As in the Vatican edition, all bar lines and intonation asterisks are editorial.  Most augmentation dots (puncta morae) are also editorial.

At the mediant cadence of introit and communion psalm verses in all modes except III, IV, VI, and XII (VIc), the episemata attached to the pes or clivis are editorial.  The oldest sources invariably give cursive neumes here, i.e. two short notes.  My use of long notes at the cadence is a concession to the current rubrical practice of alternating between cantors and schola in the introit psalm verse and doxology and also to the use of the full bar line in all modern editions.  Murray, perhaps erroneously, presumed that a mora vocis (prolongation) was understood in this context.

When the gradual verse ends on a different note than the final of the mode, the authentic version is given for those who wish to repeat from the beginning.  Either practice is permitted by the rubrics, but ending after the verse seems to be far more prevalent; therefore the altered version is printed first, e.g., for the last Sunday after Pentecost.  I have retained the asterisk and repeat sign before the jubilus of the alleluia as a concession to the modern practice of prolonging the neume only on the repetitions, which appears to be required by the preconciliar rubrics.

Although they do not come into question in the printed editions, I wish to comment on two further editorial matters: first, the liturgical Latin pronunciation.  It is highly unlikely that the current Italianate Latin pronunciation was in use in the tenth century, either in Rome or elsewhere.  To cite but one well-known example, the widespread interchangeability of gracias and gratias in medieval manuscripts surely implies an identical pronunciation for both spellings, which is not the case for Latin pronounced like modern Italian.  My own retention of the Italianate Latin with my choirs is done in the interest of liturgical uniformity, not historical accuracy.

Finally, the matter of historical tuning must be mentioned.  Ross Duffin has documented that mathematically equal temperament of twelve truly identical half steps (semitones) was not realized until as late as 1917.  We know that not only the various modes, but also different keys, formerly had distinct “flavors," for lack of simpler description.  It seems probable that either Pythagorean tuning or what we now know as just intonation was the predominant tuning standard in the Middle Ages; which of the two systems is more historically appropriate for purely a cappella Gregorian chant is disputed, and it is possible that both were in use simultaneously (see this 2024 presentation and paper by Geert Maessen).  Relative to twelve-tone equal temperament, mi, la, and ti are slightly but noticeably higher in Pythagorean tuning and slightly but noticeably lower in just intonation (five-limit tuning).

Not to digress—but considering that solfege was not developed until the eleventh century, it might be better for us to use earlier terminology: A, B, E (and, respectively, H, I, M, and P, according to the digraphic notation of the Tonary of St. Benigne, Montpellier H 159; see here for an illustration in square notation).  As one also well-versed in the “four-shape" system of early American music, which traces its lineage to the system of solmization used in Elizabethan England (and referred to in Shakespeare's King Lear) and, ultimately, medieval music theory concerning tetrachords, I recognize that the relative pitches in question are those called la and mi in “fasola" singing, with two iterations of la in each octave.  If we wish to recover the original sound of Gregorian chant based on the evidence of the most reliable sources, it will be necessary to address not only the restoration of text, melody, and rhythm, but also pronunciation, tuning, breathing, and tone production.