I'm a bit confused about what exactly defines a diminshed 6th scale- does it have to be built off of a major scale, or can I also get a diminished 6th scale by adding a flatted 6th to a minor scale? Thank you.
The Diminished 6th or 6th Diminished scale is a major scale with the addition of a flatted sixth scale degree. For example, a C diminished sixth scale would be
C D E F G Ab A B C
The minor scale already contains a lowered sixth, so a diminished 6th scale cannot be created that way.1
The scale and its uses are discussed in the article "Creating Lines with the 6th Diminished Scale" by Ivan Gygi for the website Jazz Guitar Today.
In short, the inclusion of the b6 allows for alternation between the M6 chord and the viio7 chord (or, as the article points out, V7b9).
Again, in the key of C
Scale: C D E F G Ab A B IM6: x x x x (CEGA) viio7: x x x x (BDFAb)
IanRing.com calls the scale the "Major Bebop" scale and adds that
Named the "Diminished Sixth" scale by esteemed Jazz educator Barry Harris, because it's a combination of the major scale with a diminished seventh on the II, and consequently on the IV, bVI, and VII as well. Forming tertiary chords from this scale unleashes excellent harmonic possibilities, and chord progressions that pivot smoothly into other keys.
1 However, adding a raised seventh to the relative natural minor scale would create a mode of the diminished 6th. For example,
A B C D E F G G# A is an A natural minor scale with an added G#, but uses the same pitches as the C diminished 6th scale.