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How do I write out this chord?

You probably want an H13/D# or an H7/D#, because there doesn't seem to be enough dominant motion going to the second bar. I've never seen a m7(b5) used in that context - its far more likely to be an Fdim7, or very technically speaking an E#dim7 (since it's going to an F-type chord). The minor 7's resolution on the Fm7(b5) to the fifth of the F#m7 is far less strong (major second) than the resolution of the diminished seven to the fifth (minor second). Yeah, but I really dig this kind of progression.
 
You probably want an H13/D# or an H7/D#, because there doesn't seem to be enough dominant motion going to the second bar. I've never seen a m7(b5) used in that context - its far more likely to be an Fdim7, or very technically speaking an E#dim7 (since it's going to an F-type chord). The minor 7's resolution on the Fm7(b5) to the fifth of the F#m7 is far less strong (major second) than the resolution of the diminished seven to the fifth (minor second). Yeah, but I really dig this kind of progression.

Thanks for the feedback on the progression. :)

When I played this on guitar, the second chord didn't sound "right" to me with a 7th added so I'll stick to the H6/D#. It might fit well in a solo over the chord though. Btw, I want the G# as the top note throughout the progression except from the last bar.

I already thought of the alternative of using an Fdim7 instead of the half-diminished Fm7b5, but to me the latter sounded smoother in the progression although less dominant. Going to Fdim7 sounded a bit too kliché to me, but I guess it's a lot about taste. And of course voicings matters a lot when speaking about chords like these.
 
Thanks for the feedback on the progression. :)

When I played this on guitar, the second chord didn't sound "right" to me with a 7th added so I'll stick to the H6/D#. It might fit well in a solo over the chord though. I also want the G# as the top note throughout the progression except the last bar.

I already thought of the alternative of using an Fdim7 instead of the half-diminished Fm7b5, but to me the latter sounded smoother in the progression although less dominant. Going to Fdim7 sounded a bit too kliché to me, but I guess it's a lot about taste. And of course voicings matters a lot when speaking about chords like these.

It depends on how you voice it, of course. I can see how on a guitar it might be difficult to voice it with the D# on bottom, G# on top, and B, F#, and A in the middle,
 
I thought H usually signified Bb. So much for being an American and using our movable 'Do' solfege system.

Now that you mention, in many of my physics books, H = B/u, where "u" (omicron, in greek alphabet) is the magnetic permeability of any material but we have to step into magnetism theory and that should go to off-topic forum :D

Many of us could find that wiki link quite interesting to understand the magnetic principles in the pickups.
 
German H = Standard B

German B = Standard Bb


Most people here in Scandinavia (don't know about Germany) advice against using B for Bb though, because of the obvious risk of misunderstanding. So I use mainly H and Bb because it can't be misunderstood that way. However I'm trying to move away from H and learn to use B instead because that's what the rest of the world do.
 
I'm pretty sure it has to do with the temperment systems of the Renaissance and the concepts of musica ficta, or early attempts are writing chromaticism. Bb and F# were the first accidentals to be used, and I guess people in Northern Europe didn't like the concept of a flat - just sharps, so added a note letter to account for the pitch B natural. I'm not entirely sure, that's just a guess, you'd have to get a musicologist to tell you the real reason why.