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(see Fr. Krasuski, "Ueber den Ambitus der grego- rianischen Messgesange", Freiburg, 1903). Melodies of the fourth mode having a constant b fiat fall in badly with the theoretic conception of a fourth mode having b natural as its normal note, and some antiphon melodies of that mode, although they use no 6 flat but have a as their highest note, e. g. the Easter Sunday Introit, are out of joint with the psalmody of that mode. It would, therefore, seem certain that the eight mode theory was, as a ready made system, imposed on the existing stock of plain chant melodies. Historically the first mention of the theory occurs in the writings of Alcuin (d. 804), but the " Paleographie Musicale" (IV, p. 204) points out that the existence of cadences in the Introit psalmody based on the literary cursus planus tends to show that an eight mode theory was current already in St. Gregory's time. From the tenth century forward the four modes are also known by the Greek terms, Dorian, Phrygian, Lydian, and ]\Iixol3-dian, the plagals being indicated by the prefix Hj-po. But in the ancient Greek theory these names were applied to the scales e-e, d-d, c-c, b-b respectively. The trans- formation of the theory seems to have come to pass, by a complicated and somewhat obscure process, in Byzantine music (see Riemann, "Handbuch der Mu- sikgeschichte", I, §31). The growth of the melodies themselves may have taken place partly on the basis of Hebrew (Syrian) elements, partly under the influ- ence of the varj-ing Greek or Byzantine theories.

Rhythm. — Practically, the most important ques- tion of plain chant theory is that of the rhj'thm. Here again opinions are divided. The so-called equalists or oratorists hold that the rhythm of plain chant is the rhythm of ordinary prose Latin; that the time value of all the notes is the same except in as far as their connexion with the different syllables makes slight differences. They hold, however, the prolongation of final notes, 7nora ullima: mcis, not only at the end of sentences and phrases but also at the minor divisions of neum groups on one sj'Uable. In the Vatican edi- tion the latter are indicated by vacant spaces after the notes. The mensuralists, on the other hand, with Dechevrens as their principal representative, hold that the notes of plain chant are subject to strict meas- urement. They distinguish three values corresponding to the modern quavers, crotchets, and minims. They have in their favour numerous expressions of medieval theorists and the manifold rhythmical indi- cations in the MSS., especially those of the St. Gall School (see Neum). But their rhythmical translations of the MS. readings do not give a satisfactory result, which they admit themselves by modifying them for practical purposes. Moreover, their interpretation of the MS. indications does not seem correct, as has been shown by Baralli in the "Rassegna Gregoriana", 1905-8. We may mention here also the theory of Riemann (Handbuch der Musikgeschichte, I, viii), who holds that plain chant has a regular rhythm based on the accents of the texts and forming two-bar phrases of four accents. He transcribes the antiphon "Apud Dominum" in this way:

ct CO - pi - o - aa a - pud e-um re-dempti-o.

This looks quite plausible. But he has to admit

that this antiphon suits his purposes particularly, and when he comes to more complicated pieces the result is altogether impossible, and for the long final neumata of Graduals he has even to suppose that they were sung on an added .\lleluia, a suppo.sition which has no historical foundation. Possibly the melodies of Office

antiphons, as they came from Syria, had originally some such rhythm, as Riemann states. But in the process of adaptation to various Latin texts and under the influence of psalmodic singing they must have lost it at an early period. A kind of intermediate position between the oratorists and the mensuralists is taken up by the school of Dom Mocquereau. With the oratorists they hold the free combination of duple and triple note groups. With the mensuralists they state various time values ranging from the normal duration of the short note, which is that of a syllable in ordinary recitation, to the doubling of that duration. Their system is based on the agreement of the rhj^hmical indications in the MSS. of St. Gall and Metz, and recently Dom Beyssac has pointed out a third class of rhythmical notation, which he calls that of Chartres ("Revue Grcgorienne", 1911, no. 1). Moreover, they find their theories supported by certain proceedings in a large number of other MSS., as has been shown in the case of the "Quilisma" by Dom Mocquereau in the "Rassegna Gregoriana", 1906, nos. 6-7. Their general theory of rhj'thm, according to which it con- sists in the succession of arsis and thesis, i. e., one part leading forward and a second part marking a point of arrival and of provisional or final rest, is substantially the same as Riemann's (see his "System der musikali- .schen Rhj'thmik und RIetrik", Leipzig, 1903), and is becoming more and more accepted. But their special feature, which consists in placing the word accent by preference on the arsis, has not found much favour with musicians generally.

Forms. — Plain chant has a large variety of forms produced by the different purposes of the pieces and by the varj'ing conditions of rendering. A main dis- tinction is that between responsorial and antiphonal chants. The responsorial are primarily solo chants and hence elaborate and difficult; the antiphonal are choral or congregational chants and hence simple and easy. Responsorial are the Graduals, Alleluia verses, and Tracts of the Mass, and the responses of the Office. The antiphonal type is most clearly shown in the Office antiphons and their psalmody. The Mass antiphons, especially the Introit and Communion, are a kind of idealized antiphon type, preserving the general sim- plicity of antiphons, but being slightly more elabo- rated in accordance with their being assigned from the beginning to a trained body of singers. The Offerto- ries approach more closely to the responsorial style, which is accounted for by the fact that their verses were at an early period assigned to soloists, as ex- plained above. Another distinction is that between psalmodic and what we may call hymnodic melodies. The psalmody is founded on the nature of the Hebrew poetry, the psalm form, and is characterized by recita- tion on a unison with the addition of melodic formulae at the beginning and at the end of each member of a psalm verse. This type is most clearly recognized in the Office psalm tones, where only the melodic formula at the beginning of the second part of the verse is wanting. A slightly more ornamental form is found in the Introit psalmody, and a yet richer form in the ver- ses of the Office responses. But the form can also still be recognized in the responsorial forms of the Mass and the body of the Office responses (see Pal. Mus., III). Of a psalmodic nature are various other chants, such as the tones for the prayers, the Preface, some of the earlier compositions of the Ordinary of the Mass, etc. The hymnodic chants, on the other hand, show a free development of melody; though there may be occasionally a little recitation on a monotone, it is not employed methodically. They are more like hymn tunes or folk songs. This style is used for the anti- phons, both of the Office and of the Mass. Some of these show pretty regular melodic phrases, often four in number, corresponding like the lines of a hymn stanza, as, e. g., the "Apud Dominum" quoted above. But oftentimes the correspondence of the melodic