I continually urge my critics to judge my edition against the adiastematic neumes found in the triplex editions.  Besides attachment to the outdated Vatican and Solesmes editions, common objections to my edition are what some consider an excessive number of rhythmic markings resulting in a cluttered appearance, the lack of a special strophicus form distinct from the punctum, the lack of adiastematic neumes, and the use of square Gregorian notation instead of standard modern notation.  I have used the horizontal episema to mark the ordinary long note, which Cardine called the normal syllabic value, both in isolation and in composition.  The distropha and unison tristropha retain the same appearance as in the Vatican edition; Laon 239, on which my edition is most closely based, writes the short strophicus notes as ordinary puncta, as do most sources other than those of the St. Gall school, or as a pes if the first note is lower than the repeated notes.  The Vatican notation sometimes follows Laon more closely (e.g., the strophicus and, in most cases, the bivirga), other times St. Gall (e.g., the short climacus and pes subpunctis).  Mine makes no claim to be a duplex or triplex edition, and inclusion of adiastematic neumes or the use of modern notation would increase the page count significantly.  Would there not surely be just as many complaints if I had taken another editorial approach?

My notation is geared toward singers transitioning from the Solesmes editions, and the rhythmic signs are used in a somewhat analogous way: a note with the episema is longer than the plain note, and a dotted note is longer still.  As Charles Weaver has said on a public forum, “the short-as-default value was cooked into the Solesmes typeface from the beginning, so I don't think there's much a post-Cardinian editor can do about it without abandoning the Solesmes look altogether and going to something like modern notation.”  I experimented with combinations of white and black notes, variable notehead widths, spacing modifications, dots, and assigning different values to the virga, square punctum, and diamond punctum inclinatum, but I found serious drawbacks to each of those approaches.  What other means do we currently have at our disposal to differentiate long and short note values?  The horizontal episema serves its purpose just fine.  Although intended as a practical edition for the use of a parish schola to sing according to a mensuralist interpretation, not a study edition for semiologists, the adiastematic neumes can be transcribed without difficulty from my edition—or from an accurate performance from it—by anyone proficient in writing them.

With those objections addressed, let us consider the rhythm.  The claims I make are that the short and long notes of the earliest and most reliable manuscript sources stand in exactly the same proportion as eighth and quarter notes, 1:2, and that the resulting chant has a steady beat (tactus).  It is surprisingly difficult for many singers to grasp this simple concept of chant with a steady beat but not necessarily structured according to meter, time signature, or measures in the modern sense.  Many have been conditioned to think in terms of a dichotomy between modern music organized according to meter versus chant in “free rhythm,” usually without understanding or being able to articulate exactly what that means, if anything, hence my use of quotation marks.

To the semiologists, I propose the following threefold test for any chant notated with both sets of adiastematic neumes in the triplex edition:

1. count the number of definite contradictions between the two manuscript sources

2. count the number of possible contradictions between the two manuscript sources, i.e., those that could be interpreted in such a way as to agree with each other

3. count the number of apparent ternary groupings, e.g., an odd number of short notes between longs, but taking care to interpret three-note neumatic elements such as the torculus and porrectus as short-short-long unless written entirely long

In case of contradictions, the editor must choose one reading or the other unless there is a reasonable interpretation reconciling the two.  Point 3 is the only real difficulty.  Often, upon examination of other reliable ancient sources, a solution presents itself in the form of one or several notes notated long instead of short.  When that is not the case, the previous long note can be thought of as a sort of fermata, or it can be treated like a dotted quarter note, or the following short note can be treated as a grace note.  For any chant from the first millennium, the prevailing binary nature of the rhythm will be perfectly apparent.  Short notes come in pairs.  Short and long notes are in 1:2 proportion.  There is a steady beat.

Once the problem spots have been dealt with, judge which interpretation is most consistent with the oldest sources: Solesmes, semiological, accentualist (rhetorical or oratorical), mensuralist (proportional rhythm), “pure Vatican edition” equalist, or an unspecified “free rhythm” approach.  If the adiastematic neumes can't be faithfully reconstructed from the performance, then the neumes aren't being faithfully performed.