Chords from Harmonic Major
Harmonic Major is sometimes said to be the "missing" member of the group of common heptatonic scales, the others being Major, Melodic Minor and Harmonic Minor. Whatever the value of this claim, it has some interesting chords in it.
Harmonic Major is 1 2 3 4 5 b6 7, i.e. a major scale with a flattened sixth note. For ease of reference I'll assume we're in the key of C, so the notes are C D E F G Ab B.
C Maj 7 covers off C E G and B, and is certainly the most obvious chord to pull out of this scale. The remaining notes are D F and Ab, which is a D diminished triad. Adding the C gives us Dm7b5. And G is still G7, but here extending it to the 9 gives G7b9. So you have a very standard ii-V-I to the tonic: Dm7b5 - G7b9 - CM7. This is one reason, I think, why standards-type players are unfazed by this scale (most "exotic" scales are hard to fit into show tune harmony).
We also have a set of augmented triads built on the C, E and G#, and also a set of dim 7 chords built on the D, F, Ab and B. The augmented triads can be used to construct line cliches such as CM7 - C+ - Bdim7 - C+ - Dm7b5 - G7 - CM7 with a top line going G-Ab-B-C-D-B-C. Of course, any of the dim 7 chords can also be used in place of V7.
We also have an E7, which extends to an E7#9 and can be used as a sub for G7b9 without scaring the horses, opening up some unusual basslines and resolutions involving holding the note E, G or even B over from the E7#9 to the CM7.
On D and F we can form a diminished triad with an added natural 9: D-F-Ab-E and F-Ab-B-G respectively. Depending on voicing and context these might pass for extra-sour m7b5s but they can also sound completely atonal. The missing 7 is the key to this: put it back in and you have a plain vanilla chord with a clear tonal function, but without it things are deliciously ambiguous.
But what else is in there that might be more interesting to someone who doesn't ii-V all day?
One chord that appears twice is the "sus b2" triad 1 b2 5. This crops up on the E (E F B) and again on the G (G Ab D). These don't overlap, so they nearly cover the whole scale; the only missing note is the root, C. These are well worth playing on their own and over the C bass note. What's more the inversion of this chord, the "sus #4" chord 1 #4 5, appears at the note F (F B C). Since they're related by inversion these chords all sound "of a piece" together and can open up some more modal / atonal approaches.
Some spicy, Bartockian chords are also lurking in Harmonic Major. On E and G we can form the major triad and then add the b9; if we do this without the 7 we get a distinctly polytonal sound on the cheap. Similar but not the same is the 7sus b2 sound (1 b2 5 b7) on the same notes.
There are also major triads with added 11s at the root (C E G F) and the fifth (G B D C), both of which can be far more dissonant and non-tonal than you might expect; they need to be voiced to bring out the minor second between the 3 and 4 for full effect. You can play the C version with a #5 and the G version with a b9 to intensify things when you need to, but the bare chords have that off-consonant quality that can be very useful in creating light and shade.
There's a lot to explore here but to get you started here's two octaves of Harmonic Major harmonized with one of the three chords E sus b2, G sus b2 or F sus #4:
