One is about changing the harmony of the minor scale, the other one is about the melodies it creates.
When I was discovering how to play 'out', one of the first things I learned was using the harmonic minor and melodic minor scales.
It did not come easy. The fingerings were counter-intuitive relative to my blues/rock upbringing. They also sounded strange compared to the 12 bar format of 3 dominant 7th chords I was used to playing on.
I struggled to get my head wrapped around these exotic scales, and I'm hoping that the following line of reasoning can help you grasp the concept in a much more expeditious manner.
Before we dive into music theory land, let's just make sure a few things are clear.
The basis of all western music, from Bach to the Beatles, or as they say "from Abba to Zappa"; is the V-I resolution. In the key of C, G7 to C. It's a very pleasing cadence, I immediately felt a sense of deja vu when my first guitar teacher had me play the two chords together.
Music has only three aspects: melody, harmony, and rhythm. The rhythm is the glue that holds everything together. Without rhythm, we would just have static noise. Melody is what we remember. Whether it's "Mary Had a Little Lamb" or "Stairway to Heaven", it's the melody lines that go on repeat in our heads.
Harmony can get a little more complicated. "The Beatles have great harmonies", implies that one guy knew if he was singing C-D-E, another guy could sing E-F-G and it would sound cool. I wrote a tune last year with a complicated 16th note guitar figure, and when I recorded a demo into the 'voice memos' app on my phone, I asked my band how they wanted me to play it. "Just play the chords in that section, so I can hear the harmony", the bass player replied. He didn't want to hear the complicated lick I wrote, he wanted to hear the chords for that section. Melody is one note at a time, harmony is more than one note at a time.
Coming back to how you keep those two scales straight: in the C major scale you have V-I (G7-C) which creates a pleasing cadence (tension and resolution) for the ear. To go v-I in the C minor scale, does not create resolution. The v chord is minor, a lower case Roman numeral.
However, if we take the G-7 chord (G Bb D F) and raise the third one half step to B natural, we would have a G7 chord (GBDF). And we would then have a pleasing V-i resolution to the Cm.
The Cm scale's *harmony* was thus changed from:
C D Eb F G Ab Bb C (1 2 b3 4 5 b6 b7)
To the notes:
C D Eb F G Ab B C (1 2 b3 4 5 b6 7)
And this is the Harmonic Minor scale. We changed the *harmony* of the minor scale to get V-i resolution.
But there's bad news: in creating that V-i resolution, we neglected the scale itself. The major scale is built completely off of whole steps and half steps, whereas Harmonic Minor has a glaring minor 3rd, from the b6 to the natural 7th; giving the scale it's distinct 'Eastern' sound.
So, in playing *melodies* using that formula, they can sound a bit weird. If you just take that Ab and raise it by 1/2 step, you now have a scale constructed completely from whole steps and half steps: the Melodic Minor scale.
Ok, let's recap:
The 'Pure' Minor scale (no V-i)
C D Eb F G Ab Bb C
1 2 b3 4 5 b6 b7
The Harmonic Minor scale
C D Eb F G Ab B C
1 2 b3 4 5 b6 7
The Melodic Minor scale
C D Eb F G A B C
1 2 b3 4 5 6 7
In short, take the pure minor and raise the 7th (change the harmony) so you get V-i. Harmonic Minor.
Take harmonic minor and raise the 6th too, so melodies don't sound like 'that Egyptian scale, dood!'. That makes the *melodies* more pleasing to the ear. The melodic minor scale.
Pure minor (Zero notes are changed).
Harmonic minor: chords go V-i but sounds eastern (One note is changed).
Melodic minor: V-i and the scale is built from all 1/2 steps and whole steps (two notes are changed).
P, H, M.
A mnemonic device you could use is 'Please Hurry, Man'.
There is a great book called "The Guitar Grimoire: Scales and Modes" by Adam Kadmon which diagrams not just every fingering of the major scale, harmonic minor, and melodic minor and all of their modes in all 12 keys; but harmonic major, Neapolitan major and minor, whole tone and symmetrical diminished scales, and various pentatonic scales too.
Adam Douglass has been playing guitar for 25 years and teaching for a good 20. He currently resides in Brooklyn, New York where he is an instructor; and plays with his band doing his original music, jazz standards, or whatever other gigs might come his way. His guitar of choice is the Fender Stratocaster, though if money were no object he'd have 3 or 4 of everything. He prefers tube screamer-like overdrives and clean boosts, with touch of analog delay. Hit him up at firstname.lastname@example.org, as he is always happy to discuss interesting topics.