Pietro Aron's 1525 treatise, the Trattato della natura e cognizione di tutti gli toni di canto figurato, provides great insight into theoretical notions of the time. Aron strove for an easily comprehensible and simple explanation of the contemporary theoretical system. Indeed, in light of the musical works then being composed, one may say that Aron's theory is, in certain aspects, oversimplified. Analysis of the Agnus Dei I and II from Josquin's Missa Pange lingua should bear this out.
An important concern of Aron's, and the one addressed in the Aron excerpt included by Strunk in his Source Readings in Music History, is determination of mode. In the present case, this would be done by noting the final note of the tenor, for the mode of the tenor establishes the mode of an entire four-voice composition. The final note in question is b. B is not a regular final, but as an irregular final is the confinal for the third and fourth tones (Phrygian and Hypophrygian modes). Indeed, the final sonority is e-b-e', and the species of fifth and fourth and their placement in this one sonority are consistent with the third tone (Phrygian).
Although the work does appear to end in Phrygian, there are a number of criticisms of this method of mode determination that may be made. First, one may question the use of the tenor as the critical voice. The tenor historically contained the cantus firmus, but here the Pange lingua melody is distributed in fragmented form throughout all four voices; the musical structure is in no way based on the tenor. Much more importantly, little of the work is actually in Phrygian. The beginning of Agnus Dei I, for example, is very clearly in a mode Aron did not recognize: Ionian. In mm. 15 in the altus, the skip c-g and back appears several times; the scalar pattern g-a-b-c' is used twice, clearly establishing species of fifth and fourth of TTST and TTS, respectively. The melody is on c' at the cadence in m. 5. The range fits into Hypolydian, but aside from the obvious problem with species, Aron states that Hypolydian melodies cannot end on c because of the lack of an appropriate difference. The fact that Aron neatly sidesteps the whole issue by choosing not to deal with segments of a work but looking only at the end keeps one from getting a full appreciation of the modal structure.
Were Aron to concede the existence of the Ionian mode, he would see one of his concepts come into play in mm. 610 of the altus. The extension of the range to include the c'-g' area is an example of modus mixtus. In going from c-g' the altus has covered both the authentic and plagal portions of the Ionian mode (if the plagal portion may be admitted to be the fifth above the authentic rather than the customary fourth below).
In mm. 1011 a phenomenon takes place that our modern ears would detect as a modulation to Aeolian (another mode that Aron did not recognize). Josquin gets there via a series of parallel 6/3 chords. Aron would have disapproved, as he felt that 6/3 chords were harsh and should be avoided whenever possible.
The Aeolian sound persists for only a few measures; the music soon establishes itself in Dorian. In fact, Aron might have made a good case for mm. 1115 being in Dorian. The ranges are possible: the superius and tenor using the authentic portion and the altus and bassus the plagal. The Dorian cadence in m. 15 establishes Dorian clearly. In the course of the imitative section from m. 17 to the end of Agnus Dei I an Ionian sound is re-established, largely due to a g-c motion in the bassus. Thus it is somewhat of a surprise when the section closes on an e-g-b-e' sonority that is itself in the mode of the entire movement, Phrygian.
The ranges of the individual parts do little in Agnus Dei I to support Phrygian. The superius range is d'-d''; this range and the species of fifth and fourth used in much of the section suggest Dorian. The altus, as mentioned earlier, spans a c-g' range. Aron would probably have to regard this as Mixolydian, modus mixtus, but the fifth and fourth species do not support such a contention. The tenor spans d-f'; it is the voice whose range, at least, is closest to Phrygian. But it goes no higher than d' until m. 18; up to that point, Dorian seems a more likely description. The bassus range is G-c'. Glareanus would have no trouble in classifying this in terms of range and species as Ionian, modus mixtus. What Aron would do is questionable; he would probably ignore it and refer only to the tenor. Perhaps Aron would claim as well that the species even in the tenor, inconsistent as they are with Phrygian, illustrate his concept of modus commixtus.
In short, Aron's desire for simplicity actually directs one's attention away from fascinating manipulations of mode achieved by Josquin.
In Agnus Dei II, an argument for Phrygian is slightly more convincing, but large portions of it employ other species and, once again, Aron would be forced to describe these portions as modus commixtus when an actual change of mode seems more to the point. The ranges in Agnus Dei II are c'-d'' for the superius, d-g' for the altus, d-e' for the tenor, and G-a for the bassus. The tenor range is believable for Phrygian, but the species seem more consistent with Dorian (modus commixtus again?).
A few additional comments on ranges might be made. It seems likely, according to the overall ranges (c'-d'' for superius, c-g' for altus, d-f' for tenor, and G-c' for bassus), that only the superius was intended for women's voices; the altus range seems appropriate for a modern tenor (especially if, as many contend, pitches of named notes were lower in the Renaissance). The extreme range of the altus and its wide skips (including many octave jumps) would make for some interesting performance problems. Josquin did not hesitate to cross adjacent voices, particularly altus and tenor (e.g., mm. 811 [in m. 8 the tenor is at one point fully an octave above the altus]).
Cadences are frequent in Agnus Dei I; much less so in Agnus Dei II. When they occur, they very often do not sound final because motion continues in one or more voices. They are recognizable by the major sixth to octave motion mentioned by Bergquist in his article. The first such cadence appears going into m. 4; the M6octave motion takes place in the bassus and altus, with the bassus as the upper part! Bergquist says that Aron mentioned the frequent use of the same note for the antepenultimate as for the final in a cadence. Such a cadence is found in the superius and tenor going into m. 9. Here a 76 suspension is used. Another such cadence is found going into m. 11 in the tenor and bassus; it illustrates also the necessity of sometimes using musica ficta to assure that the penultimate interval is a major sixth. This cadence also uses a 6/3 chord as penultimate; Aron probably would have frowned upon this.
Josquin seems to prefer a full triadic texture; exclusively perfect consonances, even at cadences, are becoming more the exception than the rule. The final sonority of the Agnus Dei I is a full triad; yet at the end of the Agnus Dei II Josquin bows to tradition by moving to the open fifth after first establishing a triad.
Josquin uses imitation widely, preferring the strict (fugal, as Aron calls it) variety. Both sections of the movement begin with the same melodic pattern in each of the four voices as they enter in turn. At the beginning of Agnus Dei I, beyond the identity of the first four notes in all voices, imitation continues between the altus and bassus and between the superius and tenor. The pitch interval by the modern terminology is a unison in all cases. By Aron's method (the interval between the two voices at the moment the comes enters) the altus-bassus imitation would be at the unison, but the superius-tenor imitation would not be classifiable, since the tenor is resting when the superius enters. An example of imitation at various intervals occurs from m. 17 to the end of Agnus Dei I in the superius, altus, and tenor. Imitation is also used to a great extent in Agnus Dei II as indicatedespecially toward the end of the movement. In regard to both sections, the general statement may be made that toward the beginning of the section imitation is usually at the unison (using the modern convention of describing the interval according to the first note of each entrance); the time interval is relatively long; and the pattern occurs only two or three times. Toward the end of each section, imitation occurs at various pitch levels; entrances come in more rapid succession (stretto); and there are more repetitions, often involving three or all four voices.
It is not clear from the Strunk excerpt and the Bergquist article how many other analytical concerns are discussed by Aron. But from what is available in those sources, it seems that Aron's theory equips one only to scratch the surface of the music of such a creative composer as Josquin. Even one primarily accustomed only to the music of the common-practice period can identify with many of the structural and functional elements as well as the expressive content of Josquin's music; Aron's theory is then but a starting point for meaningful analysis.
Aron, Pietro. "From the Trattato della natura e cognizione di tutti gli toni di canto figurato." In Source Readings in Music History: From Classical Antiquity through the Romantic Era, pp. 20518. Edited by Oliver Strunk. New York: W. W. Norton & Co., 1950.
Bergquist, Peter. "Mode and Polyphony around 1500: Theory and Practice." In The Music Forum, vol. 1, pp. 99161. Edited by William J. Mitchell and Felix Salzer. New York: Columbia University, 1967.
Josquin des Prés. Missa Pange lingua. 5th ed. Das Chorwerk, ed. Friedrich Blume, no. 1. Wolfenbüttel: Möseler, n.d.