FΔ7(9/13 no 3rd)

Take four consecutive white keys on a piano and see what chords you can make. Sorry to be anticlimactic, but here are the answers. They can each be named by the second note:

C, D E, F:            D-9

D, E, F, G:           E-7♭9

E, F, G, A:           FΔ9

F, G, A, B:           G9

G, A, B, C:          A-9

A, B, C, D:          B-7♭9

B, C, D, E:          CΔ9

None of these contains a 5^th degree, but that’s OK since the natural 5^th is the least important degree there is. Notice that they group into four categories based on the pattern of whole and half steps:

W, W, W:           G9

H, W, W:            CΔ9, FΔ9

W, H, W:            E-7♭9, B-7♭9

W, W, H:            D-9, A-9

One more pattern, allowed by the harmonic and melodic minor scales, is possible:

H, W, H:             A-Δ9 (for instance) = G#, A, B, C

H, H, H would be a 4-cluster, e.g A#, B, C, D♭. This is not easily played on the guitar and not super useful musically, outside of atonal concert music. My favorites of the chords from this list are the minor7♭9s, e.g.

D, E, F, G = D-(9/11)

     = E-7♭9

     = FΔ7(9/13 no 3rd)

     = G13 (no 3^rd)

Though they're all the same chord, most of the voicings below will have F in the bass, so I'll use that third name from here out. This chord type sounds phenomenal in the close voicings permitted by the ukulele. Two close voicings are fingerable on the guitar (these will be an octave lower than their versions on the uke):

FΔ7(9/13 no 3rd)

X8575X or

X(10)(12)(9)(6)X

That second one, with a 6-fret stretch, is not a beginner chord. Try exploiting an open string to make it easy, e.g.

E7(9/13 no 3rd)

X(9)(11)(8)X(0)

It helps if you play fingerstyle. Sorry about that one! These denser chord types tend be either quite ergonomic or maddeningly difficult to fret. Here’s an moderately difficult drop-2 form:

FΔ7(9/13 no 3rd)

X(8)(12)(9)(8)X

And a lovely drop-3 form

FΔ7(9/13 no 3rd)

(13)X(14)(12)(15)X