Teatro Ponchielli) along with his brother Antonio. He was a member of the Societ? filarmonica of Cremona and contributed to its activities as a composer and performer. He also performed in Tuscany, Piedmont, France, Germany and Austria (where gave a concert in teh Karntnerthortheatre in Vienna).
    Hw wrote a number of compositions for the horn, variations for the piano, symphonies and two operas: Bianca (never performed) and Malek-Adel, which was staged fairly successfully at the Teatro della Concordia in 1853.
    To improve the natural horn then in use, Bergonzi applied keys similar to those used on other brass instruments (bugles and trumpets) in order to obtain a chromatic range. The corno da caccia was in fact only capable of producing the sounds of the natural series of harmonics, in addition to a few notes that were obtainable by placing the hand inside the bell or by relaxing the tension of he lip muscles (a technique called "falsetto"). However this keyed corno da caccia, producing a chromatic scale throughout  its range [see the scala, above) was different from other keyed instruments in one respect: its "trombini", which were kinds of small funnel to amplify the sound issuing from the four key holes and make it sound more like that coming out of the bell. Twice Bergonzi submitted his "new" instrument to competitions that were aimed at promoting national enterprise and organized by the Imperio Regio Instituto di scienze, lettere ed arti di Milano.
    In fact it was at the above institute, now called the Instituto lombardo -Accademia die scienze e lettere, that we came across the papers concerning Bergonzi. Among them, there were also two letters in which he applied  to take part in the competitions, various other documents  including a notarial act identifying the horn builder, a "fingering" chart [see above], two unpublished letters from Giovanni Simone Mayr and the report of the panel of judges; but what was not found was a drawing, giving an adequate ideal of the corno da caccia itself. After failing the test the firs time, the instrument was awarded a silver medal on 7 October 1824.
    Bergonzi died in Cremona on 29 September 1839. 






 
Acknowledgments
Special thanks to Gabriele Roccetti for permission to use illustrations and quotations from his article "Benedetto Bergonzi cornista, compositore e inventore cremonese (1790-1839)" published in Recercare, 1990.


Notes

1. The base horn was an "American Standard" model single F valved horn made by Cleveland Musical Instrument Co. which was founded in Euclid, Ohio in 1920 and purchased by H.N. White in 1925. After the valve set was removed four holes were drilled based upon measurements found in the fold-out appendix of The French Hron, by Reginald Morley-Pegge. The goal of the experiment has been to understand the principles of the keyed horn and get an idea of its sound quality. Two unsigned examples of keyed horns in B♭ both having three keys giving the pitches of D, E♭, and F are found in the collection of the Historisches Museum Basel (1980.2056, 1980.20570. Gabriele Rocchetti (1990, p. 157-158) is of the opinion that Bergonzi's horn had a central tuning slide and could by put into different base (open) keys using terminal crooks.
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2.  L?Imperiale Regio Istituto di scienze, lettere ed arti di Milano held biennial competitions with the aim of enhancing the domestic industries. This institution, now called L?Istituo lombardo. Accademia di scienze e lettere, is still active and has in its archives the correspondence regarding the ?corno da caccia con chiavi" designed by Bergonzi. That Bergonzi held the corpus of the horn with the right hand is also suggested in its name, corno da caccia since that was the practice with horns of the hunt. Two decades later, when valved horns were being developed in Italy, the valves were placed on the player's right next to the bell apparently to improve sound projection. See the horns by Daniel Meinl and  Ferdinando Roth.
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3. The great Italian virtuoso and composer, Luigi Belloli (1770 - 1817)   was born in Castelfranco (Bologna) on February 2, 1770, into a very musical family.  Two of his brothers were also horn players: Giuseppe (1775 - ?) and Agostino (1778 - 1839) who is remembered primarily for his etudes for horn. It has been supposed that Luigi was a student of the great Bohemian virtuoso, Giovanni Punto. From 1790 to 1802 Luigi Belloli was principal horn in the service of the Duke Ferdinand of Parma. It was while in Parma that Belloli married Teresa Paglia, who herself came from a family of horn players in that city.  Their two sons, Giovanni and Giacomo, both became horn players and studied at the conservatory in Milan.  In 1803, the year following the death of his patron, Duke Ferdinand of Parma, Luigi Belloli moved to Milan to become principal horn at Teatro alla Scala, In the summer of that year he composed two ballets for La Scala: Il Trionfo di Vitellio Massimo, and La Distruzione di Pompejano.  On April 23, 1808 Belloli was appointed professor of horn, trumpet, and trombone at the newly formed Milan Conservatory with an annual salary of 1400 lira.  While there he wrote a method for horn that he used in his teaching but which unfortunately has since been lost. According to the contemporary music writer Carlo Gervasoni he had a "very pure sound and brilliant execution." In addition to the several ballets that were performed at La Scala in his lifetime he also composed several pieces for horn including at least two concerti dedicated to his supposed student, the immensely talented Giovanni Puzzi.  Luigi Belloli's career was cut short prematurely and quite suddenly at the age of forty-seven on November 17, 1817 from an attack of apoplexy. At the time he was still actively engaged at the La Scala and as recently as September 27 had performed in a production of Felice Romani's Adele di Lusignano
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4. According to Reginald Morley-Pegge (The French Horn, p. 26):
The earliest attempt to make the horn chromatic by mechanical means appears to be that of a Bohemian named K?bel who, about 1760, invented an instrument he called Amor-Schall. Accounts of this instrument are lacking in precision, but it seems to have been a horn with two closed keys near the bell, so placed that one of them raised the pitch a semitone and the other a tone. Over the bell itself was a sort of pepper-pot lid the purpose of which, presumably, was to minimize as far as possible the disparity in tone colour between the bell notes and those obtained by means of the keys. this was not, of course, the first use of keys to cover side holes in lip-reed instruments, for the larger cornetti had been provided with them at least a century and a half earlier. 
This account (later repeated in Fitzpatrick, The Horn and Horn-Playing, p. 107) was based on an entry in Ernst Ludwig Gerber's Historisch Biographisches Lexikon der Tonkunstler (1790,  v. 1, column 742) regarding K?lbel who had been employed by the Imperial Court in St. Petersburg, Russia.  In 1995. however, pan and ink sketches were found that suggest the Amor-Schall was in fact a type of omnitonic horn with an early an valve mechanism  (see Tarr, 2003, pp.16-17).
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References
Baines, Anthony: Brass Instruments, Their History and Development. New York: Charles Scribner's Sons, 1976. ISBN 0684152290

Br?chle, Berhard, and Janetzky, Kurt: Kultergeschichte des Horns, Ein Bildbuch / A Pictorial History of the Horn. Tutzing: Hans Schneider, 1976 ISBN 3795201799

Fitzpatrick, Horace, The Horn and Horn-Playing and the Austro-Bohemian tradition from 1680 to 1830, London, Oxford University Press, 1970

Klaus, Sabine: "Jagd- und Waldh?rner in der Musikinstrumenten-Sammlung des Historischen Musems Basel", Jahresbericht 1999, Historisches Museum Basel, 2000

Morley-Pegge, Reginald: The French Horn. A Benn Study, Music, Instruments of the Orchestra. London: Ernest Benn Limited/New York, 1960.

Rocchetti, Gabriele: "Benedetto Bergonzi cornista, compositore e inventore cremonese (1790-1839)",  Recercare, v. 2, pp. 151-171,  Fondazione Italiana Per La Musica Antica (FIMA), Rome, 1990

Tarr,  Edward H., East Meets West: The Russian Trumpet Tradition from the Time of Peter the Great to the October Revolution, with a Lexicon of Trumpeters Active in Russia from the Seventeenth Century to the Twentieth, Pendragon Press, 2003

Waterhouse, William, The New Langwill Index of Wind Instrument Makers and Inventors, pub.Tony Bingham, London 1993


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