If you'd like to read an elaborate version of this introduction ('Towards a different, possibly more historical view of Bachs' Violoncello'), click here. The sheet music mentioned in this text can be downloaded below (not in the text).
Modern opinions about Bach's Violoncello & Violone and some striking historical data.
by Lambert Smit.

To my best knowledge the research that I started in january 1999 was the first attempt to establish the identity of Bach’s Violoncello
in close connection with the identity of his Violone.

In recent times small ‘da braccio’ bass instruments were made by Rudolf Eras (who before 1970 made instruments for Christoph Aißlinger and Andreas Gilly, two former students of Ulrich Koch), John Ferwerda (1984), Samuel Peguiron (who before 2002 made an instrument for Jean François Schmidlet), Dirk Jacob Hamoen (2000), Hendrik Woldring (2001), Dmitry Badiarov (several instruments, the first in the spring of 2004) and Chaim Achttienribbe (2006); my hypothesis can be realized in living sound.
Dmitry Badiarov made several instruments for himself and several musicians, among them Sigiswald Kuijken, Ryo Terakado, Samantha Montgomery.
Especially Sigiswald Kuijken propagates the use of his small Hoffmann inspired copy by playing Bach’s cello suites and Bach’s obbligato-parts for Violoncello piccolo in cantatas.
Dmitry also plays
Violoncello piccolo obbligato-parts with the Bach Collegium Japan and all Bach’s cello suites in concerts and CD-recordings. See website of the Bach Collegium Japan and Dmitry Badiarov’s website: dmitrybadiarov.com.

6 May 1999 in the Dutch radioprogram ‘praatpaal’ I expressed my hypothesis that Bach wrote BWV 1007-1012 for a shoulder held cello instrument, the
Viola da spalla of the German lexica of Bach’s day.
Later, however, I wanted to avoid the modifier da spalla for instruments that are so small that putting them
‘on top of the right shoulder’ would make the bowing action nearly impossible (see ‘4-string violone da brazzo’ in this website).

Authors who wrote and write on the identity of Bach’s
Violoncello are:
Heinrich Husmann, Ulrich Drüner, Mark Smith (in Bach-Jahrbuch 1936, 1987 and 1998),
Dmitry Badiarov (dmitrybadiarov.com),
Laurence Dreyfus (Bach’s Continuo Group, 1987);
Gregory Barnett (JAMIS 1998) discussed the Shoulder cello;
David Chapman (GSJ, June 2003) discussed the Violone/double bass.

My research is based mainly on Bach’s treatment of
Violone, Violoncello and Basso Continuo.

The very first composition in which Bach prescribes a
Violoncello is cantata 71, 'Gott ist mein König', performed 4 february 1708 in Mühlhausen. This Violoncello music calls for an instrument tuned G-d-a-e* small enough to be played with diatonic violin fingering.
This part is unique, and quite exceptional, in that its range is from G to e flat*; wherever the
basso continuo in the other bass voices go lower than the G, the Violoncello plays those notes one octave higher.

The great Bach specialist Alfred Dürr (p. 797 in
'Die Kantaten') stated: 'Bach evidently had at his disposal an instrument with the lowest string, tuned G' and Christine Fröde who edited this work in the NBA says in her preface: ’With respect to the Violoncello, which serves as a bass instrument of the flute choir, it seems evident that a smaller instrument tuned G d a e1 was used, because the cello part goes up to e flat 2 and pitches below G are avoided.’ (Neue Bach Ausgabe, Serie I, Band 32, 1, p. VI)
If a small instrument like this is held like a violin, the notes, particularly in the 6th movement, suggest very obvious fingerings.
13 March 1708: Bach's relative, Johann Gottfried Walther, court musician in Weimar (where in July of that same year, 1708, Bach was to become court musician and organist) defines the Violoncello of Bach's days and surroundings unequivocally:
’The Violoncello is an Italian bass instrument resembling a Viol; it is played like a violin, i.e. it is partly supported by the left hand and the strings are stopped by the fingers of the left hand, partly however, owing to its weight, it is attached to the button of the frockcoat [...] It is tuned like a Viola’. (Praecepta der Musicalischen Composition in Jenaer Beiträge zur Musikforschung, Band 2, ed. Peter Benary, Leipzig 1955, p 161)
NB: We can take it for granted that the
Violoncello, as a bass instrument, was tuned C-G-d-a, one octave lower than a Viola.
The Violoncello in Bach’s cantata 71 differs from our normal or ‘baroque’ cello.

* If it is true that Bach’s works (other than BWV 71) ask for a Violoncello that was a relatively small ’horizontally’ held cello - as all German documents from 13 March 1708 (Walther) to 1758 (Adlung) seem to suggest -, then it seems logical that Violone was a fitting term for the instrument next in size, namely a C-G-d-a cello which was too big to be played in the ‘horizontal’ position of a Viola da spalla and therefore would have to be held vertically. Several sources support my hypothesis, while there is little compelling evidence to exclude it.
For example, the Vocabulario degli Accademici della Crusca (1729) states:
‘Violone: low-sounding stringed instrument, also called Basso di Viola, and if it is of a smaller size, Violoncello’ (‘Violone: Viola di tuono grave, che si dice anche Basso di Viola, e Violoncello, quando e di minor grandezza’. See Grove s.v. Violone.)
and Hawkins:
’Violone [...]it seems that this appellation was formerly given to that instrument which we now call the Violoncello.’ (J. Hawkins, A General History of the Science and Practice of Music (1776: repr. of 1853 edn New York, 1963), 603.