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A simple barre (first finger across all 4 courses at the same fret) will give the following set of 'modal' chords:

Fret open 1 2 3 4 5 6 7 8 9 10 11 12
Chord D D#/Eb E F F# G G# A A#/Bb B C C# D

Useful chords in this tuning:

D major 5450 = fret positions on the lowest to highest course.

Major Minor Modal Works!
D 5450 0054 D 5350 D 0000 D 0054
E 2622 E 2522 E 2222 E 0222
F 3303 F 3333 F 0330
G 5955 5559 G 5855 G 5555 G 0550
A 0242 A 0232 A 0202 A 0220
B 2124 B 2024 B 2424 B 4200
C 3235 C 3135 C 3535 C 0032

A common technique, is to use the capo to change key without changing the fingering of the chords. The Works! chords make this easy. The Works! chords are all what can best be described as -ish. That is A-ish, C-ish etc but they make a very good accompaniment to traditional music.

A good set of chords to learn are those in the 'Works!" column for D, G and A plus the one in the B column which gives a convincing B minor. Capo to the 5th fret, the same positions give G, C and D plus E minor.

In fact, with these few shapes and a capo, it is possible to play in D (and Bm), Eb (and Cm), E (and C#m), F (and Dm), F# (and D#m), G (and Em), Ab (and Fm), A (and F#m). You could go further up the fretboard but it starts to get too high in pitch. B (&G#m) at 8 and C (&Am) at 9 might be achieveable.

A common chord sequence is Am - G which is easily obtained lower down form the A Works! and G Works! simply sliding the fingers between the two. You can even get the full run of A, G, F, E by sliding from frets 7-5-3-2.

Many traditional tunes are in D, G, A or their relative minors (Bm, Em, F#m not so much) or are a close modal alternative such as Dorian or Mixolydian modes so can be easily played in this tuning.

There are many other possibilities with this tuning, these are just a few to get you started!