I think you might want to check on your definitions again. Your distinction of responsorial and antiphonal is correct, but the definition of antiphon as a noun is considerably broader.

In the Ordinary Form, what I have written is very standard usage. I chose this terminology because many who are entirely unfamiliar with the propers will have at least heard of entrance and communion antiphons. The Roman Missal, for instance, specifies "Entrance Antiphon" and "Communion Antiphon", and even the Breaking Bread prints entrance and communion antiphons along with the readings.

Also, with regard to Gregorian chant specifically, in his book Gregorian Chant, Willi Apel speaks of both Office Antiphons and Mass Antiphons, and of Mass Antiphons, he mentions Introit, Communion, and Offertory.

However, your broader point about a wider application is well taken, and I can make an addendum to the article in that respect. Thank you. :-)

In the Ordinary Form, what I have written is very standard usage.

MJO's point is thus relevant, whether we wish to take it or not.

To Dr. Weaver's observation: the Requiem offertory is certainly a responsory even in the Roman tradition, though I think that in the Solesmes gradual of 1974, the verse is optional. I don't really care for doing the Offertoriale verses myself; both of the offertories beginning Jubilate Deo are long enough. So too Precatus est Moyses. (I know, the Mass isn't about how long people suffer, but the reality is that the priest would wait an awfully long time to continue with the preface if we did the verses.)

Also, FWIW (not much perhaps!): the term "lesson" is sometimes used in handmissals when the sole reading is from a prophet or another book of the Old Testament or from Acts or Revelation, but invariably in the ceremonial books, it's always an "epistle", even on Epiphany and above all on weekdays of Lent except for Ember Saturday, where the readings are from the OT, and then "lectio" is used to distinguish this for the first reading etc. on Ember Wednesday, Ember Saturday (on those days), and on Good Friday. Conversely, all of the readings (four or twelve) of the Paschal Vigil before the Mass of the vigil are prophecies, but they are not technically all from the prophets. It's why it's inappropriate to use the "prophecy tone" for the main reading that is sung after the collect.

Scholarly opinion now holds that the offertory was originally a responsorial form which over the years has been shorn of its verses.

A good and commendable book about the offertory is
'Inside the Offertory: Aspects of Chronology and Transmission',
by Rebecca Maloy,
Oxford, 2010.

This thread becomes more and more interesting, even if we've wandered a little far from the original discussion. I love singing the offertory verses at Mass, and I would be interested in hearing how others incorporate them; I will describe my own practice below. Of course Patrick has his own edition of several of them as well at his site.

I often sing a verse at the novus ordo Masses at my parish. This is easy because I'm the only one singing and I usually sing à la Cardine/Guilmard for the propers, so I use the Offertoriale triplex, which I believe I got from Andrew Mills some time around 2009. Even though we always use incense, I still find I seldom have time for anything but the first verse and a short repetendum. When I'm by myself I sometimes sing straight from Maloy's edition, but I find her "Hiley" engraving style (what Tom Kelly once called "tadpoles") minimally helpful with regard to rhythm and performance style.

Usually what we do at our Sunday Mass in the old rite is that we sing the offertory chant and then we sing a polyphonic setting of the same text (Lassus, Palestrina, etc.). Occasionally, we will sing verses, especially if the chant is already so long that singing a polyphonic setting would require the ministers to wait. In such cases, i have generally added Mocquereau rhythm signs to the Gregobase versions, and I base them roughly on the indications in the Offertoriale triplex, together with phrase architecture and the like. I do this mainly because my schola is used to singing in that style and we don't really rehearse. It's very much a Mocquerellian house style heavily influenced by my predecessor David Hughes and by my own teachers. From the point of view of Gregorian rhythm studies, it's a pretty interesting exercise, since it is decidedly not the same as using an episema or dot to mark every sign of length in the old MSS. It's more like trying to conform the aesthetic of the verses to the more well known rhythmic profile of the respond. It's humbling to mark a certain thing that seems successful when alone and then realize that it doesn't lead to such good results with a Mocquerellian schola. Of course, Ott is also much heavier with the use of half bars than the Vatican Edition, which also requires some adjustment.

Since the conversation has shifted, for the sake of future readers, I'll include last year's article which I wrote on the offertory chant and its verses.

https://www.chantacademy.com/post/advent-ave-maria

Full disclosure: I do use the word "antiphon" for the offertory chant, for the reasons stated earlier. (You'll notice that I do also use the word "respond".) These blog articles are meant to be entry-ways for people new to Gregorian chant, so some of the academic subtleties pointed out earlier in this thread, particularly by Patrick, are not noted.

@CharlesWeaver makes an interesting observation about the schola singing the verses. Willi Apel posits in his book that the verses may have been written for different soloists, as they often have widely different ranges and and characteristics. I find Apel's perspective to be rather convincing, especially after attending a couple of Marcel Pérès' workshops here in Saint Louis, Missouri, last year, in which he spoke quite a bit on the Oral Tradition and the established practice of improvisation in Gregorian chant. The reading that I've done supports the idea that verses for the more elaborate chants were originally sung by soloists, or at least by a smaller subgroup of the schola.

Edited to add: I shared this article in a social media group last year and was soundly pounced upon by an established author of the PrayTell blog, who said that the Offertory is a thing of the past, and that the word itself should no longer be used with regard to the post-Conciliar Mass. Numerous references to the GIRM which explicitly name the Offertory did not dissuade him. SMH.

some of the academic subtleties pointed out earlier in this thread, particularly by Patrick

I'm not sure I pointed out any academic subtleties, but ok.

Angela - could you say more about Marcel Peres' comments about the oral tradition and improvisation in chant?

@Charles_Weaver I don’t know if you’re the one adding them to Gregobase (which as Olivier Berten seems to have disappeared, is quickly becoming a repository for unpublished editions which by definition cannot be proofread by others)… but despite my preference and situation, if you do get around to publishing your edition as a complete PDF, that’d be useful.