The instrument was made per this research:
http://www.geocities.com/emile_meuffels/history/piccolo.html
>>Besson also started to manufacture high F trumpets and high E-flat trumpets with a crook to D.12 From 1894 Alexander (Mainz, Germany) also made a high F trumpet, designed specially for the Second Brandenburg Concerto.
>>Adolf Scholz (1823-1884) from Breslau (Germany) played Bach’s trumpet parts from 1850 onwards. First on B-flat trumpet, later on piccolo flugelhorn in F (of unknown origin). He didn't get famous because he never played outside of Breslau.
http://www.npj.com/homepage/teritowe/jsbgm.html
Giacomo Meyerbeer's Letter to Adolphe Sax About the 2nd "Brandenburg" Concerto
http://books.google.com/books?id=gqZav_nOtQEC&pg=PA30&lpg=PA30&dq=bach+f+trumpet+in+the+2nd+brandenburg&source=web&ots=2XpZBLX6fH&sig=6Qy_vfRQJTLeUv1oFQOts8_yqVY
Page 30
http://www.amazon.com/Bach-Brandenburg-Concertos-Freiburg-Orchestra/dp/B00005NFZS
>>As an old (ex-)trumpet player, I always pay special attention to the second concerto. Several things caught my eye (ear?). The trumpet player is Friedemann Immer. I don't know much about him, but he did a good job. I have one other recording including him, a Musical Heritage B-minor mass. Amazon gives six CD search hits on him: another Brandenburg, two other CDs, and three "limited availability". Their DVD search give none. (Searching on "Actor"; it's set up for movies.) He is playing an unusual trumpet. It is probably in F, and has three or four "shortening holes"(also called note holes, under the right middle fingers and thumb; he never uses the middle finger, so I'm not sure about that one.). These occasionally show up on natural trumpets to bring certain notes closer to in-tune. I've never seen four. In a fair amount of hunting through resources I have not been able to find one even approximately like it. There is a well known engraving of Gottfried Reiche, Bach's Leipzig trumpeter, holding a coiled trumpet reported to be likely the one used in the second concerto. No note holes are evident. Any natural trumpet playing in the clarino register (the octave with a nearly complete diatonic scale) is physically demanding. F is a high trumpet to begin with, and the second Brandenburg goes one note over, to high G. Immer, no spring chicken, negotiates the concerto with no sign of strain or effort -- quite an accomplishment. Only a small minority of trumpeters can even play the piece. He (or maybe head fiddler von der Goltz) has chosen not to trill the Fs in the opening or closing figures, even though the echoing oboe does so. This is unique in my experience. (When trilling, Immer uses a jaw trill, instead of the more common tongue or even shake trill.)
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http://www.brass-forum.co.uk/cgi-bin/yabb2/YaBB.pl?action=print;num=1164528039
Eskdale George [Salisbury], 21.6.1897 in Tynemouth - 20.1.1960 London,
started playing cornet in the St. Hilda's Colliery Brass Band. From 1932 till his death he was solo trumpet in LSO. He recorded the Haydn concert, this was a great success. In October 1935 George Eskdale recorded the 2nd Brandenburg Concert using a trumpet in F, he was accompanied by the LSO.
George Eskdale was professor for trumpet at Royal Academy of music and the
Trinity Colleg of Music.
Source: Friedel Keim - Das große Buch der Trompete ISBN 3-7957-0530-4
It would have been the small model (F one tone higher than our standard Eb trumpets today.)
The Long F trumpet, a 4th lower than our standard Bb, was really the precursor to the standard Bb, and its general use in orchestras would have died out by the time Eskdale was recording.
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This Schoenberg work for trumpet in F is probably the one pitched an octave lower which is often used by many composers like Debussy in La Mer.
Nachtwandler (1901) for Soprano, Piccolo, Trumpet in F, Snare Drum, and Piano by Arnold Schoenberg. Pub. Belmont