Cm Bb Ab Bb Cm
Eb Bb F
If the tonic is
C, then analyze it in
i ♭VII ♭VI ♭VII i
♭III ♭VII IV
I used jazz style analysis and put flats before minor mode chord roots.
All the chords are diatonic to a
C minor key signature except the last one.
The chromatic alteration from the
C minor key signature in the last chord is a change of the tone
A is the sixth scale degree, the submediant, which is one of the modal scale degrees.
When you alter modal scale degree this way, especially when it results in major/minor/diminished triad quality changes swapping chords from the relative major/minor modes, you can call it mode mixture.
You could describe the
F chord, the
IV as "borrowed" from
C major. Technically that is the correct use of music theory terminology. But, you could also say that the
F chord shifts the music into the dorian mode (
C D E♭ F G A B♭ C).
The harmony of the quoted passage doesn't use tonic/dominant harmony. So rather than calling it functional harmony, and we certainly don't want to start talking about modulations and secondary dominants, because none of that style harmony is happening, we can say it's modal style harmony. In that case, personally, I think it's a little more helpful to call this mode mixture and mention dorian mode, rather than calling it borrowed harmony.
I think you can "test" the mode mixture/dorian idea. Just ad lib with the lower portion of a minor mode
C D E♭ F G and accompany with dorian chords
F. I think you get the "sound", the tonality, of this passage of the song. The actual vocal part of the song moves about that lower minor scale region then drops from
A natural for the "finally home" lyric, accompanied by the
F chord. Then it goes back to
Cm. That's dorian harmony.
The ending is interesting. If I hear it correctly it is
A♭ B♭ G♭ Ab+ C. That second to last chord is
A flat augmented. The chords are not entirely derived from a
C whole tone scale, but a whole tone feel is pretty strong. That doesn't really fit in with the mode mixture stuff, but the whole tone scale can lend a mystical quality and I imagine that fits the mood of overall piece.
The only remaining option that I know would be some form of "picardy", obviously not the classic picardy third, just a fun surprise expecting a minor chord and getting a major chord. But I find those two explanations kind of lazy.
The very last chord changes the tonic
Cm chord to
C major, and that would be the classic picardy third usage.
For the use of
F major rather than
Fm, I would not call it picardy third, but mode mixture.
I think there is a sort "surprise" element with mode mixture, although I tend to call it "colorful." The "surprise" comes from the
A having been flat at one point, but then a moment later becomes
A natural. A lot of people won't consciously recognize the music theory details, but their ears recognize something is going on. You can find this type of harmony in Renaissance music and styles that emulate Renaissance music.
I think a big part of the "mixing", the alteration of certain tones from a strict mode, was to avoid diminished intervals both harmonic and melodic. I don't see that was necessarily the case in this song, but it's something to be aware of. Notice how the chord roots in
Cm B♭ A♭ B♭ Cm move by steps rather than fourths and fifths? That's a common thing in modal harmony. Depending on where you do that in a mode, you can run into diminished intervals. When those diminished (or augmented) intervals are altered to keep everything perfect and major/minor intervals, the end result is mode mixing. For example, in
Dm C Bdim, drop the
B♭ to get
Dm C B♭ and now it's in
I don't mean to digress so far from the song, but I think this is an important part of the modal/mode mixture "trick." Mode mixture by diminished interval avoidance.
Of course that doesn't mean total avoidance. Symphony X introduced augmented intervals for the ending. You use a half diminished chord in your progression.
Another "trick" to point out in your progression is the
A♭ F movement. That is a chromatic mediant, which has some similarity to borrow chord harmony, another good way to get harmonic color.