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While improvising today, I discovered that you can create some quite cool, melancholic sounds by adding the tritone to a harmonic minor scale. For A minor, the resulting scale would be

A B C D D# E F G# A

I guess, I'm not the first one to discover this, which got me wondering, whether there was some kind of a name for it.

The two uses that I found were to either play around the fifth (like E F E D# E), or to use it in conjunction with the raised seventh of the harmonic scale.

Analyzing the scale, it occurred to me that the D# is actually the major seventh of the dominant chord, which makes the second use quite logical (major third and major seventh of the dominant chord).

Are there any better insights into the use of the tritone with a minor scale? And is there a name for it?

...A B C D D# E F G# A

Just the list of tones isn't enough to describe in a meaningful way what is happening. It could have various musical meanings.

• 
  D# could be a chromatic passing or neighbor tone.


• 
  D# could be the temporary leading tone of E, harmonically V/v
  

A lot depends on the harmonic context. Even if you have playing only a single melodic line there is usually an implied harmonic context. The harmonic context will really be the thing that informs us about what it could be called.

Even this... E F E D# E ...isn't really enough to say.

D# looks like a chromatic neighbor tone, but whatever you played before it could imply something else.

...use of the tritone with a minor scale

That wording sort of implies a harmonic tritone. If you aren't playing A and D# simultaneously or outlining A to D# in some way, that wording might be a bit misleading. At least for me I would be expecting to hear the discordant sound of a tritone. Just E F E D# E alone won't necessarily produce that tritone sound.

Adding the D♯/E♭ into your playing isn't much to do with the harmonic (or any other) minor.

It's a flat 5 in blues, or a sharp 4 in jazz. Take your pick - especially if you're a guitarist..!

It's a note that's been used and used since the early 1900s, as so out of tune it sounds really good.Works just as well in major keys too.Since it's between the sub-dominant and the dominant notes in a diatonic situation, it doesn't really fall into either camp. Did the player mean to play a semitone higher, or a semitone lower? What the heck, it's sweet and sour!

You may have been doing many different things with the notes, depending on how you emphasized the notes in relation to a beat you heard in your mind. Maybe you just flirted with the blue note - maybe you played something "modal" ... but perhaps you were outlining chord changes with the notes you played. Maybe your playing lead yourself to imagine chord changes you weren't even outlining! With the notes listed you could arpeggiate e.g. an Am, Dm, F, E7 chord. Or a Dm6. Or maybe you just played an A note and imagined something like a Dm? It depends on many things. Extra things that can be done by adding a D# note are e.g. B7, which would be a "secondary dominant" for Am. Or an F7 which could be seen just as a bluesy IV chord for C, but perhaps a bit like a tritone substitute for B7.

I really can only guess what really happened with your improvisation, but here's an example of something that could be done with the notes. First there's just an improvised solo guitar line, trying to outline a melancholic progression. Then there's the same solo, but with piano and bass accompaniment.

Many chords of the accompaniment use notes outside the set you listed. But when it comes to melodies, what you play is not all you hear! :)

Like you said in your comment, you may have just found the tip of an iceberg. To develop a sensitivity for harmonic changes, and an understanding of what it is that you're painting with your improvised solos, I recommend learning to accompany songs with chords by ear. I, IV, V, etc. C - F - G - C. Am - Dm - B7 - E7 - Am, etc. In my honest opinion, knowing harmony so that you can recognize and improvise chord changes, and how the melody notes interact with the changes, is a key to musical playing that's missing from some young players these days. They want to "play scales" or modes, but don't have a hands-on understanding for functional harmony. New pop songs seem to use just pentatonic scales, which are ambivalent about harmonic turns. A pentatonic scale can be played almost anywhere without knowing what's happening with the chords, and on the other hand, a pentatonic melody can be quite freely accompanied with chords. But when you play these notes that you have in your set - B, F, D#, G# - not so! That's heavy stuff, it says something about possible harmonic changes. :)