Has any credible musicologist explained that the double variations in Bach's Partita 1 for solo violin are a variation on the entire harmonic progression from the last movement and not just the bass line in a published work that I can cite?
Bach himself commented on the Goldberg Variations that he didn't really enjoy writing variations "because the harmony never changes". Sorry, I don't have a reference but it's probably quoted one of the early biographies like Forkel or Spitta. So maybe there isn't much to be "discovered" or "explained" about your observation of the same fact in the Partita.– user19146Aug 31, 2017 at 0:41
I'm just looking for a "credible" source which I can cite on Wikipedia about this since on Wikipedia it claims the variation is only on the bass line and apparently unless something is said in a published work it's not "credible" on Wikipedia. I know there is a lot to explain about how Bach varied the harmonic progression and how he added non-harmonic notes since I myself can find a lot of nuance and deliberateness in how he did so, but I hope that indeed there isn't much to be discovered here and that there is a published work out there that explains these variations correctly.– user875469Aug 31, 2017 at 1:58
In the age of Figured Bass, the "bass line" is the harmonic progression. That's what makes it infeasible to accompany most Bach pieces with strummed chords since you would end up with an inordinate number of chord changes and a lot of somewhat unusual chords.
It's somewhat easy to overlook this in Bach's work since the bass line tends to end up much more sellable as melodic material on its own than with many other composers.
So your realization is not exactly sensational.
The figured bass may notate the harmonic progression but it in itself is not the harmonic progression until it is realized and notes are added in other voices. In Bach's doubles, the chords are exactly the same as the last movement except voiced differently. It's not just the bass line that is the same. You could have the same bass line and different chords. Sep 1, 2017 at 1:41
"You could have the same bass line and different chords": I'm not sure if it's just a language problem, but if the bass is figured, no, you couldn't. A figured bass (or basso continuo simple.wikipedia.org/wiki/Basso_continuo) does indeed unequivocally defines the harmony. Sep 6, 2017 at 12:51
If a bass line is not figured though, for example because it is not intended as an accompaniment for a keyboard instrument, then you're right, by it self it does not fully define harmony. But I think it is safe to assume that there is an implied harmony which is very much in the head of the baroque composer and it would be very unstylistic to use different harmonies for different variations. Sep 6, 2017 at 12:59