Gavin,

Actually I have my students do exactly this for their first MH 1 project. If you are using the Grout/Palisca/Burkholder History of Western Music, look at the organum duplum setting in the anthology by Leonin. Take any gradual and treat it in the same way. As far as theory references, that's a good question. I'll look around and see what I can find. Micrologus by Guido talks about organum, for a period theory treatise.

My schola wanted to try organum for Christmas chant. We are trying organum some parts of the chant, but it seems be hard for for the group who has to sing 4th below the melody suddenly at certain points. Awkard for their voice line. Incantu, did you find that step by step method you mentioned above?

Glad this got bumped; I had forgotten all about it. Here is the bibliographic reference (from an article by Alejandro Enrique Planchart in A Performer's Guide to Medieval Music, ed. Duffin):

Anonymous I. "Tractatus de Consonantiis Musicalibus," in Edmond de Coussemaker, Scriptorum de Musica Medii Aevi, 4 vols. (Paris, 1864-76; reprint Hildesheim, 1963), I, p. 300.

The whole article is about organum and mentions several other prime sources on the subject.

I just ordered Alejandro one. It looks good.
Thanks
Mia

In my limited experience with organum and single-sex ensembles, it seems to be easier for folks to sing a 5th above as opposed to a 4th below.

So Mary Jane, when the group sings the 5th above only in certain parts of the chant, do you have them sing the melody and jump to 5th above melody when it's time, or they just join only for that parts? I hope I'm making any sense to you.

For Advent Sunday Mass, we add a drome note to the 'Mary Berry' version of O Come, O Come Emmanuel & On Jordan's Bank (Praetorius). This works out well since we use no organ for any part of our EF Mass with the exception of the Third Sunday. The drone note can work well with some short propers as long as the piece does not wander far from its original tonal center. However adding a drone could sound 'gimicky' if used too often.

Are we only talking parallel organum here? Gets kind of old. I'll take that Leonin and Perotin discant organum that MJ doesn't want any old time!

There's a whole lot of improvised organum between strict parallel and composed discant. But parallel should be easy enough to accomplish. Try it on the verses only of Veni Emmanuel. I'd start on D, so it doesn't get too high for the tenors (who sing with the altos "below" the melody).

I picked up that treatise at the university library. Should be a fun weekend. I get to translate Latin on the fly!

Gustave Reese has a lot of examples in his Music in the Middle Ages (1940, Norton).

And by the way, "organum" is a variety of techniques, not just parallel melody a fourth or fifth below/above. The Enchiriadis for example describes a free organum that uses oblique motion at the opening until an interval of a fourth is reached, after which the piece proceeds in parallel until closing on the unison.

"John Cotton" calls free organum "diaphony" and observes that it mixes unisons, octaves, fifths, and fourths, all while valuing contrary motion (!) and voice crossing, and describing various ways of dealing with spacing.

A French description in Ad organum faciendum puts the organal part above the chant and recommends avoiding the tritone by consistently using the b-flat. (Others tried to avoid it by prohibiting the organal voice from descending below the fourth or third tone in the lowest tetrachord.)

The Winchester Tropers has 150 two-part organa for responsorial chants of the Mass and Office, Ordinary, tropes, and sequences. Surely someone has made a modern transcription of it.