Pitch axis theory

Pitch axis theory is a musical technique used in constructing chord progressions. The tonic is used as the bass note, and melodic scales are chosen according to the chords that lie beneath them. "A variety of scales or modes are used, all built around the same tonic pitch."
The pitch axis is the pitch common and most important to the tonic of the initial key and all chords in a chord progression.
Concept.
Each of the seven modern modes is obtainable from any of the others by a sequence of diatonic rotations; by such a sequence, for example, C Ionian (C-D-E-F-G-A-B) becomes D Dorian (D-E-F-G-A-B-C), which becomes E Phrygian (E-F-G-A-B-C-D), and so on, until the original C Ionian mode is obtained. Therefore, each of the seven modes of any of the twelve major keys is a mode of the other six in that particular key.
Pitch axis theory suggests that for each mode, there is a chord that accompanies it. When that chord occurs, the corresponding mode should be used for the melody or for soloing.
The more common modes, along with their chords:
This is the first part of pitch axis theory. The second step is implementing these modes as chords built on a common root. This is best shown with an example.
Examples.
For example:
 lydian
 ABCDEFG
 |
 aeolian -— A -- locrian
 ABCDEFG | ABCDEFG
 mixolydian
 ABCDEFG
Thus the non-diatonic chord progression constructed from chords diatonic to each mode:
 | A5♯11 | A7sus4 | Fmaj7/A | A7sus4 |
 |A-lydian|A-mixolydian|A-aeolian|A-mixolydian|
Joe Satriani: "Satch Boogie".
"No better demonstration of the Pitch Axis device exists than the famous tap-on bridge of 'Satch Boogie'", originally played only on the fifth string.
Joe Satriani: "Not of This Earth".
This song is fully based on the pitch axis of E. The chords E major 13, E minor 7 sharp 5, E major 13, and E 7 suspended 4 imply a transition between E Lydian, E Aeolian, E Lydian, and E Mixolydian. This pattern continues throughout the song, keeping a strong feel of tonality while changing through the modes in a rather disorienting way.
The chord E minor 7 sharp 5 is not a perfect match for E Aeolian. When spelling out the mode to use over this chord, instead of thinking of the chord as E minor 7 sharp 5 (E-F♯-G-A-B♯-C-D-E), think of it as E minor 7 add 6 (E-F♯-G-A-B-C-D-E). Otherwise, the E diminished scale might be a good choice (E-F♯-G-A-A♯-C-C♯-D♯-E)
It is also important to note than in conventional music theory, there is no such thing as an E minor 7 sharp 5 chord. This chord (spelled E, G, C and D) is really a first inversion C major chord with an added 9th (the D), which could also be thought of as a C major chord with an E in the bass, or C/E. From here you could choose to use either a C Ionian or Lydian scale, which would correspond to an E Phrygian or E Aeolian respectively. Whilst this might seem to be making the chord more complicated, it also helps to explain the relative lack of tension and 'major' sound of the chord.
Dream Theater: "Lie".
The transition to the guitar solo in Dream Theater's "Lie" is built on Pitch Axis Theory. The bass and guitar play the root (B) while the keyboardist implies the chords in the progression: B5, B minor 7, B minor 6, G root B and A root B.
The scales used for each of these four chords are B Aeolian (natural minor), B Dorian, C♯ Mixolydian, and E Aeolian, respectively. However, as these are all diatonic modes, they can all be thought of as being based on the root of B. If the scales are shifted to start on B, then the progression appears as B Aeolian, B Dorian, B Lydian, and B Phrygian.
Artists who use pitch axis theory.
These artists use pitch axis theory and shifting modes in their music.