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This has to be in D? major. The chord progression V/ii - iii - IV - I - IV/IV - vi - V/V/vi (or V/iii) - V/vi makes a lot more sense. When all but only two of the chords are borrowed, the key is probably not right.
I tried to type the symbol, but it shows as a question mark, I meant D flat major.
Yeah, something was offputting about it to me as well. There is little doubt that Bb is the tonal center though - Try listening to the last measure and then the first beat of the next, and then stopping it. It's a bit of a fanfare overlaying a cadence, that really solidifies the tonic despite the Bb is also first note of the melody. I do think you've indicated the right signature, as this in Bb minor (a relative key of Db major) is recognizable as a minor progression but with an authentic cadence. That is, when treating the Abmaj6 as VII, in the 2nd bar (incorrectly transcribed as Fm originally - There is a noticeable Eb, at 311 Hz, matching the bass rhythm. While it could be a harmonic of the bass it is several levels more intense than any other harmonics in the mid range, and in every other measure it is a chord tone.)
Even though most of the chords are borrowed from Bb minor, the song is still in Bb major, because there's never a Bb minor chord in the progression. The bII is called a Neapolitan chord, which is diatonic in the Phrygian mode, Locrian mode, and Neapolitan scales.
@retroboy The Bb minor is sitting right there in the sixth measure, I'm not sure how you are missing it. And you are right IIb (Cb major) is the neapolitan chord which is here used in place of the diatonic ii dim (C dim).
Oops, I guess what I meant to say was that the Bb minor chord is never really tonicized like the Bb Major chord is. I guess this progression could be viewed as a Bb Major progression with only borrowed chords except V, or a Bb minor progression that starts on a Major I chord.
Darkjoy [Verse rev 7]
Just edited the ending and some of the Melodyparts which were in the wrong length.
@kamyarkaviani You said: "When all but only two of the chords are borrowed, the key is probably not right." but that's not right. Abmaj6, Gb, Db and Bbm all fit into the diatonic triads in the key of Bb minor.