What do 'dominant' and 'plagal' mean in medieval music?

Question

In classical style brief definitions would be...

Dominant: a major chord, built on the tone a perfect fifth above the tonic, used to form authentic, half, and deceptive cadences.

Plagal: a cadence type (disputed by some) moving from a chord without the leading tone to the tonic chord.

Can someone offer brief descriptions for the meanings in medieval music? Of course, more than a sentence is fine. I just would like something concise.

My current understanding is 'dominant' is a tone other than the tonic that the melody tends to center around. I'm not sure I really understand how that dominant would really be treated. In E Phrygian C is the dominant. Won't centering around that start to sound (perhaps only to modern ears) like C major?

Plagal is the form of the scale where the tonic is placed in the middle of the ambitus (?) a 4th above lowest tone and a 5th below the highest tone. When a plagal scale was used did the melody actually confined to that ambitus? Like is D Hypodorian were the A's the lowest and highest tones.

Answer 1

I consulted Van Aristoxenos tot Stockhausen by Louis Peter Grijp & Paul Scheepers, two of my professors when I studied musicology in the nineties.

In medieval treatises on music theory, generally eight tonos (gregorian modes) are described, in four authentic-plagal pairs

tonus                   finalis   tenor/dominant
1 protus autentus       D         a
2 protus plagalis       D         F
3 deuterus autentus     E         c
4 deuterus plagalis     E         a
5 tritus autentus       F         c
6 tritus plagalis       F         a
7 tetrardus autentus    G         d
8 tetrardus plagalis    G         c

The finalis is the finishing note in a basic tonal system:

Γ A B C D E F G a b c d e f g

Which we could write in modern notation as:

G A B c d e f g a b c' d' e' f' g'

In the authentic mode the melody would be mostly above the finalis. In the plagal (derived) mode the melody would be both below and above it, going at most a fifth above the finalis.

The tenor or dominant is a reciting tone.

Some authors noted that practise did not always follow their schemes so well. Different ending notes (finalis) would be used, ranges exceeded.

The Greek names for modes were added later on when towards the renaissance there was growing interest in studying ancient Greek texts.