Hiley:

Early medieval writings on chant help but little in understanding how note-lengths were differentiated.  One group of related writings, which was discussed at length by Vollaerts (1960), among others, has little to do with the matter, for it refers to the final notes of chants, of their phrases and sub-phrases.  As Bower has explained (1989, ‘Model’), this is done by analogy with the grammatical structure of the text being sung: the musical delivery should reflect the grammatical structure, by making the hierarchy of text-units clear.  This group of writings includes the Scolica enchiriadis (ed. Hans Schmid 1981, pars 1, 86-7), Guido of Arezzo’s Micrologus (ch. 15), and the commentaries on the latter by Aribo (CSM 2. 48-50, 65-70) and in the Commentarius in Micrologum (ed. Smits van Waesberghe 1957).  Several of Guido’s comments refer also to proportional relationships between ‘neumes’, that is, between phrases of chants; some neumes will be of equal length, while the lengths of others will stand in a proportion of one to two, one to three, two to three, or three to four.  This does not refer to the durations of individual notes.

Two other passages have also been adduced in support of a metrical interpretation of the different note-lengths.  The Commemoratio brevis of the late ninth century contains a number of references to the different speeds of singing appropriate to different occasions or types of chant, to the maintainance of a steady tempo (except for controlled variations such as a ‘rallentando’), and also to long and short notes.  Towards the close of the passage it is said that these are in the proportion 2:1:

Breves must not be slower than is fitting for breves; nor may longs be distorted in erratic haste and made faster than is appropriate for longs.  But just as all breves are short so must all longs be uniformly long, except at the divisions, which must be sung with similar care.  All notes which are long must correspond rhythmically with those which are not long through their proper inherent durations, and any chant must be performed entirely, from one end to the other, according to this same rhythmic scheme.  In chant which is sung quickly this proportion is maintained even though the melody is slowed towards the end, or occasionally near the beginning (as in chant which is sung slowly and concluded in a quicker manner).  For the longer values consist of the shorter, and the shorter subsist in the longer, and in such a fashion that one has always twice the duration of the other, neither more or less.  While singing, one choir is always answered by the other in the same tempo, and neither may sing faster or slower. (Ed. Bailey 1979, 103.)

Since the Commemoratio brevis belongs to the same manuscript tradition as the Scolica enchiriadis, one naturally asks if the long notes referred to here are those at the ends of grammatical units, the ‘syllables’, ‘neumes’, and ‘periods’ of chant. . . .

It seems most unlikely that practice was uniform everywhere [six pages earlier he says that a rhythmically differentiated way of singing chant was quite widespread].  It is true that sources are in general surprisingly uniform in their grouping of notes and even in the placing of such special features as quilismas.  And the correspondences between Laon 239 and Eastern sources (and other early sources to varying degrees) in matters of rhythmic detail cannot be overlooked.  But the agreement is general, not exact.  Any claim to have identified an ‘authentic’ performance tradition should be treated with caution. (David Hiley, Western Plainchant: A Handbook, pp. 384–5)

Commentary:

Hiley’s claim of only “general” agreement between Laon and “Eastern” (St. Gall?) sources is shocking and causes me to question the extent of the preeminent scholar’s practical experience.  Those of us who have studied or sung from the triplex editions recognize more than a “general” agreement between L and E or C.  There are some chants where the agreement is 100 percent, many where it is 98 percent or better, and rather few where it is less than 90 percent.  Is it of no consequence that the manuscripts under consideration are the oldest extant and nearly complete Gradual, Laon 239, and the oldest St. Gall sources?  It may seem to Hiley “most unlikely that practice was uniform everywhere,” despite being “quite widespread,” but it seems most unlikely to me that the oldest reliable manuscripts, presumably written some 350 miles apart, represent local versions of rhythmic chant that only happen to agree by coincidence.  If, on the contrary, it is not a matter of local variants but rather a universal tradition, the uniformity in note grouping and “placing of special features” ought to be totally unsurprising.

Academia will eventually have to come to terms with the possibility that the oldest extant sources together transmit the first-millennial rhythm fairly reliably and that the alterations apparent in later sources are just that: alterations, not the authentic tradition.

See here for the received historical narrative.