Although I have offered no phrasing, articulation, pedal, or tempo indications, many of these ideas are implied by the sheer notation. For example, the solitary sixteenth notes on beats one and three of measure 1 in the secondo part of Invention No. 2, “Con Salsa,” should be played staccato. The syncopated dotted-eighth-note chords after beats two and four of measure 3 of Invention No. 5, “Just Hanging Out,” should be accented.
Regarding tempo, performers are encouraged to follow their own intuitions and come up with their own speed. I think, for example, that Invention No. 11 can sound beautiful at ♩= 50 but also at ♩ = 72. The accompaniments can work at either tempo and phrasing and touch may change according to the speed. There are always many different, equally legitimate ways to interpret a piece!
Use of the damper pedal should be evident, as in the last bar of the alternate endings to Invention No. 2 and No. 8 where there is an arpeggiated flourish.
It may come as a surprise to some classical pianists that “swing” in jazz does not necessarily require the conversion of straight sixteenths or eighths to triplets, certainly not in these arrangements. Charlie Parker, Miles Davis and all other great jazz soloists would play “straight” lines as often or more often than tripletized ones. Sometimes there would be a subtle “laying back” or syncopated accentuation but not always.
There also may be a certain shift in articulation and touch but not necessarily so. Robert Donington’s description of the Baroque sound — “clear and incisive timbres” over “thick and heavy timbres” (p. 37, A Performer’s Guide to Baroque Music, New York: Charles Scribner’s Sons, 1973) — could just as easily describe an appropriate jazz sound — but not always: tenor saxophonist Coleman Hawkins had a breathy, vibrato-laden sound that contrasted sharply with Lester Young’s smooth and direct approach. Bessie Smith’s thick and luxurious voice, as demonstrated in “St. Louis Blues” (1929), is miles away from the clear and nimble sounds that came out of Mel Tormé’s mouth, as in his version of “Route 66” (1964), but they both belong to the jazz tradition.
And, as in the Baroque era, different keyboards are possible for these duets. What if one pianist played the Invention on a Kawai baby grand while the second pianist played the jazzed- up accompaniment on a Yamaha electronic keyboard? Bach himself was open-minded when it came to the keyboards of his day — harpsichord, organ, or clavichord — and he even seemed to embrace the fortepiano late in his life. If Bach was amenable to different sounds (converting a violin concerto to a harpsichord concerto, playing a prelude once on the organ and then on the clavichord), shouldn’t present-day performers also be creative and sonically free-thinking?
Finally, and obviously, pianists should feel free to change or add notes if the fancy strikes. Bar 34 of Invention No. 9, for example (one of many!), may very well accommodate extra notes, whether a chord, arpeggio, or added riff — or all of the above. Make the Urtext your text!