When I first read the term "chromatic minor" in the question title I was dismissive of the idea. Then I read the textbook description in Stephenson's What to Listen for in Rock and I realized it's a good description of rock harmony.
I don't think this tonality is as strange as the other answers and comments suggest.
First. let's recognize chromatic minor is a description of classic rock, a musical style most people are familiar with. If you are familiar with the sound of The Rolling Stones, The Who, etc., this tonality should not sound bizarre. So, let's reserve judgement and compare with common practice harmony and see what we get.
There are 9 chords in chromatic minor. The chords of the tonic and supertonic each have two variable forms so we get 4 chords from those scale degrees, then single chords for the other scale degrees give us the remaining 5 chords.
For the purposes of this comparison I will consider the
V chord - the major triad with a raised leading tone - a diatonic chord in minor key music. Technically it is chromatic, but in common practice minor key music the
V is an essential, primary chord, so I will consider it diatonic.
The five chromatic minor chords
bVII are diatonic minor key chords. The major triad
I can match up to a Picardy third final tonic chord in common practice, but that is not how the chord is used in chromatic minor, so this is a point of difference between the two systems. The two supertonic chords
N and major
II certainly are not diatonic, but they are common chromatic chords in minor key harmony. However, it needs to be pointed out that Stephenson uses the
II symbol specifically instead of the secondary dominant
V/V symbol to indicate the chord's identity in chromatic minor is not a secondary dominant. This is another difference between the two systems. Finally the major
IV can be found in minor key harmony, but in common practice the chord can frequently be a minor triad. The subdominant in chromatic minor is fixed but in common practice minor it is variable.
Of the 9 chromatic minor chords, only three -
IV - stand out as not aligning with common practice minor key harmony. In other words, if we eliminate only the
IV chords from chromatic minor, we could make common practice harmony with the remaining 6 chords
bVII. The main limitation is not having minor subdominant chord variants like
It was pointed out in another answer that chromatic minor uses all 12 chromatic tones. But this is in no way unique or strange compared to common practice minor. In common practice minor, scale degrees are altered all the time in normal harmony
^2 lowered for
^3 raised for
^4 raised for
V/V and _augmented 6th chords,
^6 raised for
^7 raised for major
V. Those alterations and the associated chords are normal in common practice minor, and they can be used without necessarily modulating to another key. When those alterations are all combined the complete chromatic scale is utilized. So, using all the chromatic tones is not a unique property of chromatic minor.
Also, regarding chromatic scale degrees, all scale degrees in chromatic minor exhibit alterations except the tonic
^1 and dominant
^5. Those are the two most important tonal degrees. This is another point of similarity between chromatic minor and common practice.
Now let's get to the question of root progressions.
I will limit my comparison to what I think are the commonest root progressions: descending (↓) 5th, ↓4th, ↓3rd, and ascending (↑) 2nd.
↓5th and ↓4th: except for the tritone interval between
bVI all these progression are diatonic.
i are diatonic, but all others are non-diatonic chromatic mediant progressions. Chromatic mediant chord pairs always share the same chord qualities so this is an important characteristic of chromatic minor. In common practice, ↓3rd progression result in a change of chord quality. This is probably the biggest difference in comparing the two systems.
↑2nd: this seems a bit trickier to compare, because in common practice root progression by seconds is more circumscribed that other movements. Chord need to be in first inversion or need to involve specific roots like
V to fit the common practice norms. Anyway, all the ↑2nd progressions in chromatic minor which move by whole step can be interpreted as
V, because there will be a hypothetical
I a perfect 5th below the
V, the exception is
II. The half step ascents in chromatic minor are not diatonic except
It's hard to quantify how much overlap exists between chromatic minor and common practice minor, but I think I have presented a substantial amount of overlap. If the tonic chord is minor
i you could have a lot of chromatic minor progressions that match pretty closely to common practice. In fact I think the bigger difference is voice leading. Rock uses mostly root position chords while common practice has a strict system of counterpoint norms.
Stephenson describes chromatic minor as "consisten use of a particular triad [chord] type... at the expense of scale purity." There is another super common tonality which does the same: the blues. The blues uses all dominant seventh chord on roots
^5, and while the triad portions of those chords are diatonic the sevenths are not. All the chord qualities are the same but the sevenths break the "scale purity." If we recognize the blues works with a "chord type versus scale purity" concept, then by comparison chromatic minor may seem less strange. This has no bearing on a comparison to common practice, but it's interesting food for thought.
I think the biggest difference between chromatic minor and common practice minor is the ↓3rd chromatic mediant progressions. Those really run contrary to common practice harmony. The other critical differences are the fixed quality of the subdominant and the use of a major
I tonic. Otherwise, many chromatic minor progressions can be similar to common practice progressions.