In 2008, three new alternative options for the Mass' dismissal were approved. One of these options (‘Ite in pace’) is already set to music in the Antiphonale Romanum (II, 762).
For one other, ‘Ite ad Evangelium Domini annuntiandum’, I created the attached melody, based upon the ‘Benedicamus Domino’ in feriis for tempore adventus et quadragesimae (Antiphonale Monasticum I, 545).
Something similar (one melody provided, three texts printed) arose with the Mysterium Fidei. How would you chant those, if you chanted those texts (i.e., didn't use a modern composition)?
In many of the chant Masses (and here I intentionally and explicitly exclude any ad libitum chant which will make the general rule untrue, the Kyrie and the Ite, Missa Est use the same chant. I don't have my LU in front of me, but is this melody used in the Kyrie of the same Mass? Additionally, if someone hasn't already, would you compose a chant Mass such that the Kyrie and the Benedicamus Domino matched each other?
For the other two options of the Mysterium fidei, chant settings are already provided by Psallite Domino, canti per la messa (Verona, 1997, 2006) and Singing the Mass (Solesmes, 2011). These are modelled after the antiphon Crucem tuam, just like what was done for the first option, Mortem tuam. See this thread.
As for the Ite missa est using the same chant as the Kyrie, I think that connection has been dropped after 1970. At least, the current Graduale Romanum doesn't provide any other settings of the Ite missa est than the two on p. 821 (one for general use, and one for Easter Sunday, the Octave of Easter and Pentecost). Personally, because this particular dismissal is only intended for the Ordinary Form, I therefore don't feel it necessary to have a Kyrie that matches this setting.
It would however be quite interesting to research where this custom originates from. At least, it was already known in the 14th century, as testified by Ms Toulouse 94.
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