1. Music of the Spheres. The place of music in the
cosmic pattern goes back, first of all, to the discovery
of the Pythagoreans (as reported by later writers) that
while musical strings of the same length, thickness, and
tension, when plucked, invariably produce the same
pitch, one such string divided in half always sounds
an octave higher, a segment two-thirds as long a fifth,
one three-fourths as long a fourth. An octave or
diapason was represented by the numerical ratio 1:2,
the fifth (diapente) by 2:3, the fourth (diatesseron) by
3:4. Tones were thus measurable in space, with pitch
related to frequency of vibration. It seemed, then, by
a process of analogy, that these same proportions might
be applicable to motions of an ordered and unchanging
universe, in which planets, from moon to outermost
stars were thought to move at varying speeds in fixed
and concentric circles around the spherical earth as
center—an astronomical system which, highly refined
and varied by Ptolemy, was still widely accepted
throughout the Renaissance, despite the new heliocen-
tric theory of Copernicus. Intervals between the
spheres, it was suggested (with spheres imagined either
as crystal balls or as orbital pathways of the planets),
might be similar to those revealed by strings of musical
instruments; the cosmic instrument could conceivably
produce musical sound comparable to that of instru-
ments made by man.
The Pythagorean myth of Er, recounted in Plato's
Republic (X. 614B-621D), pictured the spheres as
wheels turning on an adamantine spindle, on each a
siren singing one tone and together forming a harmony,
while the three Fates controlled the motions both of
the spheres and of the lives of men. Here was the
“Sirens harmony” described by Milton in the Arcades
(lines 63-73), sung “to those that hold the vital shears,
And turn the Adamantine spindle round,/ On which
the fate of gods and men is wound.” Philosophers after
Plato changed sirens to Muses or Intelligences, while
in the Christian context they were corrected to Angels,
who, in hierarchical order from Angels on the moon
to Seraphs on the sphere nearest to God, filled the
heavens with song. The “Crystall sphears,” in Milton's
Nativity Ode (lines 125-32), made “up full consort to
th'Angelike symphony.”
Whether or not the spheres and planets actually
produced musical sound was a question argued for
centuries, as it was still in the Renaissance. Aristotle,
believing spheres to be crystalline, denied the possi-
bility on the basis that sound, if it existed, would be
so loud as to shatter solid matter. On the other hand,
Macrobius, in his fifth-century Commentary on
Cicero's “Dream of Scipio” (De re publica, VI. xviii.
18-19), discussed seriously the “great and pleasing
sound” of the spheres, unheard by man because of the
limited range of his hearing (or because, others sug-
gested, man's soul, dragged down by his body, is closed
in by “muddy vesture of decay”). In the Renaissance,
philosophers of the occult, led by Ficino and Cornelius
Agrippa, attributed specific tones and voices to the
planets, while Aristotelians restated their Master's
argument. From the beginning, however, this music
had been most often considered a poetic symbol of
universal harmoniousness. Milton could write poeti-
cally in the Arcades (lines 72-73) of this music “which
none can hear/ Of human mould with grosse unpurged
ear,” but in his prolusion “On the Music of the
Spheres,” he saw it as a figure to symbolize in a “wise
way” the intimate “relations of the orbs and their
eternally uniform revolutions according to the fixed
laws of necessity.” Yet, on the Continent, the astron-
omer Johannes Kepler (1571-1630), who accepted the
Copernican theory that the sun and not the earth is
the center of the universe, and who, himself, replaced
the circular orbit of heavenly bodies by elliptical ones,
could not abandon the belief that mathematical har-
mony in celestial order is analogous to that of heard
music; and in
harmonices mundi (1619), he attempted
still to express planetary motions in musical notation.
Into this mathematical-musical cosmic scheme were
drawn the four elements, which Empedocles made the
indestructible constituents of all things, changed only
by motions of harmony and discord, and which Aris-
totle placed in concentric shells between the spheres
of the moon and the earth. Fire, air, water, and earth
eventually added four strings to the cosmic lyre or
made an unheard music of their own. It was not mere
whimsy that led Robert Fludd, in his Utriusque cosmi
(1617, p. 90), to picture the entire universe as a mono-
chord that reached from earth through the elements
and the spheres, each intervening space designated as
a musical interval, with the hand of God reaching from
outermost heaven to tune it. “Water and Air He for
the Tenor chose,” wrote Abraham Cowley (1618-67),
in his youthful poem, Davideis (Book I, secs. 35-36);
“Earth made the Base, the Treble Flame arose,” a song
accompanied by the sounding strings of the planets.
Man, too, “a little world made cunningly of elements,”
joined in music of macrocosmic spheres and elements.
On the authority of Pythagoras, and of Plato, who
had, in his Timaeus, envisaged a mathematically and
musically ordered universe more intricately contrived
than that suggested by early Pythagorean experiments,
men concluded that the basis of all harmony in macro-
cosm and microcosm alike is mathematical; that what-
ever exists is based on proportion or number, the con-
cordant relationships of which are revealed in music.
For this reason music was included in the medieval
quadrivium of the liberal arts—along with arithmetic,
geometry, and astronomy—where it gained a standing
as an intellective study not otherwise to be achieved.
“How valuable a thing music is,” wrote the school-
master Richard Mulcaster, in prefatory verses to Tallis
and Byrd's Cantiones sacrae (1575), “is shown by those
who teach that numbers constitute the foundation of
everything that has form, and that music is made up
of these.”
Of these numerical relationships the easiest for the
layman to grasp were the Pythagorean intervals of
diatesseron (fourth), diapente (fifth), and diapason
(octave), which by mathematical manipulation could
be combined or altered to form all other concords—for
“musick is but three parts vied and multiplied.” As
Jean Bodin remarked, in his Commonweale (1606, p.
457), Plato's numbers are so difficult that even Aristotle
had jumped over them “as over a dich,” even as Bodin,
and to a large degree, his contemporaries continued
to do. Intervals of the fourth, fifth, and octave, con-
sidered most harmonious and pleasing, symbolized for
many the harmoniousness of all creation. The com-
monwealth “decays when harmonie is broken,” wrote
Bodin (p. 455), “which chaunceth when... you depart
farthest from those concords which the Musitions call
diatesseron and diapente.” By these intervals, the music
philosopher and physician, John Case, in his Praise of
Musicke (1586, p. 44), measured proportions of the
rational, irascible, and concupiscible faculties of the
soul. On the authority of the Italian architect, Leone
Battista Alberti (1404-72), who had learned “from the
Schoole of Pythagoras” that harmony in sight is related
to harmony of sound, Sir Henry Wotton advised, in
The Elements of Architecture (1624, pp. 42-43), that
measurements of doors and windows be based on musi-
cal intervals of octave, fourth, and fifth. Music revealed
the secrets of all mathematical order, in spheres, com-
monwealth, the soul of man, and in his artifacts.
