Originally posted by Azrael
nono dude - the FINALIS is the last (and also first) note of a mode

since when you are starting on a c major scale the lydian mode starts on G - so the finalis in c lydian is G - not C

You have the lydian mode and the mixolydian mode mixed up dewd. ;) In C major the lydian (4th mode of the major scale) mode starts with F (FGABCDEF) not G, that's Mixolydian. Your right modes like lydian are referred to as authentic modes, because there finalis is the lowest note in the scale. i.e. C lydian's finalis would then be C. Modes that are hypo, the finalis is the fourth note in the scale, or plagal. i.e. C hypo-lydian is G,A,B,C,D,E,F,G. As you can see C is the fourth note in the scale.

Back to what I was saying about starting a tune on the fifth above the finalis (or fourth below). In the case of C hypo-lydian that would be G. This makes sense because G is the first note in the C hypo-lydian scale, also makes sense when you think of half plagal cadences. Hypo-modes are truly apparent in half plagal cadences (I-IV), where the finalis is the fourth. Yes they are rare, but you can see where this all works out and has some benefits.

One more thing, a tune written in C hypo-lydian would have a key signature of C major. Although the tune would start on G. Do the opposite, start on C and end on G and you have G mixolydian. If the play C lydian and end on G, that’s just G major. Remember the rule of it's not where you start but where you end, whether it's diatonic or modal. You see this abundantly clear on the modal side in Jazz.

After reading the first sentence in that last paragraph, it’s easy to see why hypo-modes were soon forgotten after the invention of the major scales. C hypo-lydian and C major have the same notes and same finalis. The concept is the you start of the G instead of the tonic, C. A concept still used today but the understanding where it came from is lost.

Ending thought.

C major : starts on C , ends on C
G major : starts on G, ends on G
C lydian : starts on C (or G), ends on C, (in G major)
C hypo-lydian : starts on G, ends on C (in C major)