There are several ways to derive note positions in modes patterns. I use semitone sequence intervals. Your first click on it to Jack Campin's website. You can click onto it from my website file on Modes too. I haven't compared mine to his in detail, but I expect them to be the same. [We've been corresponding on old Scots tunes for about 2 years now.] The second click on is more dificult to explain. Authentic/plagal has more to do with range than modes, so go to the 'Renaisance' (spelling?) modes table for the ones that are those used by Bronson (Traditional Tunes of the Child Ballads' and especially 'The Ballad as Song', where the relation between authentic/plagal and the seven normal modes are shown in the article 'Folk-Songs and the Modes') and by Huntington and Herrmann (Sam Henry Songs of the People') and just about everyone else now.

In the Irish tune code table on my website, I show how to use a keynote/mode combination so that all tunes in normal modes that don't have accidentals can be coded numerically, but with letters to indicate octave. I'm working to extending this to the general case with each note a two digit number, the first of which is the note, and the second of which specifes both sharp/normal/flat and the octave. Jack didn't like my first run through. I've just finished a revised version, but will wait till morning to recheck everything.