Yes! So the first thing to do with ANY new scale that you’re unsure of is to analyze it. So choose a key center, we’ll use the key of A for this one, and figure out all the notes that the scale uses. This page notates the root of the scale with an “n” under the root note. So this scale in the key of A is A-Bb-C#-D-E-F-G#-A. On a side note, when you write out a scale you generally want to use just sharps or just flats, not both. Another kind of rule in classical theory is to represent every note of the musical alphabet so ABCDEFG. This particular scale requires you to use both sharps and flats to achieve this. So we have our notes, now we have to write how each not functions and we write it out like this-
1-b2-3-4-5-b6-7-1. The most important notes in this scale formula are the 3 and 7. In this scale we have a MAJOR 3rd and MAJOR 7th so you could play this over ANY major 7th chord, and switch key centers with each chord so like A maj7- D maj7 you would play A double harmonic – D double harmonic IF you want to play modally. Now if the 3rd and 7th were FLAT, you would play this over a MINOR 7th chord. If you have a Major 3rd and a minor 7th, you play it over a DOMINANT 7th chord, and finally if you have a minor 3rd and a major 7th, you would play it over a MINOR MAJ 7 chord, which rarely shows up in music. So thats how to think of it in its scale form, NOW to build chords off of it.
So when you want to build chords from a scale, the basic idea is to choose a note, for instance the A, and then use every other note. So-
A C# E G# Bb D F or 1 3 5 7 b9 11 b13(#5) so you have your chord tones 1 3 5 7 and then the rest are COLOR tones which give the scale its sound and character and you can now build chords using those notes. And FINALLY you write the scales out like this for EVERY note in the scale like this-
A C# E G# Bb D F or 1 3 5 7 b9 11 b13(#5) – You can build a Major 7 chord with this or augmented 7th if you use that #5
Bb D F A C# E G# or 1 3 5 7 #9(b3) #11 ##13(b7) – This one is a bit different, its has both Major 3rd and 7ths AND Minor 3rd and 7ths. You can build ANY of those earlier chord qualities mentioned. Exotic scales get a little wonky like that sometimes. Play around with it, have fun and see what your ear gravitates to. When in doubt though, treat it as a dominant chord Bb D F Ab(G#) and the other notes as color tones if you’re going to play this scale over the chord you built. Dominant chords have a much stronger and more imposing sound than major and minor 7th chords.
C# E G# Bb D F A or 1 b3 5 #6(#13) b9 b11(3) b13 – This has a major and minor 3rd with no 7ths, but a flat and sharp 6th. I would almost treat this as a dominant with the 7th missing and treat the b3 as a #9 and the b6 as a #5
D F A C# E G# Bb or 1 b3 5 7 9 #11(b5) b13(b6)- Remember that Minor maj7 chord I said doesnt show up? well here it is. So this one also has a 5 and b5. 1 b3 b5 gives you a diminished triad, again no 7ths.
E G# Bb D F A C# or 1 3 b5(#11) b7 b9 11 13- This is a total dominant tonality through and through, its close to the lydian dominant scale. You would avoid that natural 11 and probably choose the #11 instead. As a general rule of thumb, you dont use natural 11s with major chords. they sound really unstable and not great. Im also not one to tell people what to do, so play with it and do whatever blows your hair back!
F A C# E G# Bb D or 1 3 #5 7 #9(b3) 11 13- Probably treat this as a major 7th chord or augmented 7th chord if you use that #5.
G# Bb D F A C# E or 1 bb3(9) b5 bb7(13) b9 11 b13- This one actually has no 3rds or 7ths. You can kind of build a sus2 chord, but it’s also missing the natural 5. We might need Papa Gates to chime in on how he would apply this one, if at all.
So all of this was probably VERY confusing and I probably made a mistake or two along the way, but it’s how my mind analyzes it. The reality is that you probably wouldnt write a WHOLE song in double harmonic, but it certainly is possible. I would probably just use this modally and in small doses over a major 7th chord here and there. I know this is also A LOT to take in, but it was kind of a loaded musical question. This is just a way to think about this stuff, but to REALLY apply it and get the most out of it REQUIRES you to explore it and play around. That’s the difficult part of music that many people miss or dont want to acknowledge- only YOU can put the effort into exploring these things and figuring out how YOU would use them. Personal exploration is probably the BIGGEST part of understanding music. I think that that is the reason why so many of the best players on the planet are self taught. A good person to take cues from on making chords from crazy scale would be Allan Holdsworth. He’s got some lessons online that explore this kind of thing. Im sure there will still be some confusion, so if you have any other questions, feel free to fire away!