Hmm. Your tab is a bit odd to me, but best I can follow, let's break it down into notes, so that it makes more sense (to me, at least
The underlying 'chords' (diads, really) are F#, E, A, and D. The key could be anything from E, to D, to A, to F# (with the E being an accidental). Let's look at the harmony then.
On the d string, we have - 16. Here's an F#. To harmonize with that is a D, from the d string 12th fret (or even better way to play it is A string 17th fret). This is a major shaped diad, it's just missing the fifth. I play these 'chord' shapes (root and third diad) all the time. When you play it like this, all in one form, you can see and hear the shape's tonality easily. Anything in standard tuning, with a root on the lower string, and the next note one fret back, one string up, will be major. In this case, it's a D Major diad.
D MAJOR DIAD
If you wanted the interval to be a minor third (turning this diad into a minor diad) you'd move the 16 F# note back one fret to 15, an F natural, and voila. You have D minor (the notes of the d min triad are D, F, and A).
D MINOR DIAD
Always think of this. Have your root, then fret one back, one string up = major. Fret 2 frets back, one string up = minor.
What you have on the first power chord is a very odd harmony, since the F# root is an inversion of your first harmony line's D major tonality. But having the Db/C# (9th fret on the E string) in there makes it a Dmaj7 chord, and a minor harmony doesn't vibe with a maj7 chord. But your original harmony tones work fine.
So, back to your harmony. d (14) - E. With that is d (10) - C. Again, this suggests C major, since C is the root, and E is a major third for C. If you want this minor, move the (fret 14) E back one fret to (13) Eb/D#.
And so on.
What works good, and ends up harmonious (albeit major) is