Trio Sonata in C minor, BWV 526 - Largo by J.S. Bach

ABF♯
FCGDAEBF♯
A♭E♭B♭FCGDAE
D♭A♭E♭B♭FC

(Rerecorded with an odd stop in May 2020.)

A problematic point in this piece is measure 18:

Measure 18

The combined notes in the red box are:

C
E♭B♭F C
E♭B♭
(1)(2) (3) (4)(5)(6) (7)
When I first worked on the piece, the optimizer would simply minimize the number of syntonic commas, using the notes in columns (2) u/i (5) above, tolerating that the minor third C-E♭ gets the non-ideal pitch ratio 32/27. That makes measure 18 sound as follows:

(minor third C-E♭ has pitch ratio 32/27)

Because I did not like the 32/27 minor third, I changed the notes a bit: I cut the C note (in the red box) in half, so the second chord only contains the notes B♭ and F. That gives a peculiar phrasing at that point and to obscure that, I applied similar phrasing to similar melody fragments nearby. That is what you can hear in the full version above.

In February 2019 a new score annotation type was added to the software allowing me to indicate in the score that a minor third on a particular note should definitely have a pitch ratio 6/5. In this case that would be the note C, so the minor third C-E♭ gets a pitch ratio 6/5. That forces the optimizer to use the notes in columns (1) u/i (5) above. But then we get a syntonic comma between the C notes in columns (1) and (5), making measure 18 sound as follows:

(mid air syntonic comma on C as a tone repeat)

(mid air syntonic comma on C as a 2 msec pitch slide)

When I had added this analysis (September 2019), I thought I might once get used to this pitch slide solution.

(There is yet another solution - not elaborated here - that uses the notes in columns (3) u/i (7), which produces a syntonic comma between the B♭ notes in columns (3) and (7).)

The following version is in a twelve tone unequal temperament, so you can compare.

(Kellner tuning)

Trouble grasping the difference with just intonation? The fragments on the home page may help.