I was checking a video about this subject and came across a question: when I have a lower chord like C2 G Bb D and as mirror D F# A E what determines that the mirror chord starts in D when the next example is A1 E B C and as mirror we have E F C G ?
The notion of "mirrored chords" is based around an earlier notion of an axis of symmetry. When we have a pitch (or pitches), we find its mirror image around a given axis of symmetry to find the resultant pitch.
Take, for instance, a
C. If our axis of symmetry is the
G above it, we see that our
C is a perfect fifth below the axis. Therefore, its mirror image would be a perfect fifth above
G, which would be a
D. We say that
C "inverts around
(There's a distinction here between pitch inversion and pitch-class inversion, but that's for another time.)
An easy way to determine these inversions/mirror chords is with the twelve pitch classes arranged in a clock:
Now, we look for a mirrored interval. In your original example of
C G Bf D, we see an ascending perfect fifth between
G. To find the axis of symmetry, we look for a descending perfect fifth in the mirror chord: that between
A. Now we have to find how
C inverts to
E and how
G inverts to
Basically, we can just split the difference: find the spot halfway between
D) and connect that to the spot halfway between
From this, we see that the axis of symmetry is D/A♭.
Now we can doublecheck your second example of
A E B C.
A inverts to
E inverts to
B inverts to
C inverts to
E, which gives your collection of
E F C G.
Note that not all "mirror chords" use this pitch axis; different pieces use different axes based on various compositional decisions.