Many of the items for the Sundays after Pentecost are ordered, although rarely consecutive. The Epistles (except for the 18th Sunday), Introits (until the 18th Sunday), Alleluia verses, and the majority of the Offertories and Communions are presented in order.
For example, the Alleluia verse for the 4th Sunday after Pentecost is taken from Psalm 9; the 5th, from Psalm 20; the 6th, from Psalm 30; the 7th, from Psalm 46; and so on in ascending numerical order through the Psalms.
Patterns like this (and especially their disturbances) can give us clues about history. For instance, the Communion antiphons for the weekdays of Lent are taken from consecutive Psalms--except for Thursdays. This suggests that when this pattern was established, the Mass was not celebrated on Thursdays in Lent in Rome.
James McKinnon, in _The Advent Project_, drew on evidence like this to build a hypothesis about the reorganization of the Mass propers in seventh century Rome. It's a wonderful book (although I, at least, found it hard going, and remember less than a quarter of it--clearly, I need to re-read it!)
I often cite this as a counter-argument to the idea that music should be chosen to go withe the readings or with the "theme" of the day (a la Today's Liturgy). Such an idea suggests that the music is additive, or at least subordinate to the readings. However, the idea that the sung texts follow a structure of their own apart from the cycle of readings (whichever cycle you follow) supports the practice of singing the propers for their own sake.
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