Mirror chords theory

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 ?

• In both examples, it is as if there is a mirror extending vertically from the center of the Ab in between the chords. The other note on a keyboard with this type of visual symmetry is D. Commented Mar 10, 2018 at 14:24
• Commented Mar 10, 2018 at 19:21

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 `G`" to `D`.

(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 `C` and `G`. To find the axis of symmetry, we look for a descending perfect fifth in the mirror chord: that between `E` and `A`. Now we have to find how `C` inverts to `E` and how `G` inverts to `A`.

Basically, we can just split the difference: find the spot halfway between `C` and `E` (`D`) and connect that to the spot halfway between `G` and `A` (`A♭`):

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 `G`, `E` inverts to `C`, `B` inverts to `F`, and `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.