Can you tell us a bit more about your situation? For the new rite or the old rite? Are you a priest, a layman? Do you read modern notation? Chant notation? Do you have experience singing? Playing an instrument?
For Latin readings, pages 102-109 of the Liber Usualis (downloadable as a PDF file from CMAA) have tones for the Old Testament ("Prophecy"), Epistle, and Gospel readings.
Yep, as Chonak says, I've worked from the tutorial he linked to. There's a printed version as well as the audio. I've also worked from the Liber instructions, which aren't that difficult.
For your priest or deacon, Cantica Nova has a Book of Sung Gospels which doesn't cover all the Sundays, but does cover principal feasts.
We have sets of written out readings for the Easter Vigil and (I think) for weddings. E-mail me if that'd be useful to you and I may be able to have the guy who did them send you PDF's.
This is awesome! Thank you so much all, now, does the Liber say "when" the readings may be sung? Is it all the time in any liturgical setting (baptisms, liturgy of the hours, etc.), except in certain seasons? What's the norm?
Any time is OK, but the 1967 document "Musicam Sacram" lays out a plan of which Mass parts make sense to sing first, and which can then be added, until you end up with a fully sung liturgy. In that plan, readings come pretty late in the list.
The most basic thing to sing is the dialogues of priest and congregation: they provide the setting for adding the next pieces, etc.
After many years as a cantor and a lector, I have reached the conclusion that the "lessons" (I assume you mean here the readings at Mass, and not the briefer readings at, say, Evening or Night Prayer) are better delivered when effectively read and not sung. The readings are intended to have significant cognitive value, and reading them well conveys that cognitive value more clearly.
Prayers are another matter, and, since my parish does not have a deacon, I always sing the petitions to the prayers of the faithful.
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