Semiology is the study of the signs, that is, the earliest neumes notably from the Saint-Gall and Laon manuscripts (and related manuscripts, like from Einsiedeln). It is strongly associated with Dom Eugène Cardine of Solesmes who wrote a sort of academic guide to it (helpfully called Gregorian Semiology). Solesmes, at least in the 1980s and through the early 2010s, informed its chanting via his own understanding of what this meant for music, although in some ways it didn’t change much from the older practices, even when they officially removed the rhythmic signs from the new Antiphonale Monasticum of the 2000s.

Mensuralism means that the music is measured. There are a couple of ways that I think fall under this: post-1600 chant in much of Europe is mensuralist (I think if you’re considering Solesmes anyway). It could be proportionalist, and Patrick Williams (@FSSPMusic here) would define that as the notes being in a 2:1 ratio of long to short based on his understanding of the treatises and adiastematic neumes. This requires a semiological approach because the ratio is informed by the notation particularly the Laon neumes; in contrast, Cardinian practice tends to prefer Swiss manuscripts. I think that it’s helpful to separate out using the adiastematic neumes; many European scholars and chanters consider their work semiologically-based (as I understand it) without being strictly Cardinian…although there is certainly overlap. The new Nocturnale Romanum winds up taking that approach and uses more rhythmic signs than Solesmes historically did as a result.

Then someone like Mgr Turco is not quite as strict about proportions, but he’s still using the manuscripts to inform the melody and rhythm, as well as treatises etc.

Dom Gregory Murray went back and forth on Solesmes (he also switched rather violently to prefer the English Mass, I’m told), but he also wrote a lot on proportionalism and specifically against the equalist approach of Solesmes. I would agree that for many of us the traditional approach is Solesmes, abstracting from judging that for a minute.

It’s too bad Mgr Turco’s recordings are hard to find due to copyright issues I guess. Patrick once shared a link to the gradual of this Sunday (Laetatus Sum) that is semiological but not quite strictly proportional.

The impulse to compare is a good one; Dom Mocquereau and Dom Pothier did not record the same chants but they sang in a contrasting (although very much related style) at the beginning of the twentieth century at a major event in Rome. @Charles_Weaver made us sing a chant in a contrasting style: I took the easy way out and did Solesmes and Vatican style. Others did semiological (Cardinian) approaches, and in reality I inform my own chant with the living tradition of the abbeys and occasional checking against the Graduale Triplex; it’s semiology lite. I don’t know if anyone sang a proportional chant. It’s probably the most foreign to us even though Patrick’s argument for it in part is because every other kind of music that we sing is measured!

May I also suggest that the terrain or context in which these distinctions are effectively applied and encountered are chants that are sung by scholas/choirs, rather than the Ordinary chants and responsories that are also sung by faithful in the pews?

In practice that’s the case Liam but I hesitate to say that it’s strictly true; as much as I also hesitate to speak for others. That is I get the sense that there are proportionalism advocates who would do that to the Ordinary as well.

They don’t care!

Here's the Turco recording @MatthewRoth mentioned:
https://www.youtube.com/watch?v=yj-sx-HO4Tk

Play the attached mp3 and listen to what they do with the same figure when it occurs, including the repeat of the respond:



Three out of four times, I hear the first interpretation below. The third time, I hear something closer to the second, which is what the adiastematic notations actually say: long, short-short-long, long-long.



It's beautiful singing in my opinion, but I find it difficult to justify an interpretation where the length of the fourth note is not apparent—a note affected by the addition of an episema, the letter t, and a neumatic break. It should have the same duration in each instance, that of the other long notes, namely, double the short value. It's difficult for many to accept the revolutionary idea that 1+1=2 because it's not what they think of as chantlike. So what are the paleographical/semiological, textual, or musical/artistic/expressive arguments against interpreting the figure consistently? Find another semiological recording, and there's a pretty good chance they'll do something different with it.

Most modern mensuralists are also semiologists, in the sense that they base their rhythmic interpretation on principles drawn from Cardine.

Respectfully, @Charles_Weaver, this is not so well stated. Most modern mensuralists are semiologists to the extent that they follow the adiastematic neumes. Most of us (not all!) take Cardine seriously, but what is there in my style of chant, for instance, that comes from Cardine rather than Vollaerts or Murray? Weak beginning notes, including what I call "initio debilis by comparison," are dealt with by Murray. The expressive neumatic break? It differs little from the melismatic mora vocis of the Vatican edition and the late Solesmes approach to disaggregate/praepunctis neumes well before Gregorian Semiology was published.

But would they be able to get a congregation to sing that way?

@Liam, which way do you mean? I think it would be easy to get a congregation to sing proportionally once they've become accustomed to hearing from the schola—but not with the Solesmes edition in front of them. For now, I don't touch the Ordinary or anything else the congregation sings.

@FSSPMusic Perhaps I'm giving too much credit to Dom Cardine here, but I suppose what I meant is that in the old days, mensuralists based their arguments on all kinds of things, such as assigning equal time values to each syllable in melismatic chant, etc. I'm thinking, e.g., of Riemann's version of the Te Deum.

The more recent mensuralists base their findings on paleography and its interpretation, of the type popularized by Cardine. You are quite right to point out that Fr. Vollaerts and Dom Murray do this, without being directly influenced by Cardine.

We are without the organ (not for Lent, it's a long story, but we're not even in the loft indefinitely), and oh boy the mode I Kyrie of Mass XVII is a bit of a mess; at "e-" they keep running through the peak note, and I'm like…please don't do that. The Sanctus and Agnus are better albeit I have to really fight at a couple of places. Credo IV seems to be kept together.

Vespers is fine, actually. That surprised me. (I just have to give myself pitches because I definitely don't have perfect pitch, relative or otherwise, and it's dangerous if I don't.)

(Edited)

The more recent mensuralists base their findings on paleography and its interpretation, of the type popularized by Cardine. You are quite right to point out that Fr. Vollaerts and Dom Murray do this, without being directly influenced by Cardine.

This is better worded and entirely accurate.