&dAInv. 2, BWV 773, l.h.

t~ = LONG TRILL, m. 12: 
    Bach notates long trills in the same way as the trill we encode 
as "w", but with more squiggles. I have transcribed this into a 
more modern notation, "tr" followed by a wavy line. (Note that a 
simple wavy line is said by Neumann, p. 314, to be Bach's notation 
for instrumental or vocal vibrato.)  
    The mark in m. 12 bears a pronounced upward stroke at its head, 
though (contrary to BG's reading) not the full curve of Bach's 
"Doppelt-Cadence". Possibly it signifies an "Accent und Trillo" 
(compound appogiatura and trill), but more likely this is just an 
exaggeration of Bach's usual tendency to start his trill symbols 
with a downward motion of the pen. 
    Following Neumann, p. 315-316, one might consider beginning 
this trill on an anticipatory upper grace note, before the beat, to 
avoid parallel fifths with the Ef5-F5 in the right hand. Note that 
this Invention contains numerous trills -- m. 3, r.h.; m. 13, l.h.; 
m. 23, l.h.; m. 25, r.h. -- which, if begun with an on-beat upper 
auxiliary in the conventional way, would create noticeable parallel 
unisons, fifths, or octaves. Neumann gives several alternatives 
for realizing these trills, p. 316.