From http://chananhanspal.com/scale-substitution

Scale substitution is an interesting way to superimpose certain tonalities over certain chords. Remember in the Major Scale Modes page where it is written that you should play the scale that immediately corresponds to the chord, C major chord/ C major Scale, C lydian chord/ C lydian Scale, well, in this page we are going to contradict and have a little look at scale substitution.

Let´s imagine a C minor 7 one chord vamp, here are some scale choices :

• C Dorian
• C Jazz Melodic Minor
• C Harmonic Minor
• C Natural Minor
• C Minor Pentatonic

These are the more consonant choices, however, if you wanted to play less consonant and create some dissonance and play “outside” you could try playing a C minor pentatonic then move it down a semitone to B minor pentatonic, you have to be careful how you do this but here is an example using some chromatic notes:

The reason for moving down to the B minor pentatonic is to create tension. One could analyse the notes of the B minor pentatonic scale in relation to the C minor 11 chord and find some strange note/chord relationships but it would probably be best to think of the scale as a temporary side step from the home key centre. The other option is to side step upwards and play the C# minor pentatonic and then resolve back to C minor pentatonic. 

This type of playing was introduced by John Coltrane, it is an extension of the idea of chordal ambiguity whereby the overall quality of a chord is implicit rather than explicit giving the improviser more freedom to express multiple tonalities in the improvisation. For example, if you play a basic C minor 7 chord C Eb G Bb, the chord structure is well defined and has more stability than if you were to play C F Bb. The C F Bb voicing is a 3 note chord built on fourths, and is less stable because there is no 3rd, as a result of this you have a lot more options in choosing the tonality you want to imply. 

Another option for tension is to treat the C minor 7 as a I chord and play a G altered scale, as if there was a G altered V chord present, and resolve to a C minor scale of your choice, this device is less dissonant than the previous example, but can imply forward motion, in your solo:

If we take a C7 chord and look at the possible scale applications, we have the more consonant choices :

• C Mixolydian (Dominant 7 Scale)
• C Major Pentatonic
• C Lydian Dominant
• G Dorian Minor
• G Minor Pentatonic

Some dissonant choices maybe the C half/whole step diminished, C altered or G altered.

Why?

The notes of the C h/w diminished scale in relation to the C mixolydian:

The implication is the altered sound over the regular C7. With the G altered you can think of the C7 as being the modified I chord in a II V Iand imply the V chord tonality over the C7; this application can really lift a solo giving yet again a kind of forward motion, but be careful how you resolve, remember there is no point of going outside if you don’t know how to come back in.

A quick note about modal jazz…

The type of jazz harmony that revolves around one or few chords is modal jazz. The concept of modal jazz is that you use one mode per chord, this can be challenging since you are restricted to the 7 different notes that make up one mode. A classic example of modal jazz is the album, ‘Kind of Blue’ by Miles Davis; you will notice the recordings illustrate modal playing, but in the solos, the temporal rule is broken, ie. the rule of one chord one mode, as many of the solos particularly by Coltrane will testify. This leads to the idea of bending the rules of modal jazz slightly and using the type of outside playing devices we have looked at.

In this tutorial we’ll have a look at the guitar scales, arpeggios and substitutions we can use to improvise over minor guitar chords, so we can make our guitar solos more interesting. Unless specified, we take a Dm chord as example. Here’s a roundup:

1. The Dorian Scale
   

The 3 minor diatonic scales (Dorian, Phrygian, Aeolian) are the obvious choice for playing over minor chords. Which of the 3 scales you play depends on the harmonic setting and the function of the chords you are playing over.

The Dorian mode is played over II chords, like in a II V I chord progression.

We’ll take a 2 5 1 in C major as an example:

|Dm7          |G7           |Cmaj7        |%             |
|II           |V            |I            |              |          

Over the Dm7 we play the D Dorian scale:

Here’s the scale chart for D Dorian mode in its root position:

The Dorian scale is also used to play over minor chords in modal tunes, like So What.

1. The Phrygian Scale
   

The Phrygian scale is used to play over minor chords that have the function of a III in a harmony. An example is the 3rd bar of a Rhythm Changes:

|Cmaj7  Am7   |Dm7    G7    |Em7    A7    |Dm7    G7     |
|I      VI    |II     V     |III    VI7   |II     V      |

On the Em7 in the 3rd bar we can play the E Phrygian mode. As a side note I want to point out that although you theoretically play the Phrygian mode on the Em7 in a rhythm changes, you don’t think about the Phrygian mode, just think C major (did that make sense, if not, give me a shout).

The E Phrygian scale in its root position:

1. The Aeolian Scale
   

The Aeolian scale (aka relative minor scale) is used to play over minor chords that have a VI function or a I function in minor. An example of a VI is the second chord in a rhythm changes.

The chart for the A Aeolian scale in root position:

4) D Minor Pentatonic Scale or Blues Scale

It can’t get more obvious, very useful, also in a jazz context.

5) A Minor Pentatonic Scale or Blues Scale

The A minor pentatonic scale sounds very nice over Dm7

6) E minor Pentatonic Scale

The E minor pentatonic works nice if you alternate it with D minor pentatonic (on modal tunes). It creates a tension/release kind of thing (see point 10 on this page)

7) D Minor Arpeggio

Surprisingly the Dm7 arpeggio works very well over Dm7. See also: Arpeggio 101 

8) Fmaj7 Arpeggio

An Fmaj7 arpeggio over Dm adds the 9: nice sound.

9) Am7 Arpeggio

One step further is Am7, it adds the 11 to the sound.

10) Em7 Arpeggio

Em7 sounds a little more distant over Dm, but works fine if you alternate it with a Dm arpeggio. 

D   F   A   C   +   E   G   B   D = D Dorian Scale

Examples: Triads Over Minor Chords

11) Dm6 or Bm7b5 Arpeggio

Emphasizing the 6 of a minor chord works nice if the minor chord has a tonic function and not a sub-tonic function (like in a II V). In other words, the minor chord should be the I, not the II. In other words, the minor chord should not be followed by the V (Dm7 should not be followed by G7).

Example of a minor chord with a tonic function:

| Dm7          | Em7b5    A7  |
| Im7           | IIm7b5   V    |

12) G7 Arpeggio

G7 sounds ok over Dm, especially when it has the tonic function. If you use it in a 2 5 1, you can make the b (6) on Dm7 go to #9 and b9 on G7, to the 5 of Cmaj7.

13) The Line ClichéIn tunes where the minor chord spans a couple of bars, like in a minor blues, you can use this little device called the line cliché. This technique is as old as the street and is frequently used by gypsy jazz guitarists. The line cliché is a descending line going chromatically from the 1 of a minor chord to its 6:

1 » 7  » b7 » 6
d » c# » c  » b

From: http://www.jazzguitar.be/minor_guitar_chords.html