The bulk of mainstream Gregorian chant scholarship in recent decades has been in accordance with the semiology of Dom Eugène Cardine, O.S.B. (1905–88).  A minority of writers focus almost exclusively on melodic and textual variants, taking no position on rhythm.  Others advocate a more or less equalist rhythmic interpretation, often on the grounds that the authentic rhythmic tradition is supposedly indecipherable or unknowable.  An even smaller minority adopt a mensural or proportional-rhythm approach, although I am convinced that, as more people do their homework and examine the claims made by me and others, proportional chant rhythm will become widely utilized in both liturgical and academic contexts.  Very few attempt to defend the classic Solesmes method as a historically valid style of interpretation except for reconstructing performance practice from the relatively brief period when it was in general use, for example, as incorporated into the sacred compositions of Tournemire (1870–1939), Duruflé (1902–86), or Langlais (1907–91).

I have previously lamented the fact that, while they have discredited Dom Mocquereau’s ictus placement theory, the semiologists of Cardine’s school retain the theory of non-proportional rhythmic nuances.  In the Solesmes method, a plain note (whether punctum or virga) indicates a short and indivisible note value approximately equivalent to an eighth note in modern notation.  A punctum mora or augmentation dot doubles the note value.  In between these single and double values are at least three shades of agogic nuances indicated by the addition of the horizontal episema (which looks like and has the same derivation as the modern tenuto mark), the addition of a vertical episema in the case of the salicus, retroactively on the note preceding the quilisma, and before neumatic disaggregation in the Vatican edition.

Cardinian semiology, in contrast, describes the normal or resumed/recovered syllabic value as somewhere between the diminished and augmented syllabic values: the normal value is long relative to the diminished value but short relative to the augmented value.  It is a medium or intermediate duration, not evenly divisible by two.  I cannot say with any certainty what percentage of Cardinian semiologists would concede that their diminished and augmented values stand in 1:2 proportion, but the case could hardly be clearer when we carefully examine the evidence furnished by the liquescent neumes, which can be either ascending or descending (diminutive liquescence, in Cardine's terminology) or unison (augmentative liquescence).  Perhaps someone will be audacious enough to assert that the diminutive and augmentative liquescent notes don't necessarily correspond to the diminished and augmented syllabic values.  If so, let us hope that everyone else will have the good sense to reject such a claim outright.

That brings us to what I have identified as the fundamental flaw in Cardinian semiology, to wit, the notion that the normal syllabic value differs from the augmented syllabic value.  While we occasionally encounter notes, both isolated and in composition, which have indications of lengthening beyond double the short (diminished) value, those are somewhat exceptional cases dealt with elsewhere.  Here and now let us focus on the normal short and long values indicated in Laon 239 by the plain punctum and plain uncinus (tractulus) respectively.  After having searched for contrary evidence for a number of years, as far as I can tell, no one before the nineteenth century thought that the uncinus had a different value in isolation, i.e., when a syllable is set to a single note, than in composition, i.e., within a longer neume or melisma.

For the classic Solesmes method, the isolated note became short and indivisible.  For the semiologists, it became an agogic nuance (as Van Biezen asked, a nuance of what?) subject to multiple levels and layers of interpretation:

1. the fundamental form and shape of the note itself

2. tiny variations in size

3. the addition of the episema

4. the addition of a significative letter

5. more than one significative letter, e.g. m or b

6. musical context, e.g. structural pitches and melodic peaks

7. the relative amount of time it takes to pronounce the syllable in ordinary speech

8. the tonic accent

9. the word final

10. punctuation

11. grammar and syntax

12. the spiritual significance of the text

When the same kind of note appears within a neume, also to be considered are the following:

13. its position within the neume

14. the neumatic break

These are their interpretive principles, which I don't believe I've exaggerated or mischaracterized in any way.

The uncinus, both isolated and in composition, represents a note value that is neither short nor indivisible.  It is long and evenly divisible, easily transcribed in modern notation as a quarter note, with the punctum being equivalent to an eighth note.  Making it an agogic nuance of somewhat indeterminate value is every bit as pernicious as making it short and indivisible.  In the clearest possible terms, the normal syllabic value is long and exactly equal in duration to two short notes.  In mainstream Gregorian chant studies, how much longer will the idea that 1+1=2 have to remain merely one opinion among others?  How creative, how delightfully elastic, how spiritual to pretend that 1+1=1 or 1.5 or a slight nuance of indeterminate value!  It is time to grow up.  “When I was a child, I spoke as a child, I understood as a child, I thought as a child.  But, when I became a man, I put away the things of a child.” (1 Corinthians 13:11)