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 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 Guillaume Du Fay and Tapissier 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 nearly 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). Though 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, inserted to update what was originally there. For our purposes this doesn’t matter: they are where we see the origins of what can be called “Pythagorean” music—music composed on the framework of a numerical design to which the composition of the polyphony is forced to conform.

   Thus, it is in the discant passages in the two-voice organum settings of the music composed for Notre Dame Cathedral in Paris in the late twelfth century—of which the organum setting of Hec dies in this evening’s program is a representative example—that we first hear the effects of numerical design. (Because no composer attributions are given in the notated sources, we can only speculate that our program’s organum might be by Leonin.) 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 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.

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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