MENSURALISM. — A set of theories that favor a measured rhythm for Gregorian melodies, in opposition to theories advocating free rhythm. Their point of departure is almost exclusively the tradition of medieval theorists; the lack of clarity in their writings accounts for the variety of systems, to such an extent that the supporters of free rhythm (Pothier’s and David’s accentualism, Mocquereau’s ictualism and the Solesmes school) interpret these texts in a sense favorable to themselves (Pseudo-Huchbald, in Gerbert, Scriptores de Musica, I, pp. 182–184; Guido d'Arezzo, Micrologus, ibid., II, 14–16; Aribo, Musica Aribonis Scholastici, ibid., II, 215–216, 226–228, etc.).
Mensuralist theories may be divided into two major categories. First group: the neumes of the ancient notation represent exact durations, to be grouped into measures similar to those of modern music: 2/8, 3/8, 5/8, 7/8, 2/4, 4/4, etc. For Dechevrens, the rhythmic restoration of an ancient melody is accomplished through six progressive operations, the most elementary of which is the transcription of the neumes according to an equal rhythm suggested by the variable form of the neumes. For Houdard, a neume, whether consisting of 2, 3, 4, or more notes, always and exclusively has the value of one rhythmic beat; this beat is subdivided according to the number of notes, so that the total is always equal to the original beat. Fr. Jeannin, on the other hand, does not admit the divisibility of the original beat and, setting aside a very important part of the written musical tradition, transcribes the neumes of the codices solely by means of rhythmic signs or letters, which he regards as representing the primitive rhythm. Among these, the letters with positive value are only those indicating the doubling of notes (that is, above all, the horizontal episema and the letter t = tenete), whereas the letter e has only the negative meaning of not lengthening the note. By denying the meaning of an imprecise nuance of value attributed to the signs known as rhythmic signs, this system excessively multiplies the long notes; the paleographical apparatus of Jeannin’s system, much more thoroughly studied than that of Dechevrens and Houdard, remains unpersuasive because of the insufficient agreement among the codices and the excessively arbitrary distribution of values within the divisions of modern measures. P. Wagner of Freiburg’s system is less thoroughly developed. Relying exclusively on theoretical texts, and above all on the anonymous Vatican author of cod. lat. Reg. 235, he concludes, without paleographical demonstration, that the virga (upright or jacens) is worth 2 beats, the virga with episema (upright or jacens) 4 beats, and the punctum 1 beat; these values are retained for the individual elements of more complex neumes. From paleographical equivalences, the laws of Gregorian composition, and the aesthetic consequences of practical application, the opposing school concludes, on the contrary, that the radical neumes (virga, punctum) do not have the value of exact duration, but indicate the relative pitch of the sound before the appearance of the musical staff.
Second group. Since medieval theorists had compared Gregorian rhythm with the scansion of metrical verse, modern theorists attempt to discover in the neumes the various groupings of short and long notes capable of representing the framework of all the classical metrical feet. This group includes the bishop of S. Dié, Foucault, Prof. Gastoué, and, at an earlier stage, Ferretti. In the scientific field, the investigation is not complete, and certain established facts render the value of the mensuralist theory precarious. In practice, during liturgical functions, Gregorian melodies are not to be performed according to a mensuralist system (cf. Responsum of the S. Congr. of Rites to the bishop of Roermonde, 25 July 1934: Acta Sanctae Sedis, 40 [1907], p. 533; 43 [1910], p. 148).