I imagine that the simpler mode 7 chant is just an older, less elaborate version of the other. (I don't have my graduale with me, so I can't check if there are any dates printed.) The mode 4 is probably a version from a mediaeval source that Pothier & Co. liked when they put the new books together---IIRC, the old Medici/Ratisbon Gradual only had the one mode 7 setting. This aren't facts, they're just educated guesses.
And like all the ad libitum chants, they are there to be used when you feel like it, there are no hard and fast rules about which chants to use when.
I know I've seen the simple mode VII used in the Pontificale Romanum. I believe it's used a time or two in the blessing of certain objects, but I'm not too sure about that.
Triplex gives XIII s. for the usual mode 7 tone (ed Vat I); X s. for the simpler (ed Vat II); and XII s. for the mode 4 tune (ed Vat III). The last is the only one with neumes, from Mont-Blandin.
John Schauble and the Holy Family Choir of Dayton, OH regularly use the simple tones for Advent and Lent, respectively. Can't remember which for which, though.
As a corollary, is there ever anything against adding psalm verses? Couldn't one add psalm verses to the Asperges as to the Introit or the Communion? Or is there something against that?
Adding psalm verses to the Asperges (or Vidi aquam): yes, this is possible. Although the Graduale Romanum doesn't mention anything about the number of psalm verses, the Graduale Simplex does:
Et repetitur antiphona, pro opportunitate, post unumquemque versiculum psalmi 50, p. 86
So, the antiphon can be repeated after each of the verses of Psalm 51(50). For the Easter Season this is Psalm 118(117).
As far as extending the Asperges, one could also pick and choose which parts to have polyphonic, perhaps? If it is that you know you always need it lengthened, you could do just the repeated antiphon as polyphony. If you are simply getting to the Gloria Patri and realizing you are going to need extra time, you could add a polyphonic GP, and maybe also the antiphon, as well... Choosing a setting based on/interspersed with chant could certainly help with the necessary picking/choosing.
What a wonderful idea! I don't know if I'll ever get to use it, but I had no idea that it existed, so that added knowledge has enriched my love of the liturgy and the treasury of Sacred Music.
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