MENSURALISM. - The body of theories that favor a measured rhythm of Gregorian melodies, as opposed to the theories favoring a free rhythm. The starting point is almost exclusively the tradition of medieval theorists; the scant clarity of their writings accounts for the variety of systems, so much so that the supporters of free rhythm (the accentualism of Pothier and David, the ictualism of Mocquereau and the Solesmes school) interpret these texts in a sense favorable to themselves (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, 215-16, 226-28, etc.).
Mensuralist theories can be divided into two broad categories: 1st group: the neumes of the ancient notation represent exact durations to be grouped into measures similar to the measures 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 carried out in 6 progressive operations, of which the most elementary is the translation of the neumes according to an equal rhythm suggested by the variable form of the neumes. For Houdard a neume, whether of 2, 3, 4 or more notes, is always and only worth one rhythmic beat: this beat is subdivided according to the number of notes, in such a way that the total is always equal to the first beat. Father Jeannin, on the other hand, does not admit the divisibility of the first beat and, setting aside a very important part of the written musical tradition, transcribes the neumes of the codices only with rhythmic signs or letters that he regards as representative of the primitive rhythm; in these, the letters having a positive value are only those indicating the doubling of the notes (that is, above all the horizontal episema and the letter t = tenete), while the letter e has only a negative meaning of not lengthening the note. This system, by denying the significance of nuance of imprecise value recognized in the so-called rhythmic signs, multiplies long notes to excess; the paleographic apparatus of Jeannin's system, much more studied than that of Dechevrens and Houdard, remains unconvincing because of the insufficient concordance among the codices and the far too excessive arbitrariness in the distribution of values in the slots of modern measures. Less thorough is the system of P. Wagner of Fribourg. Relying solely on the texts of theorists and primarily on the anonymous Vatican text of cod. 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 equivalences, from the laws of Gregorian composition and from the aesthetic consequences in practical application, the opposing school concludes instead that the radical neumes (virga, punctum) do not have the value of an exact duration but serve to indicate the relative pitch of the sound before the appearance of the musical staff.
2nd Group. Since medieval theorists had compared Gregorian rhythm to the scansion of metrical verses, modern theorists attempt to find again in the neumes the various groupings of shorts and longs such as to represent the framework of all the classical metrical feet. To this group belong the Bishop of S. Dié, Foucault, Prof. Gastoué and, at first, Ferretti. In the scientific field the inquiry is not closed, and certain established facts render the value of the mensuralist theory precarious. In the practical field, in the liturgical functions the Gregorian melodies are not to be performed according to a mensuralist system (cf. Responsum of the S. Congr. of Rites to the Bishop of Roermond, 25 July 1934: Acta Sanctae Sedis, 40 [1907], p. 533; 43 [1910], p. 148).