Thanks for all the replies!
If I remember correctly I believe it is the same melody of the canon of the Bridegroom Orthros of Holy Week.
Flipping through my Triodion (Ekdoseis Fos) the only match I could find was Ode 3 of the canon for the Bridegroom Matins of Holy Wednesday, though it is all in Tone 2.
He is not aware of any notated versions of the communion preparation canon. While the Greek-language canon was originally written in meter, it has not been translated into English that way. The HTM prayer book does not give prosomia for the odes, so it would be impossible to know how to properly sing the canon.
Actually, the HTM translation goes further and gives you the entire
heirmos for each Ode of the Canon (which work in the same was as
prosomia), while in most Greek Horologia they're merely indicated. I only know how to sing the first
heirmos (Come, O ye people), but basing myself on that, the English translation can also easily be sung to the original melody.
The
heirmoi are as follows:
Ode 1 - Δεῦτε λαοί
Ode 3 - Ἐν πέτρᾳ με τῆς πίστεως
Ode 4 - Έλήλυθας έκ παρθένου
Ode 5 -Ὁ τοῦ φοτὸς χορηγός
Ode 6 - Ἐν ἀβύσσῳ πταισμάτων
Ode 7 - Εὶκόνος χρυσῆς
Ode 8 - Τὸν ἐν καμίνῳ τοῦ πυρός
Ode 9 - Ἀνάρχου γεννήτορος
So the proper melody for the canon is not the problem. My question was more whether it would be necessary to learn all of the above heirmoi by heart (if so, a link to the notation for those would be very much appreciated), and then sing the canon accordingly, or whether there was a book somewhere where the text of the canon was accompanied by Byzantine notation. Alas, such a book doesn't seem to exist.
That being said, you can still sing the canon freestyle in Tone 2 if you know how (apparently there are not very many canons written for Tone 2, so it can be unfamiliar). The syllables will not match from verse to verse, but you can still do it.
That's what I've been trying to from time to time. Always ends up a bit clumsy though.