The minor blues is a great place to explore Melodic minor, and you can get a lot of very different sounds with it.
In this video, I am going to show you how you can use Melodic Minor on an A minor blues, the different colors that are in there, not only on the minor chords but also melodic minor modes like Lydian dominant and altered dominant sounds.
Let’s start with a solo chorus on the song and then I will down what is going and give you some variations and exercise to use in your own playing.
The backing track I am using in this video was made by Quist, and if you want to play over it then there is a link in the description to it on his channel.
Blues Licks With Melodic Minor
The first few phrases are sounding more like a blues phrase than a bebop line, and this is also an option with melodic minor.
The material I use is really just playing around the basic chord tones: Am6, which are great for sounding like blues, almost a BB king flavor. In the example I kept it a bit more plain with the phrasing, but you could also play the line with a few slurs and grace notes like this:
Here, I am mostly just using the Am6 or F#ø arpeggio, so if you take an arpeggio like this:
Notice that an Am6 arpeggio is the same as an F#ø arpeggio, so as you can see here, where F#ø is in fact an inversion of Am6 (and the other way around)
then you can work on making phrases that sound more like blues phrases, like this:
Making the phrases shorter, and a bit more focus on rhythm usually does the trick.
Another option is using double stops like this:
You Need To Know This For ANY Scale You Want To Use
Something I first want to also cover here that is extremely important and something you ALWAYS ALWAYS ALWAYS want to check out for any scale you want to use in a solo: The Diatonic Chords!
You will see this coming back all the time in this video, and knowing them will give you 1000s of things to play.
For A minor Melodic we have these diatonic arpeggios:
You should check those out like this, but also in a position to really get these into your system 
You already saw how this was useful for the Blues phrases, let’s look at some of the other options we have using Diatonic Arpeggios
Beautiful Notes and Diatonic arpeggios
The next phrase in the solo is a combination of two arpeggios: Cmaj7#5 and Am6, both played descending.
This is, again, the Am6 arpeggio and then the diatonic arpeggio from the 3rd of the chord Cmaj7(#5).
The Cmaj7(#5) works great because it spells out the upper part of the minMaj7 chord and adds a 9th:
AmMaj7: A C E G#
Cmaj7(#5): C E G# B
(Secret) Altered dominant
The chord in bar 4 is a super-imposition, so I am adding a chord to the song that is not really there, and it is creating tension that then resolves a bar later.
In this case, I am adding an A7alt which then will resolve to the Dm6 in bar 5.
A7 altered is the same as Bb melodic minor, and the line is also clearly related to a Bbm shape.
This is because the Bbm over an A7 gives us some altered notes and the 3rd of the chord:
Bbm: Bb C# F
against A: b9 3 b13
The Line uses the Bbm triad and adds in a C which is a #9 on the A7alt.
Being Vague On Purpose But Sounding Great
The phrase on the Dm6 chord is a little less clear, but is a nice example of using a structure as a motif.
The first bar is a statement coming from an Esus4 triad, and this is echoed in the 2nd bar as an Asus4 triad playing the same melody.
Checking out sus4 triads is under-estimated but very much something you want to do to have some more options, just like you want to explore the diatonic triads and arpeggios of the melodic minor scale.
The Lydian Dominant
The final cadence in a minor blues is a V chord and then also the tritone substituted dominant for that chord.
In Am that is E7 and the tritone substituted dominant for this: F7.
In the solo example, I playing the F7 as a Lydian dominant, which is a very common scale choice for a tritone substitute, and I use the altered scale for the E7, so both of these sounds are rooted in melodic minor, and two of the most common sounds you need to know.
For an F7, the Lydian dominant scale is the same set of notes as the C melodic minor, and I am using the Ebmaj7(#5) arpeggio combining it with a trill.
Ebmaj7(#5) is a good way to have a melody with many of the important notes in the chord:
Eb G B D
b7 9th #11 and 13th.
The Altered Dominant
The E7 altered is also a melodic minor sound, being the same set of notes as F melodic minor.
The line is in this case based around a few notes of an F minor triad and then a Dø arpeggio.
The m7b5 arpeggio on the b7 is a great arpeggio for getting the sound of an altered dominant across with the
Dø : D F G# C – b7 b9 3rd b13
Here I am resolving it to the 9th on the final tonic chord and also combining these with the maj7 and the maj6 to really get that rich tonic minor sound
A Great Arpeggio Combination
In the final, bar I am using a combination of an Abmaj7(#5) and Fm triads for the altered chord, again using some of the same structures to get that sound across on the altered dominant.
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