Below is the the Harmonic Minor Scale and it's diatonic arpeggios.  This PDF is similar to those for the Major Scale and Melodic Minor Scale, so check out those posts if you haven't.  The PDF outlines the Harmonic Minor, it's seven modes and the diatonic arpeggios.

As with the other Scale PDFs, it might be worthwhile to start with the arpeggios for each mode.  Not only are they less notes to focus on, but they are lines in themselves that make succinct, harmonic 'sense' out of the modes.  Once you understand the chord tones for a mode, then you can 'flesh out' the rest of the scale around it.

For the novice jazzer, it is less useful to understand this material for compositional movements, than to just be aware of the arpeggios that are buried within this scale.  While the Harmonic Minor is a great choice for the Min-Maj7 chords and sounds in tunes like Nica's Dream and Nardis, the harmonic minor is probably most used in jazz for altered sounds -- using the Phrygian Dominant over a #11 chord or the Ultra-Locrian for tri-tone colors over a functional Dominant.  Just learning the harmonic scale will give you access to these sounds, but being able to pick out all the arpeggios within it can give you a richer starting point for your lines.

Another key use of the Harmonic Minor in jazz is the 'Barry Harris' approach.  Barry Harris has a whole cosmology of scales and tones that starts with chromatics, splits into diminished and ends with sixth chords.  The 'Barry Harris' scale -- the Major#5 -- is really the third mode of the Harmonic Minor in this PDF.  Check out his 'Sixth-to-Diminished' theory which is at the heart of his teachings.  If you act as if the Third Mode of the Harmonic Minor is the 'One' chord for Major tunes, you can develop a unique perspective into the tunes of the Swing and BeBop era.  Either way, if you are familiar with the arpeggios in the Harmonic Minor and Melodic Minor scales, you will be able to spot them when transcribing the lines of Charlie Parker and other boppers when they go 'outside' the harmony.

Below is a reference for learning the Melodic Minor Scale diatonically.  The Melodic Minor is sometimes referred to as the 'Jazz Minor' due to its applications to Jazz.  You may have gotten hip to the fact that the 7th mode of the Melodic Minor can be used serve up altered sounds over a functional Dominant (a V going to a I).  At some point I also realized that the fourth mode of the Melodic Minor can be used over #11 Dominants.  Learning the totality of the scale with diatonic context of all the arpeggios will give much greater command over these sounds.

While the Melodic Minor only differs from the Major scale by one note, I still find myself struggling to visualize it thoroughly over the fretboard, certainly more than Major scale.  My ability to visualize the Major scale was significantly bolstered by learning all the diatonic arpeggios in the scale, across all the scale 'boxes' where the modes sit with the root on the sixth string.  Learning arpeggios also significantly strengthened my ability to generate lines strongly outlining the harmony. 

You can focus on parts of the neck by breaking it up into 'r6 mode boxes'.  These scale 'boxes' I term with the 'r6' meaning 'root is on the 6th string.'  For instance, 'III-r6' represents the way the notes sit when you play the Phrygian scale with its root on the sixth string.  This lines up as a box, or chunk of the fretboard which is easier to concentrate on, especially at first.

Just like the the Major scale, there are seven notes in the Melodic Minor.  Each of these seven 'degrees' has a mode, chord, and arpeggio associated with it.  Modes are simply the same notes of a scale arranged with a different note serving as the root.  The arpeggio for each degree can be found by skipping every other note in the mode until the next octave is reached.  An arpeggio is basically the notes of a chord played sequentially.

Below are the scales and chords for each degree of the Melodic Minor Scale:

​The Melodic Minor scales are:
I  - Melodic Minor (R, 2, b3, 4, 5, 6, 7)
II - Phrygian #6 (R, b9, b3, 4, 5, 6, #6)
III - Lydian Augmented (R, 2, 3, #4, #5, 6, 7)
IV - Dominant #11 (R, 2, 3, #4, 5, 6, b7)
​V - Mixolydian b6 (R, 2, 3, 4, 5, b6, b7)
VI - Locrian #2 (R, 2, #2, 4, b5, #5, b7)
VII - Super Locrian (R, b9, b3, 3, b5, #5, b7)

The accompanying chords are:
I  - Min-Maj7 (R, b3, 5, 7)
II - Min #6 (R, b3, 5, b7)
III - Maj7 #5 (R, 3, #5, 7)
IV - Dom.7 #11 (R, 3, 5, b7)(#11)
​V - Dom.7 b13 (R,3, 5, b7)(#13)
VI - Min7b5 (R, b3, b5, b7)
VII -Min7b5 (R, b3, b5, b7)
​
I recommend starting with the Melodic Minor arpeggios in the middle section of the PDF.  Take four or five days and run over the arpeggios for one mode (probably start with Min/Maj7) in all the different r6 mode boxes.  Maybe put on a relevant backing track and definitely a metronome.  By the fifth day, you should really concentrate on connecting between the boxes and try to work horizontally or diagonally.

After you have the arpeggios, the scales are just the rest of the notes to flesh them out.  Start with the most useful scales for playing over Dominants, like the Lydian Augmented and Super Locrian.

Finally, learn to run all the arpeggios within a particular mode box.  This will reinforce both the scale pattern and the diatonic progression within the Melodic Minor.

While you are not going to necessarily find a lot of complex harmonic movements of the Melodic Minor in Jazz tunes, learning the diatonics of the Jazz Minor will give you greater facility at minor two-fives and the ability to super-impose these scales in other applications.

The Altered scale is the seventh mode of the Melodic Minor (aka Jazz-Minor) scale.  It is a great scale for finding leading tones over a "functioning" V in a ii-V-I.  These leading tones are 'outside' the Key center of the ii-V-I, which create even more tension over the already tension-inducing V.  This tension of the V is resolved when you get back to the I.

The typical way to play the Altered scale (aka Super-Locrian), is to sight the root of the Altered scale on the root of the dominant.  Alternatively, you can sight the Melodic Minor's root on the b9 of the V chord -- one semi-tone up from the root of the V.

The Super-Locrian/Altered scale is really the 7th mode of the Melodic Minor -- the root of the Altered scale is the 7th degree of the Melodic Minor scale.  Additionally, there are other modes of the Melodic Minor that work nicely over dominant chords in other situations.  

The Lydian b7 (4th mode of Melodic Minor) works great over Dominants with a #11.  If you are familiar sighting the altered scale, you can sight the root of the altered scale on the #11 of the Dominant. Or you can sight the root of the Jazz Minor on the 5 of the V.

For a Dominant with a #5, you can play the Mixolydian b6 - the fifth mode of the Melodic Minor.  Sight the start of the altered on the 3rd of the V chord you are playing over.  Otherwise, sight the Melodic Minor starting on the 4.

Finally, a Dorian b2 (3rd mode of the Melodic Minor) works over a Dominant with a #9 or a b9.  Sight the altered scale starting at the V chord's 13.  Or sight the Melodic Minor on the b7.

I learned the Melodic Minor via the Altered Scale, so I tend to sight with the Major 7 of the Melodic Minor.  But it is really best to sight the Melodic Minor.  When you first learn the Altered scale, your melodic lines will probably sound quite foreign if you think of the 7 of the Melodic minor as the root -- similar to when you attempt to play the Locrian mode out of context.  The 7's of the scale are really pulling the westerner's ear toward the next tone up, which is the root of the key.

If you play lines with the Melodic Minor in mind, you will still be creating tension on the V with the outside note, but the lines will sound a little more familiar and groovy somehow.  The best way to inflect the Melodic Minor sound is to focus on notes in the Melodic Minor arpeggio 1, b3, 5, 7.  This isn't the end approach to take with the substitute modes, but it worth starting with.  By focusing on the Melodic Minor arpeggio, you will begin to see the other modes in relationship to the Melodic Minor harmony.

The chart provided shows all the Super-Locrian, Lydian b7, Mixolydian b6 and Dorian b9 modes against the Mixolydian of a V chord.

In addition, I've broken each of my mode boxes out and repeated the information for each neck position.  The name 'r6-vi' Aeolian Box is my description of the 4-5 fret position where the Aeolian Mode for would start with its root on the 6th guitar string (low E).  That is the shape of the notes in the position, but the V is still the root in this context.

With the mode boxes, I've also stripped this box down to the arpeggios for each mode.  The yellow ring indicates the Root of the Melodic Minor.  Therefore, for the right-hand, stripped down box of the Super-Lociran, Lydian b7, etc., shows the Melodic Minor arpeggio, with the yellow ring as the root.  This outlines how to play a really strong Jazz-Minor sound against these altered dominants.

Try looping a passage with an altered dominant like a Dom #11, and find the mode of the Melodic Minor (Lydian b7 in this case) that works best over it.  Play the melodic minor mode over the V chord -- maybe even imagine the arpeggio of the V chord dimly sitting 'underneath' the mode you are playing.  Then try and make a line solely comprised of the Melodic Minor arpeggio before resolving to the next chord.  Try this in various positions over the neck until you start to see the juxtaposed relationship.  You should practice until you can see your Mixolydian notes or your V arpeggio, and then immediately super-impose the applicable Melodic Minor mode, understanding the 'essential tones' (3rd & 7th) of the substitute mode.

Once you are facile at seeing each mode in relation to the Dominant arpeggio the V, you can begin focusing on structuring lines that really capture the essential tones of the V chord while also including the altered notes of the chord on the lead sheet, pulling you toward resolution with an essential tone of the one.

I made this chart to highlight the Essential Chord Tones (ECTs) for each chord in a diatonic progression relative to the numbers in the Key scale (Ionian Major).  My shorthand for this concept is the "Diatonic Exchange Rate." 

When you play the root of the ii chord, you are just playing the second note of the Key scale.  The third of the ii chord is simply the 4 of the Key scale.  If you think of just these number for each chord in the progression, you can focus on the intervals of the Major scale instead of thinking about arpeggios relative to the Major scale.

I thought this might be helpful to come back to in light of chord solos.  In a chord solo, we have a melody, say on the 'B' string.  For each note we want to accompany with a chord, we have to find at least one ECT common to the chord for the rest of our fingers.  For a ii chord, we would really implicate a minor strongest if we have the flat 3rd of the ii.  Instead of finding the root of the ii and then finding its b3, I would rather just go directly to that note, which happens to simply be the 4 of whatever key I'm in. 

The chords are ordered in 4ths/5ths, common to progressions in Western music.  If you go bottom to top, you are moving in 4ths.

On the second page I grouped the ECTs in order of precedence.  Minors differentiate themselves from Major by virtue of the b3, where as Dominants differentiate by the b7.  You will see a pattern here: moving in 4ths, the third is the seven of the next chord in the sequence.

In the PDF below, I have diagrammed the arpeggios in each 'mode box' for diatonic chords with the 'diatonic exchange rate' pasted on each note.  I excluded the IVmaj7 on the first page for room, but it is diagrammed on page 5.  I also added some extra diagrams for altered dominants.

This chart shows the 'boxes' or scale patterns I typically visualize across the neck for a key.  Each box corresponds to a mode with the root on the sixth string.  If you don't know what a mode is, it is just the notes of a Major scale, but with the root on a different key.  For instance, Dorian is the major key scale if you use the second tone as the root.  Mixolydian is the mode if you use the fifth tone of the major scale as the root.

In the 'CAGED' method, each box also corresponds to an open chord fingering (and it's arpeggio).  For instance, the open C chord fits over the r6 Phrygian fingering (that starts on the 6th string).

I've also included the intervals to the I chord.  I used roman numerals for the ii and V to impress that these numbers are where the scales start for other chords in a diatonic (major) progression.* The ii-V-I is about the most important progression in jazz, so being able to visualize the relationship of these roots are key.  However, it extends to all the diatonic chords.  The root of the vi chord is always on the 6th tone.  You can see with the Aeolian mode (which starts on 6) that 'Aeolian' is a perfect scale to play over the vi chord.  Phrygian is the best mode to play over the iii chord, etc.

I also included the Locrian and Lydian modes, although I don't visualize them so much.  They are so close to the other fingerings, it is harder to distinguish which box you are in.  It is good to practice all modes to see how the sound, however. 

It is essential to know where the 7 is in the major scale however.  It is not only a 'guide tone' of a I7 chord, but it is the root of the vii chord - always a min7b5.  When you know all the intervallic relationships, you can quickly find a root based on the progression -- then position a chord and find the scalular notes or arpeggios.

*It is too unwieldy to use roman numerals throughout the chart because 'iv' and 'vi' get confusing.

Thanks to the CAGED method, I know the shapes of all the major scale positions well.  But I'm still lagging visualizing a mode if the mode's root is not on the first or sixth string.  I made this chart to help me memorize the shapes for all the modes for all the roots.