Commons of Saints and Sunday Week 1

Is there any particular reason why, on solemnities without a Proper Psalmody, the Liturgy of the Hours asks us to pray the psalms and canticle from Sunday morning of Week 1? I mean as opposed to Week 2?

I bet it has something to do with the particular Psalms/Canticle on Sunday I, but I have no idea what the significance would be.

I guess Sunday I was just the designated Celebratory day or something.

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