The symmetrical diminished or octa-tonic scale consists of a series of half-steps and whole-steps (or whole and half, depending on when it is started). This organization also generates sets of triads, each a minor third apart. In addition, those triads may be either major or minor. Many jazz phrases utilize a symmetrical relationship of these triads, using either minor or major triads. This is convenient because it creates patterns that repeat very frequently and the strength of using the same triad-type gives the line a sense of cohesion. However, more interesting shapes can be made from combining triads of different modes.
I have recently begun focusing my practice on combining a major triad with a minor triad a minor third above the root of the major triad. For instance, combining a C Major and Eb Minor triad generates these tones: C, Eb, E, Gb, G, Bb. When each of these triads are alternated in arpeggiation very interesting melodic shapes appear. In addition, since these conveniently create sets of three note, interesting rhythm shapes can be implied.
Try experimenting with these shapes and see how they impact your improvising.
Best,
Lynn