This third page of the Diminished Scale mini-series covers

• Rationalization of the white-key tonic diminished scales;
• Whole-tone/semitone diminished scales starting on the black keys.
  

Rationalizing the white-key-tonic diminished scales

You've now built up whole-step/half-step diminished chords on all the white keys.

Because the diminished scale is built on the diminished chord tones, which are a minor third apart, the diminished scale built on D, for example, uses exactly the same notes as a diminished scale built on F (a minor third above) and B (a minor third below).

The same is true for C and A:

…and for E and G:

That duplication means that white-key diminished scales starting on C, D and E cover all the white key tonics.

Identify the white-key tonics C to B in the diagrams above. What fingering rules, if any, can you draw?

Diminished Scales - Black-key tonics

The white-key diminished scales you're now familiar with also provide whole-step/half-step diminished scales starting on any black key diminished chord tone. Just step down or up in minor thirds (three semitones) to the next white key, and there is the white key tonic which gives the scale-tones and the fingering.

Again, diminished scales built on white keys C, D and E cover all five possible black key tonics. Here's the C-D-E diagram again with the black-key diminished scales they generate marked.

Your practice building whole-step/half-step diminished scales on all the white-key tonics means you can start from ground zero and work out the whole-tone/semitone steps, using the fingering of the 'parent' white-tonic scale. (Two 1-2-3 plus one 1-2 fingering groups will always somehow finger the eight diminished scale tones.)

Or your 'feel' for the whole-step/half-step diminished scale might just kick in and give you the scale you want.

The example keyboards shown below are fingered for continuing up or down; you might well substitute convenience fingers at either end.

The notes of the D sharp/E flat and F sharp/G flat (tonic) scales are the same, since the tonics are a minor third apart:

The same is true for the A sharp/B flat and C sharp/D flat scales:

The G sharp/A flat diminished scale is one-of-a-kind, though:

You can download the MS for these five Black-key-tonic Diminished Scales here.

The demonstration video shows the whole-step/half-step diminished scale built on the five black keys ascending from D sharp/E flat.

Stripping out the duplicates, you will cover all five black-key tonics if you practice from just the group-of-three black keys.

Add to these your three white-key-tonic diminished scales and you have the basis for an effective practice strategy.

Now go on to Page Four of this series, and practice some patterns made of segments of the diminished scales. These patterns, and the fingering challenges they present, are typical of practical music-making and improvisation.