Is there a mode which contains the following notes?
E flat D D flat C
Is there a mode which contains the following notes?
E flat D D flat C
That's a very unusual collection of notes to find together (except as passing tones). There is no diatonic or melodic minor mode that contains three consecutive semitones, or does it occur in the heptonia tertia, double harmonic scale, or phrygian dominant scale. Likewise, you won't find these notes together in any common pentatonic, hexatonic, or octatonic scale.
One place where these pitches could co-occur is the chromatic scale, which contains all the notes you'll find on a normal piano.
X: 1
T: Chromatic scale
K: none
M: none
%%stretchlast yest
C^CD^D EF^FG ^GA^AB c2|
cB_BA _AG_GF E_ED_D C2|]
Another place is the Scala Enigmatica in the key of D. The Scala Enigmatica includes a minor second, augmented sixth, and major seventh, which gives it three consecutive minor seconds around the root, though it would be very strange to write these notes as you have here.
X: 1
T: Scala Enigmatica
K: none
M: none
%%titlefont serif italic
%%stretchlast 1
D_E^F^G ^A^B^c d3|
d^c^B^A =G^F_E D3|]