Excerpt from Gregorian Chant according to the Manuscripts by Dom Gregory Murray, O.S.B. (full PDF here)
Summary of “The Rhythm of Gregorian Chant” from Rhythm, Meter and Tempo in Gregorian Chant by Dr. Jan van Biezen; the examples in square notation are available here
“Tradition of Durational Values in Gregorian Chant" by Arthur Angie (in The Caecilia, 1934, vol. 60, no. 10–11)
Collected Articles on Chant Rhythm by Dom Gregory Murray, O.S.B.
Gregorian Chant: A History of the Controversy Concerning Its Rhythm by John Rayburn
Rhythmic Proportions in Early Medieval Ecclesiastical Chant by Fr. Jan Vollaerts, S.J.
Mensuralism & Historically Informed Performance Practice:
under the direction of the late Fr. Roman Bannwart, O.S.B., on Spotify and YouTube; these recordings generally agree with the semi-mensuralist rhythmic theories articulated by Dr. Dirk van Kampen in this article
Note: Most if not all of the following sites presuppose a nuanced, non-proportional rhythmic interpretation.
Graduale Authenticum - the best online resource for viewing the oldest manuscripts; arranged according to the novus ordo Roman calendar
Graduale Synopticum - same edition and numbering as the Graduale Authenticum, with different search options; the Antiphonale Synopticum is accessible at the same site
Introits from the Graduale Novum - triplex edition incorporating the melodic corrections of the AISCGre working group published in the journal Beiträge zur Gregorianik
Graduale Restitutum - duplex edition incorporating the AISCGre melodic corrections, arranged according to the novus ordo Roman calendar; normally the same reading as the Graduale Novum
Offertoriale Restitutum - duplex edition with offertory verses
Graduale Renovatum - Royce Nickel's edition; normally the same reading as the Graduale Novum and Graduale Restitutum
Graduale Lagal - Chris Hakkennes's edition; arranged according to the novus ordo calendar
Graduel Neumé - Solesmes edition, pre-Pius XII, with St. Gall neumes copied by Dom Cardine
Graduale Duplex - Vatican edition with St. Gall neumes; arranged according to the novus ordo calendar
Several chants in duplex and triplex editions with melodic corrections from the Académie de chant grégorien, Brussels
Solesmes Method & Editions:
Church Regulations concerning Chant Editions:
Col Nostro (Italian) motu proprio of Pope St. Pius X authorizing the Vatican chant edition and permitting the approval of other books only if the variations in the chant come from good manuscripts (paragraph D)
Pietras Dubia & PCED Response (2018) tolerating chant editions and interpretations other than Solesmes/Vatican, no. 24; note that Pérès and his disciples use editions that sometimes differ considerably from the Vatican edition
Patrick Williams: organistAL at aol dot com