E natural minor consists of E F# G A B C D E.
Here is how E natural minor sounds
E harmonic minor consists of E F# G A B C D# E.
Here is how E harmonic minor sounds
I love how the D# adds alot of tension and a touch of mystery to the scale. The D# creates tension by wanting to resolve towards the tonic of the scale, the E. Harmonic minor is used very widely in jazz and rock music.I always have to think of Slash from Guns 'n' Roses when I hear the harmonic minor scale since he uses it extensively in his soli.
Have a listen to the Sweet Child of Mine solo (at 2:34). The first half and the high speed fill are entirely in Eb harmonic minor (it's just E harmonic minor but his guitar is tuned down by a semitone) and then the scale resolves to Eb natural minor which creates the 'release' feeling.
Here is a bit of music theory about why harmonic minor is actually called 'harmonic' - it all has to do with chordal harmony. But don't worry, it's very simple
E major consists of E F# G# A B C# D# and the chords you can build with this scale are
A very classical chord progression is I - IV - V - I, which in E major would be E - A - B - E. Here is what it sounds like
It does have a very classical feel to it doesn't it? I like the tension created by the dominant chord (the B) and the resolution to the tonic.
Now let’s see what happens when we do this chord progression in a natural minor scale. In E natural minor, the chord progression is Em - Am - Bm -Em. Have a listen!
Hm, kinda lacks the tension doesn’t it? That’s because the dominant is actually a minor chord. The chord lacks the D# that would make it a major chord to create the tension and lead back to the tonic of the scale. In order to give this natural minor scale a more harmonic feeling, we need to make the dominant chord (the Bm) a major chord. We do this by raising the seventh degree, the D#, by a semitone – and thus we get harmonic minor.
The progression has the feeling of a minor scale, but the same harmonic tension as the progression for the E major scale. Harmonic minor is a great sounding scale and you caneasily switch between the D and the D# while the harmonies of the song progress over the E minor scale. Have a listen to some other of Slash's soli - he has an amazing feel for when to introduce more tension by using the harmonic minor scale