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The dimished 7 chord is a 'symmetrical' chord, made up of 4 notes, each a minor 3rd away from its neighbours: 1-b3-b5-6
It is used as a replacement for a dominant 7 chord a semitone below one of its notes, or to move between different chords.
Standard scale choice
Use the diminished scale! It alternates the intervals wholetone-semitone-wholetone-... for the whole octave: 1 2 b3 4 b5 #5 6 7
Notice that it is possible to build a major or a minor triad on every other note of this scale. It sounds good to build up lines from the arpeggios of these triads. Also notice that anything you play can be repeated exactly up a minor 3rd, and up another minor 3rd, and so on...
The four notes of any particular diminished chord can also be found within four different harmonic minor scales (1 2 b3 4 5 b6 7): the ones built (i) a semitone above the root of the chord, (ii) a major third above the root of the chord, (iii) a perfect fifth above the chord, and (iv) on the b7. The harmonic context will determine which of these sound good - not all of them will in every chord progression.