The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped.
Dmadd9 is D, F, A and E — Dm with the ninth added, and no seventh.
It sounds sharp-edged. The ninth grinding a whole step under the minor third is the edge an m9 softens.
Minor tonic — a triad with one colour on it.

| D | F | A | E |
|---|---|---|---|
| 1 | ♭3 | 5 | 9 |
Also written Dm(add9), Dmin(add9) or D-add9. The same chord either way; which spelling you meet depends on who wrote the chart.
The same operation one voice further down: the third voice from the top falls an octave and becomes the bass.
That leaves a bigger hole under the top three notes, so a string gets skipped: the muted string in the middle is the shape, not a mistake.
Dmadd9 has 9 of them, on strings 5-3-2-1 and strings 6-4-3-2, from open position up to the 13th — every inversion the chord has: D in the bass, F in the bass, A in the bass and E in the bass. The one to learn first is the D shape at the nut.
5 of them sit on strings 6-4-3-2, so you can run the inversions up one set without changing strings — which is the whole reason to learn them as a family rather than as separate grips.
All 9 common shapes as fret numbers, lowest string first. Hover or tap one to see it drawn.
How you get to it. The turn that lands on Dmadd9 is Em7♭5 to A7♭9: the ii and the V of D minor, which is where a minor tonic is usually arrived at rather than simply begun on.
In which keys. Every note of Dmadd9 belongs to C major (the ii, the supertonic), D minor (the i, the tonic), F major (the vi, the submediant) and A minor (the iv, the subdominant).
Every note of Dmadd9 is in D dorian, D natural minor, D harmonic minor and D melodic minor.
Change one note of Dmadd9 and you have Dm (drop the ninth), Dsus2 (drop the minor third), Dsus2sus4 (the minor third becomes the fourth), Dm6 (the ninth becomes the sixth), Dm69 (add the sixth) or Dm7 (the ninth becomes the flat seventh).
Dmadd9 is a minor chord — root, minor third, fifth. Minor chords on every root.
The common shapes and the derived voicings come from different places, and both are explained in how this site is built.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.