Heavenly Harmonies:
Music of the Spheres

February 2000

Program Notes

I.  Primordial Vibrations  
Processional Introit:  Exsurge, quare obdormis Domine? plainchant
Beata viscera Perotin (fl. c. 1180-1220)
Kyrie "Cunctipotents Genitor" compilation: plainchant, organum from Codex Calixtinus, and polyphony from Messe de Nostre Dame by Guillaume de Machaut
II.  Humans in the Cosmos  
Nu alrest lebe Walther von Vogelweide (German, 13th c.)
Conductus:  Flos ut rosa floruit anonymous, Paris, c. 1175
Hymn:  Te lucis ante terminum plainchant
Motet: Alma chorus Domini Mathurin Forestier (fl. c. 1409-1535)
III.  Perfect Proportions  
Motet:  C'il s'entremet/ Nus hom/ Victimae anonymous, French, c. 1260
Gradual:  Sciant gentes plainchant
Sederunt principles Perotin
IV.  Human Passions and the Spheres  
Ondas do mar de Vigo Martin Codax, Galicia, 13th c.
Se je souspir Guillaume de Machaut
Salve, Regina plainchant
Salve, Regina Johannes Ockeghem (c. 1410-1492)
V.  Return to Center  
Regina celi letare Antonie Busnoys (c. 1430-1492)
Agnus Dei (from Messe de Nostre Dame) Guillaume de Machaut
Communion: Introibo ad altare Dei plainchant
Concluding prayer: Ite missa est (from Messe de Nostre Dame) Guillaume de Machaut


This program is meant to evoke the past.  We are connecting to the past through two things:  the sound of very old music, and the worldview that was dominant in Western Europe wen this same music was created.

This program is not merely a nostalgia trip, some vague journey down a lane beyond the memory of anyone in this concert hall.  To do that, to sentimentalize the past of to portray it as simply quaint or charming on our present-day terms, would be to miss the purpose of this program.  Rather, our intent is to introduce and, to the extent we cab, immerse you in a sound-world AND a way of looking at the world which are almost completely lost to us.

For most of recorded human history—that is, from the 6th century B.C. to the late sixteen century A.D.—people between the Atlantic Ocean and the Caspian Sea looked at things through a cosmic lens far different from the one in current use.  Despite the onset of Christianity’s teachings and morals, another worldview—arguably more potent and more all-encompassing than even the Church—dominated Western thought and arts, including music.  This was the “great theme,” first expounded by Pythagoras and perpetuated by such disciples and masters as Hermes Trismegistus, Plato, Boethius, and Marsilio Ficino.  The idea is this:  The world is simple and perfect, describable by perfect simple numerical proportions and perceptible to humans through our imperfect sense.  What we can perceive are merely the earthly reflections of perfect or divine forms.  Music on earth is a reflection of the “music of the spheres.”  The heavenly bodies spin and create music, which comes to us humans as vibrations we can perceive and even possibly hear. 

This isn’t a bad way of looking at the world, through it might seem a bit oversimplified to our hip, detached, 21st-century minds.  Some postmodernists have worked hard to debunk the basic tenants of neo-Pythagorean and neo-Platonic thought.  These critics have had some success, since the both the outside world and our perceptive and analytical apparatus have changed dramatically in two millennia. 

But is it possible that they have gone too far.  We have now inherited an impassable intellectual gulf between the scientist and the poet, the businessman and the musician.  As Jamie James says in his recent book, The Music of the Sphere,

Science has drifted so far from its original aims that even to bother with the question of its relationship to music might appear to be an irrelevancy, like chronicling the connection between military history and confectionery.  Yet every scholar of the history of science or of music can attest to the intimate connection between the two.  In the classical view it was not really a connection but an identity.

James then outlines glorious history of neo-Pythagorean thought, which I have interwoven on the next page with music-historical highlights, and presented in timeline form. 

Can you imagine, for a moment, a world in which every single sounding tone of music has intrinsic value, and could actually have an impact on your life?  Can you imagine music being that potent, that central to your being?  Can you imagine NOT having a radio, a TV, a CD player, or any other device which to fill up the “dead space” while you were going from place to place?  Can you imagine, furthermore, a life when you didn’t travel more than twenty miles from your birthplace at any time in your life, except maybe for a religious pilgrimage?  It would probably be easier to “tune in” to the idea of heavenly harmonies under life circumstances like those.  There was also much less data to assimilate on a regular basis: a single day’s issue of New York Times contains as much information (in terms if pieces of data) as a medieval person would have absorbed in his or her entire lifetime.

Pythagoras would never have understood Muzak.  To have music as a diversion, as a “throw-away” commodity, as a commercial product for its own sake, would have rankled his sensibilities.  Rather, for Pythagoras and his followers of many centuries, balance and proportion and paramount.  So wrote Aristotle in the Metaphysics:

The Pythagoreans, as they are called, devoted themselves to mathematics;…having been brought up in it they thought its principles were the principles of all things…In numbers they seemed to see many resemblances to the things that exist and come into being;…since, again, they say that the attributes and ratios of the musical scaled were expressible by numbers; since, then, all other things seemed in their whole nature to be modeled after numbers, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.

It must have been a beautiful thing, to have the whole world expressed in numbers (that is, if you’re an old math nerd like me).  The connection between music and number is not a vague thing: Plato, Boethius, and many others took great pains to show the relationship between numbers and the tones of the musical scale.  Furthermore, they argues, music has a moral function and a role in society to affect people for good; classical writings are full of anecdotes in which music does indeed soothe the savage breast. 

“Okay,” you might as, “how does this number-and-music thing really work?”  It’s quite simple.  The length of a string has a direct relationship to the pitch it makes when you pluck it.  Vary the length according to the ratios of simple, whole numbers and you get the perfect musical intervals that make up the scale. 

At its simplest, a string of length 2 will sound an octave lower than the same string whose length is shortened to 1.  (In other words, if a string sounds a middle C at full length, it will produce the C an octave higher when the string is shortened by half.)  Thus the ratio 2:1 represents the octave.  Similarly, a string of length 2 will sound a fifth lower than the same string shortened to length 2.  Thus, to continue in this fashion, the numerical ratio 3:2 corresponds to the musical interval of a fifth; the ratio 4:3 is the forth, 5:4 is the major third, and so on, down to 9:8, which is the whole tone, and 256:243, which is the half-step of semitone. 

All other intervals can be derived from these.  Different repertoires of a cappella music place varying demands on the singer’s ear.  It has been argued that the best way to sing the Machaunt Mass is with Pythagorean tuning, which requires mathematically pure thirds and slightly wide fifths.  “Just” intonation, on the other hand, uses pure fifths and slightly lowered major thirds.  As it turns out, you have to compromise somewhere, virtually all the time.  The juncture between pure math and the practicalities of fretted and plucked instruments eventually give ride in the 18th century to “equal temperament,” in which the fifths on a harpsichord or piano are made imperfect by very small amounts in order that one can play in any key.  Cheating, perhaps, but it works. 

I’m convinced that the original experiments in two-and three-part polyphony came from a combination of factors; the very cool, new acoustics of the 12th-century cathedrals; the classical and scholastic doctrines of numerically derived music, and its place in the seven liberal arts within medieval universities; the growing complexity of music notation to be able to handle rhythm as well as pitch; and sheer human curiosity.  From these humble beginnings we now have a rich, 800-year-old legacy of great polyphony, the roots of which we are happy to share with you today.  Enjoy your immersion, and let us know what it’s like to come back to the 21st century afterward. 

-Jonathan Miller