When lines are moving at a harmonic level direction does seem to be the key factor. Lowered
^6 descending to
^5 and raised
^7 ascending to
^1. Those two lines can be extended back to the longer lines
^1 ♭^7 ♭^6 ^5 descending and
^5 ♮^6 ♮^7 ^1 ascending.
Movement using rhythmic subdivision of the harmony (diminution) will use the form of
^7 that match the harmony regardless of direction.
...from an aria in the Bach, Anna Magdalena notebook, in the final three bars, two scalar lines descend in the treble, the first time the harmony is dominant and so the descending line uses raised
^7, the line is sequenced, but the second iteration is subdominant harmony so the lowered
^7 are used. Notice the cross relationship of
D, it's natural in the descent of the scale to the dominant, but the harmony is not yet dominant, then it's raised when the harmony has become tonic/dominant and
D# ascends to the tonic. The bass when moving to the final cadence uses the lowered
^6 as an auxilliary to the dominant degree, but the chord is a subdominant
When viewing the harmonic level movement in that piece it's important to note the difference in treatment when the dominant is part of a half cadence versus the dominant moving to the tonic. Notice at the fermata the descending line in the treble, the chord is dominant, but the leading tone (
D#) does not ascend to the tonic, because it's a half cadence, it's ending on the domimant. In harmonic terms there isn't a leading tone ascent and so the line is "free" to move in any direction. In the next bar the
D# is part of a dominant chord moving in a deceptive progression and it ascends to the tonic. It ascends here, not because ascending lines in minor use raised tones, but because the essential harmonic movement of the progression is the leading tone to tonic.
...from the Bach's Two-Part Inventions, in the bass there is a descending line which is sequenced, on the first descent the harmony is not dominant and the lowered
^7 are used, in the second iteration the harmony is dominant and the raised
^7 are used - despite the line descending. The essential harmonic tones of the dominant chord are pointed out with blue arrows, the descending line uses the raised
^7 to match the dominant harmony, but it moves freely downward, because it is just decorative motion, diminution of the chord.
The is also an interesting occurrence of the augmented second in the third bar. That interval is supposedly avoided or filled in, but it seems to me there isn't a problem using it when the line is a decoration of a dominant chord, especially descending.
The end of bar 2 and all of bar 3 are an elaboration of the dominant chord. Within that dominant harmony there is lots of "freedom" or direction for the lines. When the movement is finally happening at a harmonic level, the lines follow the more obligatory directions: bar 3 to 4 treble
Bb C Bb Ab descending through dominant to mediant, bars 3 to 4 the bass
E♮ up to
F ascending to the tonic.
...from Bach's BWV 851, there is a nice example of a cross relationship with degree
^6. The middle of bar 13 moves through a dominant in a deceptive progression. The harmonic rhythm is fast so each tone moving to and from
^6 is real harmonic motion and all the expected directional tendencies are fulfilled.
^6 is natural as it ascends to a dominant harmony which in turn ascends to the tonic for form the deceptive progression. At the same time the bass from from the dominant to the
^6 degree, and because the
^6 at that point in the bass is not moving to a dominant or leading tone - but rather away - it is not raised. A beat later, in the treble, the
^6 appears again but as part of a subdominant harmony, it is not raised but is part of an auxilliary motion around
Notice the difference in treatment of raised
^7 in the ascent here
B♮ C♯ D where each tone is part of harmonic movements dominant to tonic, versus the example in the two-part invention where the movement is decorative within a single dominant chord and the line freely ascends and descends.
This the systematic treatment of
^7 in minor. The treatment is strongly directional when occurring at the harmonic level, but ascends/descends freely on the decorative/diminution level.