is '4 minor' sub-dominant?
With no other info I would assume "4" means the Roman numeral in harmony
IV, and when the chord is minor it's written in lowercase
Whether the chord is major or minor doesn't matter, it's the root of the chord that makes its identity a subdominant.
'4 minor' can be substituted with ♭VII7 (backdoor V of 'backdoor ii V') which often resolves to 'Tonic'.
I think this is mixing up the basic elements of the backdoor progression. In that progression the
♭VII is a sort of substitute for
V as both chords can harmonize tone
^4 of the scale.
V sort server the same function in that sense as dominants.
The subdominant comes into the backdoor progression as a sequence of roots by descending fifths. If
ii V I is descending fifths to the tonic, the backdoor progression maintains part of the root changes by preceding the
♭VII with a descending fifth from the subdominant
IV. The minor
iv is used further the borrowing from the minor mode.
Interestingly, both progressions end up with the same basic functional categories. Chords
IV are considered forms of subdominant, pre-dominant harmony. Again,
♭VII has a substitute dominant role. So
IV iv ♭VII I and
ii V I both fulfill the same function: subdominant > dominant > tonic. The backdoor progression gets the job done with a lot of modal "darkening."
'4 minor7' is temporarily non-diatonic and contains the ♯5 of the key centre as well as the ♭3.
Just one quibble.
iv7 would be tones
^4 ♭^6 1 ♭^3, in
C major it would be spelled
F A♭ C E♭.
If the tone really was
♯5, it would be
C major. You might find that in a chord like
E7 moving to
Am. The raised tone then takes on the role of dominant harmony.
That brings up a point I think worth making. Tonal changes in the direction of the subdominant involve lowering tones, think adding flats. Tonal change in the direction of the dominant involve raising tones, think adding sharps.
Raising a tone for
♯5 suggests a leading tone and dominant harmony whereas lowering a tone for
♭^6 suggested borrowed harmony.
It's interesting how all the lowered tones of the backdoor progression both use borrowed chords and put an emphasis on the subdominant.