While most diatonic chord progressions are based on the relations of the roots, some chromatic progressions can be thought as movements of voices.
1. If we have a minor triad in root position, and we move the 1st down and the 5th up by a semitone, then we get a minor triad in 6/3 position, and the root of the new chord is below the old one by a major third.
Let`s see an example in D minor. The chords are: Dm, Bbm, F#m, Dm. The semitone movements are repeated 3 times, to get back to Dm, because 3×4 = 12. I made two notations for the same sounds, and have to mention that these are only demonstrations, in a real composition the rule of smallest movement should be considered.
1.1. This notation makes the emphasis on the 6/3 position of the new chords, produced by the semitone steps.
1.2. The second notation emphasizes the common notes, which remain the same through the transitions.
1.3. You can listen to this progression by this mp3 file: p1.mp3
Or an example for the usage of this transition can be a composition of mine: “Comfortable darkness”
2. We can do the same with major chords, although the result will be different. The resulting chord remains major, but gets into 6/4 position, and its root is higher by a major third.
Here is an example in B major. The chords are: B, D#, G, B
2.1. Again, the first notation puts the emphasis on the 6/4 position of the new chords.
2.2. The second notation emphasizes the unchanged notes.
2.3. You can listen to this progression by this mp3 file: p2.mp3