Below is a chart of the Major Scale and Diatonic Arpeggios on guitar.

The pdf contains the Major scale with the seven modes, broken out into positions of the fretboard for a vertical fingering of each mode.  These 'boxes' of fingerings -- which I've termed R6 mode boxes -- are the shapes I memorized to learn the fretboard.  I call them R6 Mode Boxes, because they are distinct shapes of vertical fingerings for each mode with the Root on the 6 string.  They are chunks of the fretboard I can instantly visualize and distinguish -- giving me bearings on where everything else is.

By learning vertical diatonic arpeggios over these chunks -- the vertical scale boxes -- you will begin to learn the layout of the Major scale over the entire fretboard.  As you learn the Major Diatonic Chord Progression moving up the neck rooted on the sixth string, these arpeggio shapes can be 'landmarks' of where you are on the neck.  From an arpeggio, you can fill in the rest of the notes that make up a particular mode.  To have complete fluency, you must understand how to arpeggiate any chord within these seven R6 Mode boxes -- with the chord's root falling on any of the six strings. That is where the third and final section of the pdf comes in -- it shows the arpeggios for each of the seven degrees within each R6 mode box position.  For each 'chunk' of the Major scale, you should be able to visualize all the arpeggios in the Diatonic Chord Progression.

When playing over changes, every nanosecond counts. For each chord in a bar of music, the 'harmonic hierarchy' below is the order in which I visualize the 'best' notes to play:

1) the 'essential' chord tones -- third and seventh -- which have a colored outline on the chart
2) the arpeggio of the chord (root, third, fifth, seventh)
3) the chord's mode, or scale tones

An advanced player will also evaluate the harmonic hierarchy of the next chord to the the equation, not to mention arpeggios and scales of substitutions or altered sounds, outside the scope of this chart.

​The Major scale is perhaps 'the' cornerstone of Western music.  The Major scale is a seven-note selection of notes within the chromatic scale (the chromatic scale contains every note on the guitar).  Each of the Major scale's seven notes (or 'degrees') have a Mode and Arpeggio linked to them.

If you shift the root of the scale to a different note of the scale, you will be playing a different mode.  As the Major scale has seven notes or degrees, there are seven Modes in the Major scale.  The 'Ionian' mode is identical to the Major scale because they have the same Root -- the first note of a scale that sounds like 'home.'  When you play the notes of the Major scale starting from the second note, you are playing the Dorian mode. This is the mode for the second degree of the Major scale.  The degrees are usually notated as roman numerals.  So we associate Dorian with the roman numeral 'II'.  While 'II' is common -- it is more correct to use a lower case 'ii' for Dorian, but that will be discussed later.  Just know that 'II' or 'ii' refers to 'the Two Chord' in a Diatonic progression.

Moving the root note along each of the degrees of the Major scale gives you each of the seven modes.  If you play all seven notes of the Major scale starting from the second note, it 'sounds Dorian.'  Eight notes up, you reach a note that sounds like you've completed a circle.  If that 'home' tone happens to be the second note of the Major scale -- you are in the Dorian mode of the Major key.

Each degree or Major scale tone (one of the 'dots' on the chart) also has an 'arpeggio' associated with its mode.  Arpeggios are a selected group of notes in a scale played sequentially.  If the notes of an arpeggio are strummed at once, that is called a chord.  Arpeggios and chords have the same notes.

The chords associated with each of the seven degrees of the Major scale are called the 'Major Diatonic Progression':

​The diatonic '7th' chords are found by skipping every other note in a given mode.  Going back to the second degree and the Dorian mode -- if we play every other note in the Dorian mode to the next octave, we get and arpeggio for 'the Two chord' -- the diatonic chord for the second degree (represented by the roman numeral 'II' or 'ii').

The arpeggio for the I and the ii in a Major key have a different quality.  The 'One' chord has a Major third and a Perfect Seventh -- creating a Major 7th chord.  The 'third' scale tone of the 'One' chord is the third 'dot' in the scale (Ionian, in this case) when ascending  from the root.  The 'seven' is the seventh 'dot' in the scale, the note just before the next octave is reached. 

The 'Two' chord in the Major Diatonic Progression is a Minor 7th chord.  That is because we are now skipping notes of the mode starting on the II (second note in a major scale now functioning as the root).  The distance from dot 'one' to dot 'three' in the Dorian scale is shorter than the distance from 'one' to 'three' for Ionian.  With Ionian, the 'third' note of the scale is four frets from the root.  However, when you count scale notes (dots) starting on the Root of the Dorian mode/scale, the 'third' note in Dorian is only three frets away from the Dorian root.  We say the Dorian's 'third' is 'flatted' one semi-tone , or one fret. 

The distance between scale tones (dots) is called an 'interval.'  Distance is measured on the guitar in frets.  The distance of one fret is a 'semi-tone'.  Two frets on the guitar represents a 'whole-tone.'  The interval's quality always depends on how the distances line up with the Major scale.

A 'flatted third' is also called a Minor 3rd, because it signals that a chord is Minor.  Major thirds (four frets) and flat-thirds (three frets) are both 'intervals.'  

All the minor chords in the Major Scale also have 'flatted 7ths.'  The 'sevenths' of these Minor chords are one fret (or semi-tone) closer to the root than with a Major chord -- they are 'flatted' from the Perfect 7th of the Ionian Major.  The differences of intervals, especially 'thirds' and 'sevenths', are what give chords their quality -- a 'Major' or 'Minor' sound.

There are four qualities of chords in the Major Diatonic Chord Progression:

• Major: Major 3rd, Perfect 7th
• Minor: Minor 3rd, Flat 7th
• Dominant: Major 3rd, Flat 7th
• Half-Diminished (aka Min7b5): Minor 3rd, Flat 5, Flat 7

Even though we have three 'Minor-Seven' chords in the Major Diatonic Progression (plus a Half-diminished -- a minor with a flatted-five), each chord's associated scales are different.  This is because at least one of the intervals (fret distances) of scale tones is different in every mode.  Every mode in the Major scale has seven notes and seven intervals.  Once again, scale tones are black dots and an interval is the fret distance from the root to said dot.  Every mode has a 'Root', a 'two', a 'three', a 'four', a 'five', a 'six' and a 'seven'.

To make things slightly more confusing (but 'hipper' for the jazzbo) all the black dots we skipped over to make any Diatonic chord will have an 'alias' called an 'extension.'  It is not important to understand extension right now -- that's something that will make more sense when you move beyond the Diatonic chords we are focusing on here.  It is useful to learn that the 'two' has a secret 'code-name' -- which is 'nine.'  An 'eleven' is code for 'four', and a 'thirteen' is code for 'sixth.'  Just be aware that each of these following equations represent the same tone harmonically speaking:

• 2nd  = '9'
• 4th = '11'
• 6th ='13'

Notice these are the notes we are skipping to make a chord.  They are outside a given scale's arpeggio or chord tones.  It is not essential to learn these code-names immediately, but I've notated the charts this way for the jazzbo.

There are three minor-seven chords plus the minor-seven-flat-five in the Major Diatonic Progression.  It is most correct to cite the Roman Numerals for minor modes with lower-case Roman numerals.  Therefore, the Diatonic minors are: the ii, the iii, the vi and a special half-diminished minor -- the vii -- which has a flatted fifth.  Again -- these roman numerals are all scale degrees counting up along our original Major scale in the Ionian mode.

While the chords of the ii, iii, and vi all have the same intervallic formula (Root, b3, 5, b7), the intervallic formula of the scale for the ii, iii, vi (Dorian, Phrygian, Aeolian) are all different.  The differences in the minor modes lay in the notes we happened to skip over making the particular mode's minor chord.  For instance, the Phrygian scale has a b9 (remember, 9 is code for 2 -- the second note in the scale). 

The point is that while the three minor-seven chords in the Diatonic progression all have the same intervals in their arpeggio (R, b3, 5, b7), the intervals of the scale associated with them are different.   Look at the sixth scale tone of Aeolian versus Dorian. If you try and play the Dorian scale over each of the minor chords in a Diatonic progression -- it might sound a little 'off' if the rest of the band is thinking iii chord or vi chord.

If you understand all of the above, you will have an excellent foundation for playing jazz or any type of western music.  The Diatonic Chords in a song's given key are what make up the vast majority of popular chord progressions.  If a song's chords are all Diatonic chords in a Major key, any note in that key's Major scale are 'safe' notes to play -- all those dots will be 'consonant.'  If you are able to play an arpeggio for a given chord when it appears in a chord progression (black dots in the second section of the PDF), those arpeggiated notes will sound extremely 'strong' harmonically.  If you orient a line with a chord's mode/scale (e.g. play Dorian over a ii chord), that will also sound very 'harmonic.'  Of course, you may well know that jazz stretches 'outside' what is is 'safe' and toys with what is 'harmonic', but I vote for learning how to walk before trying to run.

The goal is for your eyes, ears and fingers to instantly know where all the 'strong' notes (black dots) are when a particular chord is playing.  The configuration of these dots should be constantly changing in your mind with each chord.  This will take a lot of practice -- probably at least a year for a beginner working incessantly with a teacher and very likely more.  I am still finding holes in what I know many years in.  But it is possible and it is worth it! Being able to visualize all the Diatonic modes and chords of the Major scale from anywhere on the fretboard is a must for the jazz guitar player.

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 world of harmony as explained by a Barry Harris creation story...

First there was nothing.  From nothing, God created the chromatic scale -- the world for all music to inhabit.

​The world of the living is 12 notes:
World = Chromatic Scale
C, C#, D, D#, E, F, G, G#, A, A#, B

The world is divided in half, creating Man and Woman. Each of them takes 6 tones of the world.
Man: C, D, E, G, A
Woman: C#, D#, E, G, A, B

There are three babies from these parents -- all diminished. Each diminished receives 2 tones from man and and 2 tones from woman whole-tone scales. The formula for diminished is 1, b3, #11, bb7(6).  The b3 and bb7 are 'chromosomes' from the opposite parent.  All diminished scales are inversions of one of these three sets of notes.

C, Eb, Gb, A
C#, E, G, Bb
D, F, Ab, Cb

The 'Man' and 'Woman' Parents (whole-tones) are the first major scales.  They have Major 3.
Children (diminished) are the first minor scales.  They have Minor 3.

So far we know there is 1 chromatic scale.
There are 2 whole tones scales.
There are 3 diminished scales.

Those 3 diminished babies (birthed by the two diminished scales) will now have babies.  The first baby is the dominant.  You get this baby by altering one "chromosome" aka, lowering one tone a half-step.  

Dominants (1,3,5,b7) - are diminished with one tone moved down a half-step.  Each diminished can have four baby dominants. 

Example, Cdim can have B7, D7, F7, Ab7 babies.

C, Eb, Gb, A becomes
B [C down half-step], D#(Eb), F#(Gb), A =  B7

C, Eb, Gb, A becomes
D, Gb, A, C = D7

C, Eb, Gb, A becomes
F, A, C, D#(Eb) = F7

C, Eb, Gb, A becomes
Ab, C, Eb, Gb = Ab7

The diminished 'scale' is created putting two of the three diminished arpeggios together -- all the chromosomes of a diminished, and all the tonics of the baby dominants.  Following the Root world of C, that would be:
C, D, Eb, F, Gb, Ab, A, B

This is known as the 'Whole-Half' Diminished scale which starts with a whole-tone jump followed by a half-tone jump.  This gives us a Major 9 and a Minor 3.

All the diminished children (birthed by the two Whole-Tone scales) have babies.  The first baby is the Dominant.  You get this baby by altering one "chromosome" aka, lowering one tone a half-step.  

Dominants (1,3,5,b7) - are diminished with one tone moved down a half-step.  Each diminished can have four baby dominants. 

Example, Cdim can have B7, D7, F7, Ab7 babies.

C, Eb, Gb, A becomes
B [C down half-step], D#(Eb), F#(Gb), A =  B7

C, Eb, Gb, A becomes
D, Gb, A, C = D7

C, Eb, Gb, A becomes
F, A, C, D#(Eb) = F7

C, Eb, Gb, A becomes
Ab, C, Eb, Gb = Ab7

If you raise a tone of a diminished a half-step and the baby you get is a Min6 (1, b3, 5, 6)

C, Eb, Gb, A becomes
Gb, A, Db[C up half-step], Eb =  Gbmin6 (Eb-7b5)

The Half-Diminished and Minor 6 arpeggios are inversions of each other.

Raise two tones of a diminished a half-step and the baby you get is a Maj6 (1, 3, 5, 6)

C, Eb, Gb, A becomes
A, C#[C up half-step], E[Eb up half-step], F#(Gb)  =  A6 (F#min7)

The Major 6 and Minor 7 arpeggios are inversions of each other.

Lower two different tones of a diminished a half-step and the baby you get is also a Maj 6 (1, 3, 5, 6)

C, Eb, Gb, A becomes
D[Eb down half-step], F#(Gb), A, B[C down half-step]  =  D6 (Bmin7)

From the Chromatic split you get the Whole-Tone.
From the Whole Tone's intermingling, you get the three diminished.
By moving one or two tones up or down from the diminished arpeggios, you get all the Major 6, Minor 7, Half-Diminished, and Dominant arpeggios.

From each diminished:
lower one tone a half-step = dominant
raise one tone a half-step = min6 (min7b5 inversion)
raise two different tones a half-step = Maj6 (min7 inversion)
lower two different tones a half-step = Maj6 (min7 inversion)

Here is a great guide for beginners regarding jazz harmony:

The Ultimate No Nonsense Guide to Jazz Harmony

The contents are pretty much what's labeled on the tin -- straightforward explanations of concepts like:

• II-V-I and other cadences
• Secondary Dominants
• Backdoor Progressions
• Backcycling
• Tags
• Altered Harmony

​Knowing your intervals helps you quickly find the roots of classic chord progressions.  Since many chord progressions in classic jazz tunes move in fourths, it is a good idea to learn the circle of fourths and be able to move in fourths at any point on the guitar neck.  This pdf might help you locate all the perfect intervals in the major scale.

​Since the guitar is stacked in fourths, moving vertically from bottom string to top is automatically a fourths motion.  In the image below you can see how starting on the third on the low E and traveling to the high E will move you though the roots of a 3-6-2-5-1 and then to the four.  Remember that strings 2 and 1 (B and E) are tonally shifted up a fret.  The vii happens to be a tri-tone away from the IV. Tri-tones are basically a 'diagonal' away on the fretboard.

​
You can see how a 3-6-2-5-1 would look on the circle of fourths below.  Moving in a counter-clockwise motion brings you from the iii around to the I and then to the IV if you continue.  In order to get to the remaining interval -- the vii -- you would have to jump to the other side of the circle. Diametrically opposite tones on the circle are a tritone apart. 

​Here's a million dollar lesson for free from Bruce Forman on his Guitarwank podcast (episode '99R' April 4th, 2018 ~71:28).

This is a great exercise for people coming from a blues background trying to get a little jazz color in their playing.  The exercise helps get the altered sounds into your ear, even though it is a little bit of a 'fudge.'  Most importantly, it is focused on motif development rather than focusing on learning the shapes to play over each chord.  Instead of trying to re-visualize your fretboard's landscape over every chord, this exercise focuses on making phrases that resolve, i.e. 'making music.'

It is not uncommon for blues players to move their 9th voicing (for example) up a half-step to reference the IV chord. That half-step sound is what a beginner should be looking for when they are trying to 'jazz' up their playing.  If you play all the notes in this half step movement, you will feel how these notes compel you (lead you) to resolve back into the key.  This is how jazz players think.  The jazzbo is constantly introducing tension -- stretching a rubber band -- and then resolving, letting the rubber band come back to it's natural shape.

The ii-V-I is the progression to learn for jazz.  In G the progression is A minor, D7, G major.  If you line up all the notes in these chords, they are all in Gmaj.  It's a 'diatonic' progression -- all the chords' notes are in the same key. However, true jazz players do a lot of stuff to build up their tension playing 'outside' Gmaj.  I reality, it is more hip to play A minor, Ab7, Gmajor -- the tritone substitution. But let's simplify our ability to play this way without thinking to much.


The Exercise:

1) Play a simple phrase over the ii chord -- which is pretty much just a Dorian A minor -- the classic blues scale works.

2) Now repeat this phrase down a half-step.

3) Finally, resovle the phrase by ear.

Step one is the ii chord, step two is the five chord, step three is the one.  The brilliance of this exercise is it forces you to make music more than learning scales and substitutions and theory.  Practicing this helps you develop motifs, gets the altered sound in your ears, and helps you intuit where the leading tones resolve to G major.

There is a theoretical fudge to this exercise in that you are playing a minor on the five instead of a dominant.  But don't get your hackles up over this as a beginner.  Duke Ellington said, "If it sounds good, it is good."  So try to make it sound good. One of the gems of this exercise is you are forced to listen to yourself in the context of the progression.  You are listening to what you are playing because you have to repeat your own phrase.  You are not 'coloring by numbers,' but getting involved with what you are creating.  


Bonus Exercise:

1) Play a simple phrase over the ii chord (again just a blues pentatonic or dorian phrase in Aminor will work).

2) Repeat the phrase a minor third up (that's three frets or semi-tones).

3) Resolve to G major by ear.

To recap -- you are playing something melodic, committing it to memory and repeating it three frets up, then finding a note to answer in the G major scale.

Here you are essentially playing the iv minor (C-) in step two. Some people call iv- the 'important' chord.  The iv minor always wants to resolve to the one.  Now you have a whole harmonic substitution added to your vocabulary.  Try substituting the iv- in place of your five while comping.


Double Bonus Exercise:

Now let's actually play a REAL tritone substitution to get the most tension-resolution out of our line -- let's really stretch the rubber-band. Traditionally we say the tritone is Amin, Ab7, Gmaj.  But what is Ab7 -- just Ebmin with a differnt root!  The tritone is actually 2 minor thirds up from the one chord.   

1) Play a minor phrase over the ii chord.

2) Repeat the phrase 2 minor thirds up (Eb for resolving to Gmaj).

3) Resolve to the root major by ear.

With these three exercises, you've just increased your ii-V-I vocabulary about 400%!

In the Guitarwank podcast, Bruce refers to a youtube video where Josh Smith attempts to explain the same material that Bruce taught him.  I believe that video is here.  Even if you are a seasoned jazzbo -- try these exercises out.  You'll be glad you did.

Through the wonders of youtube and other social media offering ideas of what I might be interested in, I have started to investigate the teaching of Barry Harris.  Up to now, I would say my understanding of Jazz is derived mostly from the Berklee method which I found very logical and easy to get up and running playing jazz.  They have done a good job at codifying a lot, but some would argue the strategies might be revisionist.

Barry Harris, a pianist in the mix at the birth of bebop, is one such cat who has been trying to educate how the music really originated and functions.  I've seen a lot of scattered information and videos of Barry Harris teaching over the past few days, but this fellow's blog post seems like as good an introduction as any into the world of Barry Harris for guitar -- enough to give a taste of whether it is a alternative from the Berklee method you'll want to investigate.  It has a short example PDF with chord boxes and links to more in depth educational materials.

I also ran across this introduction which gets more in depth into the 'origin story' of scales an chords according to Barry Harris with some staff examples.

Additionally, I've found this chap on You Tube who's videos can stretch your thinking outside of the Berklee method into Barrytown.  Here is his mile-a-minute demo on harmonic theory which touches on some Barry Harris ideas. Worth subscribing to, Christian Miller offers the 'Altered Scale' might be a bit of a revisionist device to approximate the approaches the original bopheads probably used.  His videos move quickly and you'll need some pre-requisite knowledge, but offer some tasty lick examples, especially in this quick-fast lesson on Bop Harmony.

​This is my first attempt at a chord melody.  I was told creating a chord melody would help me memorize the chord changes for a particular song.  It has also helped me figure out a few new fingerings.

I put chord boxes above the chords, stacking alternates at times.  The hollow circles are the second or third note to play holding the position (or en route to the next chord).  If you know the melody, you should be able to figure it out -- some go to a hollow dot and back to a solid dot.

The premise of constructing the chord melody is relatively simple -- the melody should run on the top two or three strings so you can stack the rest of the chord on the bottom strings.  The melody note should always have the highest pitch of all the notes in a chord.  It is not necessary to have a chord for every single note.  I always tried to aim to have at least the essential tones (3rd and 7th of the chord) and, if possible, the root note.  Often this required some inversions.

Please let me know if I have an error or typo.

Here is my crazy mnemonic device for memorizing the Circle of Fourths.  If you haven't got a circle, try the one I made here. 

Another mnemonic  you might try is Be Ever Alert During Guitar Class (Forever).

Another mnemonic for going in the direction of fifths I've learned is Fine Classical Guitarists Demand Accurate Execution (Buddy).

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.