As a follow-up of Some remarks on Gregorian modes, I have written 3 counterpoint melodies to a cantus firmus that is written in a Lydian mode. The cantus is written in the bass, two of the countermelodies are in the alto tessitura and the third is written for soprano.
Given the tension between "writing counterpoint in a Gregorian mode" and "counterpoint as a tonal (not modal) technique" or put more simply between "no raised leading tones" and "raising leading tones", I decided to stick to the first. This to preserve the Lydian feel as much as possible. This is afflicting the ending cadence too: no V-I movement but a VI-I movement.
The cantus firmus is given in F Lydian, i.e., it roughly corresponds to F major with a natural B instead of B flat. I say roughly because we should not treat it that way, as explained before modal music dislikes the tonal idea of tension and release and a Lydian mode offers many possibilities for this approach by supplying us with notes a semitone below the tonic and the dominant. Anyway, here it is.
For tessitura reasons I will transpose it to A Lydian and put the cantus in the bass. This results in the following first-species counterpoint voices.
The reason I'm posting this is to have some reference material when implementing other modes. I'm starting with a major mode only implementation, but to show of the awesomeness of Lilypond and save my notes from yesterday's class I wrote this. When my implementation finds one of these melodies I have absolutely reached my first goal :).