Mirror Scales

Carson Farley

In a recent Youtube podcast by musician/composer/author Rick Beato (from the New England Conservatory of Music), mirror image scales were discussed:

C  D     E     F  G  A   B   C

C   Bb  Ab  G  F  Eb Db C

Obviously just an exact inversion, a reordered Ab major scale, a phrygian mode in retrograde.  Since the scales have the same interval content obviously a functional compositional relationship between C major and Ab major and the modal variants exists.  Although I am actively examining these relationships I would appreciate any feedback or comments on the mirror scale's properties or usage.  Thanks

Marcel de Velde

For what it's worth.. I think a more musical mirror relationship is made by mirroring using not a single note as the basis but instead use the interval of the fifth as the basis of the mirroring.

So C major scale C D E F G A B C would be mirrored along C-G which gives C natural minor C D Eb F G Ab Bb C.

Keith Salley

Yes, this is something I touch upon in an article I published in the Journal of Jazz Studies in 2012. There, I'm discussing a jazz tune (or two?) that symmetrically spell out ordered step collections in Bb and Gb major. At the time I was writing the article, I remember fleshing out this idea more, but that was side work that didn't go into the publication. 

If you take any rotation/mode of a major scale and run its pattern of Ws and Hs in reverse (starting from the same note), you'll produce another diatonic collection at some even-numbered level of transposition. 

Flipping the step collection around the tonic, as you do in your prompt above, produces a T8-related collection. 

Flipping around the supertonic produces the same collection, because Dorian is symmetrical.

Flipping around the mediant produces a T4-related collection—essentially the reverse of flipping around C in your prompt above. Since the Dorian/supertonic flip turns out a T0 relationship, you'll have T4 and T8 on either side, naturally.

Flipping around the subdominant yeilds T6-related collections.

T10 around the dominant and T2 submediant. Either of these is as close as you'll get to the other side of the axis of symmetry that extends from the Dorian flip.

Finally, T6 around the leading tone. 

Outside of the relationship I mention in JJS, I recall a Chopin piece—a Mazurka, I think—in one of the previous editions of the Burkhart Anthology (also involving Bb and Gb). If I were in my office, I'd look it up for you. . . The curious thing was how Chopin's melody hits upon E natural, which is the silent partner on the axis of symmetry extending from the global tonic Bb, and the only pitch class that is chromatic to both Bb and Gb diatonic collections. A similar thing happens in Brubeck's In Your Own Sweet Way, but of course Brubeck didn't actually play the E natural (Miles, and virtually everyone else who played the tune did afterward, though). 

I suppose one next step in research would be to investigate common tones (and not-common tones, such as those E naturals) between mirror-related collections. In all cases but the T6-related mirror step collections, the other end of the axis of symmetry will be chromatic to both collections. 

Have fun!

Carson Farley

Thanks Marcel, yes that is where I was heading next and that immediately occurred to me.  I appreciate your sugggestion.  

Carson Farley

Wonderful Keith!  Thankyou.  Transpositional relationships, makes perfect sense and thank you for the clarification, focus, and examples.  

Marcel de Velde

edited. nevermind sorry.