D# Half-Diminished 7th (D#m7b5)
Also written as Eb Half-Diminished 7th (Eb and D# are the same key).
Notes in D# Half-Diminished 7th
Inversions
Same notes as D# Half-Diminished 7th, with a different chord tone as the lowest note. Useful for smoother movement between chords instead of jumping around the keyboard.
Root position
D# in the bass
1st inversion
F# in the bass (D#m7b5/F#)
2nd inversion
A in the bass (D#m7b5/A)
3rd inversion
C# in the bass (D#m7b5/C#)
Open voicings
A close-position chord like D# Half-Diminished 7th can sound cluttered in the middle of the keyboard. Jazz players open it up by dropping one note down an octave, spreading the same notes wider without changing the chord.
Drop 2
A on the bottom
Drop 3
F# on the bottom
Press D#, F#, A and C# together on the keyboard and you're playing D# Half-Diminished 7th.
Also written m7b5, this is simply a minor seventh chord with the fifth lowered a semitone. It occurs naturally on the seventh degree of a major scale and does most of its work as the ii chord in minor-key jazz, carrying an unsettled, searching quality that is softer than a fully diminished chord.