November 23, 2019




from Messe de Nostre Dame
Guillaume de Machaut (ca. 1300-1377)


Hec dies (Easter gradual)
Hec dies (clausula)
Hec dies (clausula)
Hec dies (clausula)
Hec dies leticie/Hec dies (motet)
Gregorian chant, Paris, Bibl. nat. 1112
Florence, Plut. 29.1 (F) (ca. 1245)
Wolfenbuttel, 628 (W1) (ca. 1240)
Florence, Plut. 29.1
Wolfenbuttel, 1099 (ca. 1260)


Hec dies (organum) Leonin? (Florence, Plut. 29.1

A HIGHPOINT, cont’d.

from Messe de Nostre Dame
Guillaume de Machaut


O Maria virgo davitica/O Maria/VERITATEM
Ave, regina/Alma redemptoris/ALMA
Puellare gremium/Purissima mater/Pes
Alle psallite cum luya/ALLELUYA
Montpellier, H196 (Mo) (ca. 1300)
La Huelgas Codex (ca. 1325)
Worcester Cathedral, MS Add. 68 (ca. 1280)
Montpellier, H196


Agnus Dei
from Messe de Nostre Dame
Guillaume de Machaut


Mon chier amy
Eya dulcis/Vale placens
Guillaume Du Fay (ca. 1397-1474)
Jean de Noyers dit Tapissier (ca. 1370-c. 1409)


Ite missa est
from Messe de Nostre Dame
Guillaume de Machaut


Apostolo glorioso/Cum tua doctrina/ANDREAS
Guillaume Du Fay
Johannes Ciconia (ca. 1370-1412)


Kristina Boerger, Amber Evans, Chloe Holgate, Dominique Surh – sopranos
Nathaniel Adams, Michael Steinberger, Christopher Preston Thompson – tenors
Thomas McCargar – baritone
Peter Stewart – bass

This concert is made possible, in part, with public funds from the New York State Council on the Arts, with the support of Governor Andrew Cuomo and the New York State Legislature.

Commentary on the Program

by Alexander Blachly

   One of the principal teachings attributed to Pythagoras (fl. ca. 500 BC) was that sounding music on earth, as well as the unsounding “music” of a single person in harmonious balance emotionally or physically (or the “music” of individuals interacting harmoniously within a society), all were in tune with the divine “music of the spheres”—that is, the movement of the heavenly planets against the array of unmoving stars in the outermost bounds of the universe. The greater the role played by number in the design of any work of art, therefore, whether of architecture, painting, sculpture, poetry, or music, the more “musical” such a work would be. In all of the musical pieces heard this evening, from the two-voice organum setting of Hec dies for the Cathedral of Notre Dame in Paris at the end of the twelfth century, to the four “isorhythmic” movements of Guillaume de Machaut’s Messe de Nostre Dame of ca. 1360, to the mind-boggling isorhythmic motets by Tapissier and Guillaume Du Fay in the waning Middle Ages of the early fifteenth century, numerical designs of various kinds play a key role.
   Numerical designs in music are first found in the so-called “Notre Dame” polyphony from the time of the legendary Leonin and Perotin at the end of the twelfth century; more precisely, they are found in the notated sources for this repertoire, which postdate the music itself by half a century. If, as Anna Maria Busse Berger has argued, the reason for the delay is that the music was originally composed and performed by memory, we can better understand why the major notated sources for Leonin and Perotin’s music all disagree with one another on many points in their transmission of what are clearly the same basic pieces. Oral tradition inevitably involves evolution and change. One of the changes might have been which clausulae were substituted into a given organum setting over the years (clausulae being passages in “discant” texture, where the chant voice moves at roughly the same speed as the newly composed upper voice or voices—as opposed to “organum purum” style, where the tenor voice singing the chant melody does so in such slow motion that the effect is of a series of long pedal tones; the discant passages become clausulae when they have been removed from an organum setting and exist as short, independent pieces). Just as discant passages can be removed from an organum setting to become clausulae, so too can newly composed clausulae be inserted into an organum setting to replace what was there with an updated example of contrapuntal skill. Thus, while clausulae are where numerically designed polyphony first appears, some, perhaps all, of these short passages in the large-scale organum setting heard this evening are later additions, possibly even a generation later. Though these passages may not be as old as the organum purum sections, for our purposes this doesn’t matter: they are where we see the origins of what can be called “Pythagorean” polyphony—music composed on the framework of a numerical design to which the music is forced to conform.
   In our program, the tiny clausulae and motet that precede the organum all tend to have a texture similar to that work’s discant passages, with a brief repeating rhythmic pattern imposed on the tenor (the lower voice singing the chant), resulting in unusual “cadences” (breathing places) and against which the upper voice may be as sophisticatedly out of phase as possible, while still making good musical sense as counterpoint. All of these pieces’ tenors are also based on the same sequence of pitches, taken from the opening of the gradual for Easter Sunday, heard in its entirety in the large-scale organum setting. This famous melody—or at least its opening notes—served as the foundation for numerous polyphonic elaborations in the thirteenth century. In the organum setting, however, these notes are sung so slowly that it is hardly possible to hear that they are the very same as those of the chant snippet with which this section of the program begins.
   Recurring like a musical rondo in our program are movements from Guillaume de Machaut’s Messe de Nostre Dame of ca. 1360, the earliest known example of an entire polyphonic Mass ordinary composed by a single composer and preserved in manuscript sources from the composer’s lifetime as a single piece. Each movement heard this evening is based on a different Gregorian chant, each subjected to rhythmic patterning to create what is now known as isorhythm. These various repeating rhythms in the tenor voice, which sings the chants, result in note values (durations of one, two, or more beats) that repeat as a numerical substructure over which the intricate, highly syncopated upper voices dance and pause in lively juxtaposition. There is some evidence that the entire Mass was sung regularly on Saturday evenings in the Cathedral of Notre Dame in Reims, where Machaut was a canon in residence at the end of his life, and after his death still sung weekly for many years in commemoration of him and his brother, Jean, also a canon at the cathedral. According to a plaque that hung on a pillar of the cathedral near Machaut’s grave until the eighteenth century, a substantial sum of money was raised when Machaut died specifically for the purpose of paying singers to present this musical feat weekly—a most remarkable fact when one considers the musical demands of the piece. If the weekly performances happened as planned, is there another masterpiece in the Western canon prior to the nineteenth century (aside from Handel’s Messiah) to have received so many performances?
   Tapissier was singled out by Martin le Franc in his 24,000-verse poem Le Champion des dames of ca. 1440 as a composer who “astonished all Paris.” His motet Eya dulcis/Vale placens well fulfills the expectations that assessment raises, for it shifts continuously and astonishingly from one metrical pattern to another in three large sections exhibiting exact isorhythm in all four voices. Some recent writers have supposed that the fanfares of the upper voices at the beginning of each large section imply performance by instruments, but this cannot be assumed, since there is no direct evidence for the participation of instruments in motets at the beginning of the fifteenth century. Just as likely, it would seem, the fanfares are intended as vocal evocations of trumpets. The metrical shifts, which three times include a virtuosic measure of 4:3 at the level of semibreves in the second voice simultaneously with a fast 3:2 hemiola against those semibreves in the top voice, create a soundscape of subtle waves of durational values moving in and out of phase with one another in a complex symphony of numbers.
   Du Fay’s motet for Saint Andrew, Apostolo glorioso, possibly written for the rededication for the Church of Saint Andrew on the Greek island of Patras in 1426, is his only large-scale ceremonial work in Italian. It presents five voices, all in isorhythm, in a brilliant array of contrapuntal effects. A canon appended to the tenor states that this voice “dicitur bis: primo de modo perfecto et tempore imperfecto; secundo per tercium demptis primis pausis et nota sequente” (is stated twice, first in perfect modus with imperfect tempus, secondly three times faster, minus the opening rests and the note following). The melody is indeed stated twice, but its rhythmic pattern, being only half as long, is stated twice each time. Since the tenor is notated only once, it effectively defines the overall dimensions of the motet as (minus the opening peroration) 3:3:1:1, perhaps symbolically recalling the Trinity, since the event appears to be confirmation of the Church of Saint Andrew as a Christian temple in which the godhead was the three-in-one Father, Son, and Holy Spirit.
   We end our program with Ciconia’s Gloria, No. 3 in the new Complete Works, which has a canon attached to the contratenor: “dicitur ter primo et secundo ut iacet tercio per semy” (it is said three times, first and second as it lies, third [diminished by] by half). “By half” means that notes written as breves in the first and second statements will now be regarded in the third statement as semibreves, and with each semibreve equal to three minims. In opposition to French theory, where the minims would remain equal, the relationship now is that minims in the third section are a third faster, as though the whole third section is to be performed in triplets at the minim level. This actually corresponds to Italian theory, where a breve of quaternaria (of four minims) equals a breve of senaria imperfecta (of six minims). The upper voices, which are not isorhythmic, move much faster than the tenor and contratenor throughout, effectively obscuring the lower voices’ underlying isorhythmic construction. So though a listener can hardly hear the relationship in the contratenor (and tenor, which moves at the same speed), the shift of meter when the third section begins is unmistakable in the upper voices. Thus, the piece as a whole exhibits mensural isorhythm, with the same notes and the same rhythms recurring at different speeds and in different meters.
   The program charts an evocative journey from the earliest numerically designed polyphony (thirteenth century) to the sophisticated numerical structures of the Ars nova (fourteenth century) to some of the last and most intricate numerical masterpieces before the innovations of the Renaissance (early fifteenth century).

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