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) or F7sus4+9(no5) while the left hand played only F.
So the question is: is D#/F a propee name for that chord in classical standards?
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 F⁷ 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♯°⁷ with also a diminished third. Harmonically, this acts more or less like B⁷, 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.)
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 EΔ. 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.
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?
