What are some concrete melodic and harmonic tools to establish the correct tonic center in a lydian melody?
The reason for asking about lydian specifically is that there is no minor seventh for the dominant, which would seem like a sure-fire way to establish the tonic.
One of the first things to observe is that the tritone F#-C should be avoided, because it suggests a dominant sound (leading to G). Consequently, don't use the II7 chord (D7 in the case of C lydian), and don't use IVm7(b5) (F#m7(b5) in C lydian) either, because both contain the tritone. Note that the triad II (D major triad) can be used.
Progressions in modal pieces are usually rather simple, with a strong emphasis of the root chord (establishing the root), and the character note of the mode (#4 for lydian) must be emphasized (i.e. use Cmaj7(#11)). Often the root note is used as a pedal in order to make sure that the mode is correctly perceived by the listener. The harmony above the pedal is mainly used to create "sounds", and does not "function" in any other way than to establish the sound of the mode.
Also note that in lydian (and also in dorian) all notes of the scale are available tensions on the I chord, so the modal sound is self-contained and a cadence to tonic is in fact not necessary.
You can play the D7 but with the C on bass, and you can play also the Cmaj7♯11 as mentioned above (with a tritone!) .
The main thing you want to focus on is the half step relationships in the mode.
Think about the major scale. The most common cadence is the V7-I (other most common: vii°-I). Why? Short version, we have the tritone (B and F) both moving by half step into the tonic notes (C and E).
Compare this to lydian. The half step relationship has changed. Instead of F down to E, we now have an F# up to a G. It doesn't seem like much, but this change is HUGE for getting the lydian sound. Both are moving UP, which helps contribute to the brightness of lydian and why it feels higher than ionian (major).
Now the trick becomes finding lydian chords that contain both the half steps moving into the tonic notes (B to C, F# to G). The basic triad with the strongest pull is B minor. Any extended chord that contains this triad (or at least the B and F#) should work.
Hopefully this helps. Modes are a really cool addition to your toolbox once you get them under control. If you're interested, I've done a 3 part blog series specifically on the lydian mode. You can find it at my blog: Mitchell Makes Music.
