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The following is a variation with a chromatic passing note:
I V bVII VI
C G/B Bb Am
c b b flat a
r 1st r r
Because that Bb suggests F major, it may sound good to treat VI as a first inversion:
I V bVII IV
C G/B Bb F/A
c b b flat a
r 1st r 1st
Here's an extended variation:
I V bVII IV bVI
C G/B Bb F/A Ab
c b b flat a a flat
r 1st r 1st r
Sometimes we can treat that the note Bb as a 1st inversion:
I V Vm V
C G/B Gm/Bb F/A
c b b flat a
r 1st r 1st
Here's an avant-garde harmony for this chromatic line:
I VIImaj bVII VI bVI
C B Bb Am Ab
c b b flat a a flat
rr rrr
Here's a static harmonization using the inversions of the major seventh and dominant seventh chords:
I Imaj7 I7 VI (or IV)
C Cmaj7/B C7/Bb Am (or F/A)
c b b flat a
r 3rd 3rd r
In the bridge of 'The Long And Winding Road', we find this: