I was researching techniques used in classical improvisation. And I keep coming across two terms. One is "Partimento". Which is an Italian method of improvising on a bass line. Another is "The Rule of Octaves" which is a way to harmonize bass lines.
If you look at the Partimento wiki you'll see it makes use of the Rule of the Octaves. Also I was reading on how the Bach family used bass lines for improvisation. And C.P.E Bach wrote a section about Rule of Octaves in his book "Essay on the True Art of Playing Keyboard Instruments".
But I know JS and C.P.E Bach were German and Partimento is an Italian method so I'm wondering if and how there is a connection with these two. Were the Bach family influenced by Partimento and was it the basis of their improvisation?