In my opinion The Propers (English versions of the GR texts) could be composed 1) in newly composed chant style, 2) in metrical style with accompaniment, or 3) may be English versions of the GR texts set to the GR melodies (a la Palmer-Burgess or Bruce Ford). The only requirements are sensitivity to text and that the music must reveal its derivation from the historic Gregorian repertory, or from our finest post-Gregorian musical heritage - which means that mimicking 'popular' forms of music is anathema.

I've used my Hymn Tune Introits with standard SATB harmonizations.

Holy smokes, that "Honey from the Rock" was truly alarming! If you needed any proof that the Church often tries to imitate popular culture far, far too late, it's that collection of mid-'90s propers, written in 2016.

Kathy - do you have a link to your Hymn Tune Introits?

Are you talking Novus Ordo or Extraordinary Form? If Novus Ordo, the propers themselves are not technically required; so there is no official musical requirement for an introit. Kathy Pluth (linked above) and Christoph Tietze have both done collections of hymn-tune introits. Tietze: http://www.wlp.jspaluch.com/2646.htm

If you are talking choral introits, then Healy Willan did a complete series for the (anglican) calendar. Also, Richard Rice did a complete set of choral introits. I'm working on a similar collection. Attaching one here as an example.

If you are talking Latin introits for choir, of course there is the Byrd Gradualia and Isaac Choralis Constantinus (among other Renaissance-era and later settings).

I would also point out, since you are in the dangerous waters of the MusicaSacra forum, that many here believe strongly that the Missal propers are "not meant to be sung" and are not "real propers." This would be considered an issue if you are thinking of setting English introits for choir, from the Roman Missal. However, as a matter of actual fact and not ideology, two points:

1 - There is explicit mention of singing the Roman Missal introits in the first option of the GIRM (United States version) for music during the entrance procession.

2 - On about 95% of Sundays, the Roman Missal introit antiphon is an english translation of the Graduale proper. There are only a few small exceptions to this rule.

Thus, the Missal Introits may certainly be sung, and in almost all cases are exactly equivalent to the Graduale texts anyway.

Which is to say, if you are thinking of setting the Roman Missal antiphons for choir, GO FOR IT!! And ignore the nonsense :)
There is a much greater need for compositions of this type, than for more collections of Responsorial Psalms.

EDIT: I re-read the original post and see you are talking about all propers, not just introits. There is much less of a pressing need for Offertories, since there are many of these in the inherited repertoire. However, I would think that an accessible choral setting of an Offertory should always be welcome in the church. The best settings (Palestrina, Lassus, Rheinberger, etc.) tend to be quite difficult. As far as communion propers, the water becomes murkier, especially in the Novus Ordo with three-year cycles of communios on many days. Also, the need to prolong music for a lengthy procession. But again, good choral settings of communion propers should also be welcome.

These offertory paraphrases are intended to be used with Common Meter hymn tunes.

JKW,

Remember, when writing 2 or 3 voice music that this isn't 4-part music with a part missing. Also, don't think of one part dragging the other along, like an unwilling relative to a Christmas feast.

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? TD Jakes? I'm obviously showing my youth and ignorance, but who is TD Jakes?