Irregular resolution

Regarding the dominant seventh, there are many irregular resolutions including to a chord with which it has tones in common or if the parts move only a whole or half step.

[2] Consecutive fifths and octaves, augmented intervals, and false relations should still be avoided.

All three types describe a process of transforming a dominant seventh chord to a diminished seventh by raising the root by one semitone, then picking any other note in the chord and lowering it one semitone.

This works because diminished seventh chords are structurally equivalent in all of their inversions (a stack of minor thirds), so any note in a diminished seventh chord can be seen as the root note.

The most important irregular resolution is the deceptive cadence,[3] most commonly V7–vi in major or V7–VI in minor.

Irregular resolution Type I Play ⓘ . Two common tones, two note moves by half step motion.
Irregular resolution through augmented sixth equivalence Play ⓘ . [ 1 ] One common tone, three notes move by half step motion.
Regular resolution Play ⓘ . One common tone, two notes moves by half step motion, and one note moves by whole step motion.