The diminished scale is composed of alternating intervals of whole and half steps. The scale can either start with a half step or a whole step (depending on the chord it is being applied to). So, the interval pattern used to compose a diminished scale is either W-H-W-H-W-H or H-W-H-W-H-W.
Since the diminished scale is based on an alternating whole step / half step pattern, there are only 3 diminished scales to learn. Tonics that are a minor third apart share the same diminished scale. The tonics of C, Eb, Gb, and A share the same diminished scale, and they can be thought of a group 1 of the diminished scales. The next group of tonics that share the same diminished scale are C#, E, G and Bb (group 2). The final group (group 3) is composed of the tonics D, F, Ab and B. Included in the video are slides in which the scales of each of these groups are written out (in both whole/half and half/whole form). Practicing these scales in light of the three groups will aid in both understanding and memorization.
Certain harmonies lend themselves to the use of the diminished scale in musical improvisation. In addition, certain forms of the scale (whole/half or half/whole) are more appropriate depending on the harmony being improvised over. When improvising over major triads and dominant 7b9 chords; the half/whole diminished scale that shares the tonic of the current chord can be used. When improvising over minor triads, minor 7th chords and diminished 7th chords (fully diminished 7th); the whole/half diminished scale that shares the tonic of the current chord can be used. The tasteful use of these scales, in combination with the other scales we have studies, helps to provide a broader musical pallet for improvisation. This leads to the creation of more interesting and varied melodies.