Thanks for writing out the modes like that; thinking of them as based off of the Ionian and Aeolian will definitely make me a little quicker at punching them out.
Thinking of them this way helps demystify the "modes" and helps you look at your fretboard and see mode finger patterns, for example, "Dorian" finger patterns since its just a tweak to the Natural Minor scale (which like I said before, you have to deeply own that scale).
Before I was thinking, "C Mixolydian, IDPLM, 5, C B A G F, F scale has bB, C Mixolydian is C D E F G A bB C", which is obviously a terribly slow thought process, lol. Now, all I have to think is "C Mixolydian is Ionian but with b7." Very useful info, thanks!
The way you were thinking about them is absolutely correct. Music theory defines the relative modes this way, but its not the most useful way to think about them when you look at your fretboard or are thinking about the chords that would naturally work with a given mode. However, it is a powerful way to look at ANY scale, since ANY scale can have its relative and parallel modes defined in this way.
Still, by understanding them in terms of the Major and Natural Minor, all those chord progressions you already know come to mind and you tweak the chord tones accordingly, all the scale patterns on your fretboard come to mind (assuming you've master Major and Natural minor, that's critical), its simply a more functional way to look at them.
Relative Modes of C Major:
I C Ionian C D E F G A B
II D Dorian D E F G A B C
III E Phrygian E F G A B C D
IV F Lydian F G A B C D E
V G Myxolydian G A B C D E F
VI A Aeolian A B C D E F G
VII B Locrian B C D E F G A
All of the relative modes of C Major have the same key signature, C Major / A Minor, but notice the root changes for each mode.
Parallel Modes of C Major
I C Ionian, C D E F G A B C, key signature is C Major/A minor, root is C
II C Dorian, C D Eb F G A Bb C, key signature is Bb Major/G minor, root is C
III C Phrygian C Db Eb F G Ab Bb C, key signature is Ab Major/F minor, root is C
IV C Lydian C D E F# G A B C, key signature is G Major/E minor, root is C
V C Myxolydian C D E F G A Bb C, key signature is F Major/D minor, root is C
VI C Aeolian C D Eb F G Ab Bb C, key signature is Eb major/C minor, root is C
VII C Locrian C Db Eb F Gb Ab Bb C, key signature is Db Major/Bb Minor, root is C
The root is the same, but the key signature keeps changing.
Drilling down the modes of any Scale:
For example, what are the relative modes of C Harmonic Minor, (which we all know is a little tweak to the natural minor scale, it has a raised 7th), when we drill them down, that little tweak leads to some interesting modes, most notably the 5th mode of the harmonic minor scale, which is Phrygian Dominant (a mode that a lot of shredders like, Joe Satriani is all over this mode).
From my perspective, the 1st (Harmonic minor) and 5th (Phrygian Dominant) modes are the most useful mode to pop out of this scale. The others, I can just tell, aren't interesting to my ears, but Jazz guys can appreciate some of the others.
C Harmonic Minor: 1 2 b3 4 5 b6 7 1
D Locrian 6: 1 2b 3 4 5b 6 7b 1, Locrian but with a 6 instead of b6
Eb Ionian Augmented: 1 2 3 4 5# 6 7 1, Ionian but with a raised 5th instead
F Dorian #4: 1 2 b3 #4 5 6 b7 1, Dorian with a raised 4th instead
G Phrygian Dominant, 1 b2 3 4 5 b6 b7 1, its merely Phrygian with a raised 3rd which makes it very interesting since that 3 versus a b3 changes the character of the mode dramatically (which is probably why Satch and others love it, its got a phrygian/minor sound but with a major 3rd instead so it has a major character to it also, which is also why its got its own formal name, i.e. its the most useful mode to emerge from the Harmonic minor scale)
Ab Lydian: #2 1 #2 3 #4 5 6 7 1, Lydian but with a raised 2 also
B Ultra Locrian: 1 b2 b3 b4 b5 b6 bb7 1, Locrian but with a diminished 7
This stuff is pretty exciting; it will be nice to have an actual understanding of what works in jazz solos, instead of just knowing that something sounds right.
I'm a little concerned that if I begin to rely on pitch axis theory too much, I will lose some purely musical/creative ability in my soloing and get locked into always thinking about the "right" modes, but I suppose anything else would be atonal, anyways.
Well, its all very personal. And its a trade off. How much music theory comes to mind when composing/creating?
I play something (simply freely composing, noodling, working out some little melodic or harmonic nugget, not thinking about music theory at all, BUT, when I find something interesting, then, I note from a music theory perspective what is going on, because then I can load my music tool box in my mind with all the fretboard patterns, chords, chord progressions, etc. that work well.
I don't start with music theory, but at some point I always ask music theory what's going on, and then I'm ready to use things from music theory to help develop a musical idea.
Unfortunately, most of us can't simply rely on our ears and musical genious, we have to use these tools to help us from music theory, but from my perspective its not the best place to start, what you feel and hear is the best place to work from, but that's my opinion.
If you give me your email address, I will send you some files that I keep handy that pack a ton of music theory information concerning modes into a small place (like 1 page). They are useful little reference charts, some are MS Excel though .xls, not .gif or .htm