What's the deal with these trills?

[persona]

I came acros two different editions of Bach's Two Part Inventions, both of them claiming that, when playing trills, the lower note should be played first and the upper one after it (the example in the image is from invention nº4 in d minor). I always thought that in baroque music, it was the opposite way (that the higher note should be played first). Are both ways acceptable or what?

[faulty_damper]

The musical context must be considered first.  Any "rules" you may have read came from observations of performances.

In this context, it is clear that the trill starts on the principle note because of what came before it - it is an extension of the motive.  Starting on the auxiliary would sound a bit funny.

[persona]

The thing is, I used to have a teacher how taught me this invention, and he told me to play the auxiliary note first that's why I don't get it.

The reason I'm asking this is because I'm trying to learn two part invention nº15 right now, and I'm not sure how to play the trills on the eighth notes. Some editions say it should be auxiliary - principal - auxiliary - principal, while others say it should be principal - auxiliary - principal. (In some cases, the fingering actually differs if you want to play one or the other).

[thalberg]

In Baroque times, ornaments were done a variety of ways.  People have made efforts to codify them, but there's a lot of variation.

A famous teacher once told me, "no matter what a book says, we don't really know for certain what the composer would have done.  Therefore, you have to follow your ear."

Baroque trills most often start on the upper note, but they can start on the principal note.  I have a Martha Argerich recording where several of her trills start on the principal note.  Even in places where it could easily sound good either way.

[faulty_damper]

Many times, teachers will default to instructing students from a theoretical point of view while completely ignoring the musical context.  This seems to be the case with your previous teacher.

From my own experience, I once had a teacher, a self-proclaimed authority on Bach's music, tell me to start a trill on the auxiliary note in a fugue by Bach.  (WTC fugue in B Minor.)  He even lent me a copy of CPE Bach's book so I can read for myself that it should begin on the auxiliary.  Many performers, in recordings, do start the trill on the auxiliary note.  However, it is obvious that in all instances it sounds extremely bad especially compared with the alternative.  He became upset and even yelled at me because I simply refused to do it.  "I have ears" I told him.

In this context (WTC fugue in B Minor), starting the trill on the principle note makes clear that it is simply an appogiatura extended by a trill.  Starting on the auxiliary would disrupt the principle motive of the subject and you would end up with both a false harmony (not a dominant resolving to tonic) and a descending third which implies no harmonic movement on a cadence which simply sounds bad.

Use your ears during the preparation, execution, and resolution of the trill to figure out the best manner of performance.