The Dominant-Diminished Scale,

The Diminished Scale is 4 pairs of notes one Whole Step apart. Each pair is one Half Step from the next pair.

or the Symmetrical Diminished Scale comprises of a series of Whole Steps with a Half Step between each Whole Step:

This unusual scale is made up of a Diminished 7th Chord with a 2nd Diminished Chord a Whole Step below the 1st. In this case, BbDim7 and AbDim7. The sum of these two chords shows the notes of the Bb7 chord with the non-chord tones including 3 altered tension tones from the standard Bb7 chord scale, and one consonant tension note. There are a number of symmetrical licks that work with this scale over this chord. By “symmetrical”, we mean that these licks can be moved up or down a minor 3rd and still work within the scale formula and therefore over the Bb7 chord.

Inversions

John Coltrane discovered the idea of putting pairs of descending whole steps in ascending order

Let’s try moving a Whole Step lick in minor 3rds. Here’s a descending Whole Step, followed by the next Whole Step above it: B–>A, and then C#–>B.

If we move this lick, with the same fingering, a minor 3rd down, it will continue
to work over the B7 chord. John Coltrane used this idea to create this
lick, but yielding altered tones 9, #9, #11, and 13. The altered notes make the chord sound restless and needing to resolve to it’s intended tonal center, an Eb chord.

Coltrane put these ascending pairs of descending whole steps in order by beginning with alternating Diminished Chord roots.

Where to use it

By using this Coltrane pattern, we create a line that emphisizes altered tensions over the B flat chord, adding dissonance to smooth the resolution to E flat.

This kind of altered sound causes the sound of unrest, and necessary resolution. Therefore, we don’t use it for longer vamps over the chord, just at the point in which the listener wants to hear the dissonance resolve to the intended target chord. In a blues, for example, this might be the 4th measure where the I chord will go to the IV chord. In this example, where Bb7 chord would go to E(or E7). To internalize this sound, practice the following melodic example. Then play it along with the backing track.

Symmetrical scale; same scale, different chords

Have you noticed something about the symmetrical part of the scale? If this inverted diminished scale, or the B, B, C#, D, E, F, G, A always has the same pattern, the Whole Step/Half Step pattern, then what’s to say that the B7 chord has to be what is played over? We can actually begin from G note and get the same interval structure(Whole/Half) in the scale. This means we could play this same lick over the G7 blues, resolving to C. 

The lick had started on the root of the B7 chord, but now that same note is the minor 3rd note of the G7 chord, and the other notes of the lick work behind the new tonality, as well. The consonant/dissonant notes will be on different beats, which is where you’ll want to use your ears to make sure that they sound good to you.

Any note in the scale that has a whole step preceding it can be the root of the dominant 7th chord. Try this same lick over the E7 chord. The first note will be a 5 note over the E7 chord, traveling to the Majjor 3rd of the chord. It will also end on the minor 7th note of the A7 chord at the end:

As you can tell, this same scale can be used over the dominant 7th root notes of the Bdim7 chord: B7, D7, F7(E7), Abb7(G7).

Notice that these notes all fit the chord changes, but they may or may not be the consonant good sounding notes. The D example ends on the b9 of the resolution chord. Again, use your ears to decide which notes you want to put on strong beats, at the end of the lick, at the beginning, etc.

Here’s a practice backing track at a slower tempo, in all 12 keys:

Here’s the faster track, all 12 keys: