: Classical chord naming of D#/F I was playing the piano today and made up chord progression: Fm, D#/F, A#, Fm in 4/4. And I was wondering if D#/F is a propee classical name for the chord, because logically it was an F7sus2+11(no5)

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Hang on, the following discusses a different sequence (is misread the question): F/D? instead of D?/F. See bottom for the actual sequence asked about.

As already said, that bass note is an E?, not a D?. The chord is basically F? in third inversion, so the 7th is in the bass. This is in fact the dominant to the following B?, so very natural chord to have in that spot.

It wouldn't be a 7th chord if the note were D?. Classically speaking, such a note is a dissonance that always needs to lead somewhere, and ? dissonances lead upwards, ? dissonances downwards. Your chord sequence could thus be rendered

X:1
L:1/2
M:C
K:Fm
%%score (T1 T2) (B1 B2)
V:T1 clef=treble
V:T2 clef=treble
V:B1 clef=bass
V:B2 clef=bass
% 1
[V:T1] A =A | B A
[V:T2] F F | F F
[V:B1] C C | =D C
[V:B2] F, E, | B,, F,

Actually the effect is a bit clearer if the bass only went one step down:

X:1
L:1/2
M:C
K:Fm
%%score (T1 T2) (B1 B2)
V:T1 clef=treble
V:T2 clef=treble
V:B1 clef=bass
V:B2 clef=bass
% 1
[V:T1] A =A | B A
[V:T2] F F | F F
[V:B1] C C | B, C
[V:B2] F, E, | =D, F,

But even if you actually play the bass upwards after it, this progression to the (Mixolydian) subdominant B? is so standard that the bass note before would clearly be perceived as E?, not as D?.

To call that note D?, it would have to lead upwards to something that would clearly associate to that particular degree. This is certainly possible, but it would be a bit whackier than your sequence. For example,

X:1
L:1/2
M:C
K:Fm
%%score (T1 T2) (B1 B2)
V:T1 clef=treble
V:T2 clef=treble
V:B1 clef=bass
V:B2 clef=bass
% 1
[V:T1] A =A | G B | A
[V:T2] F F | =E E | F
[V:B1] C C | =B, C | C
[V:B2] F,^D, | =E, C, | F,

In this case, your F/D? is really a diminished seventh chord in disguise: D?°? with also a diminished third. Harmonically, this acts more or less like B?, as a dominant to the following e-minor.

(As patrx remarks, a better way of describing this might be as an inverted augmented sixth chord.)

The real question

Ok, so what you actually asked is a different sequence, but the answer is largely the same: classically, you're not that interested in chords but in voices. Sustaining F in bass is a (very short) pedal point, which can be used regardless of what the upper voices do. So really all we need to discuss is the chord sequence Fm - E? - B? - Fm. Well, straightforward F-mixolydian turnaround, this is very common in folky tunes and pop. With common-practice voicing, it could be rendered like

X:1
L:1/2
M:C
K:Fm
%%score (T1 T2) (B1 B2)
V:T1 clef=treble
V:T2 clef=treble
V:B1 clef=bass
V:B2 clef=bass
% 1
[V:T1] A B | B A
[V:T2] F G | F F
[V:B1] C E | =D C
[V:B2] F, F, | B,, F,

Making something of an actual D?/F would be really weird, certainly nothing you could find a classical name for.

But let's see... if we make that D?m/F, it could lead to E?. Then a little tritone substituition could still bring us back to Fm:

X:1
L:1/2
M:C
K:Fm
%%score (T1 T2) (B1 B2)
V:T1 clef=treble
V:T2 clef=treble
V:B1 clef=bass
V:B2 clef=bass
% 1
[V:T1] A ^A | =B _B | A
[V:T2] F ^F | ^G =G | F
[V:B1] C ^D | ^D _D | C
[V:B2] F, F, | E, E, | F,

Yup, works, doesn't even sound as jazzy as I though. I think that could actually still be interpreted in a more sensible way without those sharps.

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Any chord naming system that requires monstrosities like F7sus2+11(no5) or F7sus4+9(no5) is broken!

You've discovered the chord Eb/F. Eb, G, Bb with an F root. Very common in the key of F or F minor. (Calling it D#/F seems perverse, but I can't quite say it's WRONG...)

You aren't REALLY going to call that other chord A# are you?