If we take the basic C Major scale and play through it we can create a new scale by changing just one note. This is the 3rd note E.
If we flatten this E natural to an E flat note we have the C melodic “Jazz” Minor scale.
Here are the arpeggios for the C melodic “jazz” minor scale
Upper Extensions: We can add a “triad” above the arpeggios and create an upper extension on each of the melodic minor’s arpeggios.
It is a good idea to extend the tonic C minor/maj7 Arpeggio to get a good fluid fingering for it as it is a really beautiful exotic sound and can also be used over an altered dominant chord.
Another important point is to get a good fingering by using easier fingerings like the example below. [The easier the fingering the better the intervals sound on the guitar].
It is also a good idea to employ “triad pairs” that exist within the melodic minor scale. Here we have E flat augmented, F major, Cmin/maj7, and Dm7
We can also make Pentatonic’s from the melodic minor scale which fit easily in the guitarists fretting hand. Below is an example that could be played over an A minor 7 flat 5 chord [Chord 6 in C melodic “jazz’ minor scale].
Lastly, we have the dominant chord of the C melodic minor scale being G major [Chord 5]. This would normally make G seventh but due to the E flat note in the scale we can now make an “Altered” Dominant chord [G9 Augmented]. We have the note of A for the ninth and the E flat note for the sharpened 5th.