An Interesting Feature of the Modes

Instead of thinking of the modes as beginning on different degrees of a single scale, it's more challenging to play all the seven modes on a single base note.
For example, using C for convenience, you have:
Ionian: C-D-E-F-G-A-B-C.
Dorian: C-D-Eb-F-G-A-Bb-C (the second degree of Bb major).
Phrygian: C-Db-Eb-F-G-Ab-B-C (the third degree of Ab major).
Lydian: C-D-E-F#-G-A-B-C (the fourth degree of G major).
Mixolydian: C-D-E-F-G-A-Bb-C (the fifth degree of F major).
Aeolian: C-D-Eb-F-G-Ab-Bb-C (the sixth degree of Eb major, the relative minor).
Locrian: C-Db-E-F-Gb-A-B-C (the seventh degree of Db major).

An interesting routine that helps you think modally is to start in the Lydian mode and modify the modes one after the other. An interesting thing happens when you do this.

Starting on C Lydian one has: C-D-E-F#-G-A-B-C.
Flatting the fourth, you have C major (or C Ionian): C-D-E-F-G-A-B-C.
Flatting the seventh, you have C Mixolydian: C-D-E-F-G-A-Bb-C.
Flatting the third, you have C Dorian: C-D-Eb-F-G-A-Bb-C.
Flatting the sixth, you have C Aeolian: C-D-Eb-F-G-Ab-Bb-C.
Flatting the second you have C Phrygian: C-Db-Eb-F-G-Ab-Bb-C.
Flatting the fifth you have C Locrian: C-Db-Eb-F-Gb-Ab-Bb-C.

Then, what 's left to flat? The tonic. If you lower C to Cb (enharmonically, B natural), you find yourself in the B Lydian mode:
Cb-Db-Eb-F-Gb-Ab-Bb-Cb, which is equivalent to B-C#-D#-E#-F#-G#-A#B.

If you go on, playing B Lydian, B Ionian, etc., you end up with B Locrian (B-C-D-E-F-G-A-B), and when you flat the B, you are in Bb Lydian (Bb-C-D-E natural-F-G-A-Bb.

If you look at the key-signatures of the modes as you cycle through them this way, you see that they follow the circle of fifths (G-C-F-Bb-Eb-Ab-Db-Gb-Cb).

The inner logic the relations among the modes is wonderful.