Re Gregorian Chant (plainchant): monophonic. One single moving melodic line; no harmony.
It may come as a surprise to learn that there is an important similarity to jazz. No kidding! It has been asked a few times on this thread what exactly "modal" jazz is. Like modal jazz, plainchant is composed within the framework of a "mode"; modes in music as devised by the ancient Greeks. The simplest way to explain it is this:
Think of the most familiar, and simplest to visualize on a piano keyboard, scale. The C Major scale; eight successive white keys beginning on a C and ending on another C one octave higher (CDEFGABC; every scale is made up of eight notes). The first and last notes of the scale have a natural aural "pull"; the movement of a melody using that scale "wants" to end (resolve) on that note.
Sing "Happy Birthday", a very simple tune in a Major key: the melody starts on the fifth note (G) of a C Major scale and ends on a C. Now, sing it again, but this time, instead of ending on the last "you", end it on "to".
"...... Happy Birthday, dear Ro-ok, Happy Birthday, to....."
Notice how strongly your ear wants to go to "you"; to resolve. That is part of the "flavor" of a Major tonality.
Visualize the white keys on the piano keyboard again:
CDEFGABC(CDEFGABCDEFGABCDEFGABCDEFGABC etc.)
Now, instead of starting the scale on the "C", start it on the "D" and go up the keyboard to the "D" one octave higher: DEFGABCD
That is the first of the seven "modes"; Dorian mode. It is a mode very commonly used in Jazz with its own distinct "flavor"; different from Major and every other mode. It has its unique "flavor" due to the mathematical relationships of the notes within that particular scale and the subsequently weaker or stronger aural "pulls" to each note of that scale as compared to Major and the other modes.
Jazz tune in Dorian mode:
http://m.youtube.com/watch?v=DEC8nqT6Rrk