MENSURALISM. – The body of theories that favor a measured rhythm in Gregorian melodies, in opposition to theories advocating free rhythm. The starting point is almost exclusively the tradition of medieval theorists; the lack of clarity in their writings justifies the variety of systems, so much so that the supporters of free rhythm (Pothier and David’s accentualism, Mocquereau’s ictualism and the Solesmes school) interpret these texts in a way favorable to their own views (Pseudo-Hucbald, in Gerbert, *Scriptores de Musica*, I, pp. 182-184; Guido d’Arezzo, *Micrologus*, ibid., II, 14-16; Aribo, *Musica Aribonis Scholastici*, ibid., II, 215-216-228, etc.).
Mensuralist theories can be divided into two broad categories:
1. **Group:** The neumes of ancient notation represent exact durations to be grouped into measures similar to those of modern music, such as 2/8, 3/8, 5/8, 7/8, 2/4, 4/4, etc. For Dechevrens, the rhythmic restoration of an ancient melody is achieved through six progressive operations, the most elementary of which is the translation of neumes according to an equal rhythm suggested by the shape of the neumes. For Houdard, a neume, whether it consists of two, three, four, or more notes, always and only represents one rhythmic beat; this beat is subdivided according to the number of notes so that the total always equals the primary beat. Father Jeannin, however, does not admit the divisibility of the primary beat and, setting aside an important part of the written musical tradition, transcribes the neumes of the manuscripts only with rhythmic signs or letters that he considers representative of the primitive rhythm. In this system, only the letters that indicate the doubling of notes (especially the horizontal episema and the letter *t* = *tenete*) have positive value, while the letter *c* has only a negative meaning of not lengthening the note. By denying the significance of the nuance of imprecise value attributed to the so-called rhythmic signs, this system excessively multiplies long notes. The paleographic apparatus of Jeannin’s system, far more studied than those of Dechevrens and Houdard, remains unpersuasive due to the insufficient agreement between manuscripts and the excessive arbitrariness in the distribution of values within the measures of modern notation. The system of P. Wagner of Freiburg is less developed. Relying on elementary texts by medieval theorists and primarily on the anonymous Vatican manuscript *lat. Reg. 235*, he concludes, without paleographic demonstration, that the *virga* (straight or *jacens*) is worth 2 beats, the *virga* with episema (straight or *jacens*) 4 beats, and the *punctum* 1 beat; these values are maintained for the individual elements of more complex neumes. From paleographic misunderstandings, the laws of Gregorian composition, and the aesthetic consequences in practical application, the opposing school concludes instead that the radical neumes (*virga*, *punctum*) do not have a value of exact duration but indicate the relative pitch of the sound before the appearance of the musical staff.
2. **Group.** Since medieval theorists compared Gregorian rhythm to the scansion of metrical verse, modern theorists attempt to find in the neumes various groupings of shorts and longs that represent the framework of all classical metrical feet. This group includes the Bishop of Saint-Dié, Foucault, Prof. G. Stouté, and, initially, Ferretti. In the scholarly field, research is not closed, and certain established facts cast doubt on the value of mensuralist theory. In the practical field of liturgical functions, Gregorian melodies are not to be performed according to a mensuralist system (cf. *Responsum* of the Sacred Congregation of Rites to the Bishop of Roccamonde, 25 July 1934: *Acta Sanctae Sedis*, 40 [1907], p. 533; 43 [1910], p. 148).