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The Neglected Muse
Why Music Is an Essential Liberal Art
By Peter Kalkavage
“Music and rhythm
find their way into the secret places of the soul.”
—Plato
Music transcends the classroom, the concert
stage, and professional recordings. It pervades life.
Mankind has long used music in all sorts of ways, to
celebrate, to lament, to dance, to pray, to soothe or
arouse, to woo, to infuse courage and terrify an enemy, to
commemorate, to unite a community. Even the most primitive
societies are keenly aware of the power of music, and
various myths from cultures throughout the world confer on
music and musicians a lofty, even divine significance. In
some myths, notably in Plato’s dialogue Timaeus, the
world springs from the composing power of a musician-god.
That music is a vibrant part of life is
especially clear in the case of the young. Most young people
cherish their favorite music as their most intimate friend
and their absolute refuge from care and stress. When we get
older, music is inevitably bound up with nostalgia. We older
folk have only to hear a song from our youth in order to be
magically transported, as if by a familiar scent, to a
former time, place, self, or love. Music does not merely
sound: It casts a spell and conjures worlds. Music is no
mere addendum to human life, no historical accident that
might just as well have never been, but an essential part of
who we are as human beings.
Why should young people study music? One
answer presents itself on the basis of what I have said so
far: Music has a central place in the lives of young people.
For many, music is their life. Teaching music to the young
is therefore much more than conveying historical information
and technical facts, or helping students develop their
musical talent. It is more than the effort to make them
competent and aesthetically refined. In getting young people
to engage in a serious study of music, we are giving them an
opportunity to know themselves better by becoming more
precisely aware of the amazing power that music has over
them. Also, as we shall see, we are giving them an
opportunity to deepen their knowledge of the natural
world—and of our connection to it—by becoming more aware of
the mathematical order that underlies music.
Listening and Singing
In my three decades at St. John’s College in
Annapolis, Md., where all students are required to study
music for two years, I have learned that students cannot
engage in substantive musical learning without actual
musical experience. Such experience takes two forms:
listening to and making music.
Listening is an obvious requirement, but it
is harder than it might seem. What should students listen to
in their music classes, and what should they listen for?
We should, first and foremost, expose our students to great
music in the classical tradition (e.g., works by Bach,
Mozart, Beethoven, etc.) and then to other examples of great
music (e.g., folk songs, blues, and jazz)—broaden their
horizons, as the saying goes. But how to do this is
difficult. It makes sense to start with classical works that
are appealing and fairly short. For instrumental music,
single movements from symphonies, piano sonatas, and string
quartets work well. Perhaps the best “first thing” to listen
for is simply that musical works have a beginning,
middle, and end. Students can listen to a given piece
several times, each time listening for some particular
aspect of the work: a recurring theme, a rhythm, a moment of
heightened tension, etc.
But listening by itself is not enough.
Students, by singing or playing an instrument, must be made
to realize that music is not the symbols on the page any
more than a poem is the written word. Music and poem come to
be what they are only in the act of sounding. The object of
musical study is not the written symbol but the musical
event—the living phenomenon, for which the score is but the
recipe. More than anything else, singing brings music to
life and overcomes the passivity that often attends the act
of listening. In singing, students are the instrument
and the music. Most important here is not that students sing
well, but that they make their best effort. In singing great
choral works, however imperfectly, students get to
experience one of life’s most humanizing pleasures: that of
cooperating with others in the attempt to form a beautiful
whole that is more than the sum of its parts. Students thus
attain in sound the ideal of a perfected human community—a
perfected friendship that preserves differences but renders
them harmonious. To sing is to transcend the isolation and
vagary of selfhood. Such transcendence is one of the
greatest gifts of a genuine liberal education.
Music’s Connection to Math
and Nature
Music, amazing in its power over our emotions
and character, is even more amazing because it is eminently
capable of being studied. Traditionally, music is one of the
seven so-called “liberal arts.” Liberal, here, has nothing
to do with its current, political usage. It is not a synonym
for progressive. Rather, it is derived from the Latin
liber, meaning free, and is best associated with words
like liberate. The liberal arts constitute the knowledge
that free people need to guide them in their decision-making
at home, at work, as neighbors, and as citizens. The system
of seven liberal arts was first developed and taught in the
Middle Ages and has continued to strongly influence
education down to the present day. The liberal arts are
divided into a trivium (which is Latin for the three ways or
roads) and a quadrivium (meaning four ways or roads). The
trivium consists of the arts of grammar, logic, and
rhetoric; the quadrivium consists of the arts of arithmetic,
geometry, astronomy, and music. The former develops the arts
of language, the latter the arts of measurement. Together
they provide a template for a so-called “liberal education,”
whose end is not a technically trained professional, but an
educated human being.
As a quadrivial art, music has an exalted
placement that points to the long acknowledged bond that
music has with number and nature, and sharply distinguishes
it from the visual arts. The connection between music and
mathematics was established by the legendary Greek,
Pythagoras. Pythagoras discovered that the most commonly
used (and most singable) musical intervals had intelligible
mathematical counterparts.
Let’s use the octave as an example. To the
musician, notes that are one octave apart sound alike—the
only difference is that one is higher, or lower, than the
other. Modern science tells us that an octave is a musical
interval in which one note has either double or half the
frequency of another note—if one note has a frequency of 400
Hz (hertz or cycles per second), the note an octave above it
has a frequency of 800 Hz and the note an octave below has a
frequency of 200 Hz. So, the ratio for an octave is 2:1.
Pythagoras discovered this connection without
the knowledge of frequencies: He simply divided a string in
half and, to his utter amazement, heard that this division
produced the octave. Likewise, he discovered that when one
string is two-thirds the length of another, it will produce
a higher note that fits another common musical interval, a
perfect fifth (the first melodic interval in “Twinkle,
Twinkle, Little Star”). This discovery—that notes that sound
good together can be represented mathematically with ratios
of small whole numbers—was far-reaching; it suggested that
great music was not just a matter of taste and convention,
but was grounded in the very nature of the physical
universe—which could explain why humans respond to it. Our
sensuous experience of music might, in fact, be a deep if
unconscious response to an intelligible order: The most
common and singable musical intervals might be ratios
that we automatically sense. Moreover, it suggested the
possibility of a mathematical physics. If precise,
discoverable, numerical ratios were at work in the
relationships between notes separated by common musical
intervals, then wouldn’t they also be at work in, say, the
relationship between distance and the time it takes for an
object to fall to the ground?
It is easy, and fun, to recreate the
Pythagorean discovery by experimenting with different
divisions of a string on a device known as a sonometer or
“measurer of sound.” Sometimes it is called a monochord
because you need only one string to do Pythagorean
experiments. But the device works best when it has two
strings: one that is divided and another that is not, so
that it can serve as a reference pitch. A sonometer is very
easy to make, as I discovered when my son and I constructed
one for his high school science project. All you need is a
thick board, metal strings, a few screws, two small bridges
to anchor the strings at both ends, a small moveable
“bridge” that is used to divide the string at various
points, and a meter stick to take measurements. High school
students can use this simple musical instrument to verify
that the most common musical intervals do indeed correspond
to ratios of small whole numbers. They can do this in two
ways. One way is to measure off a length of the string that
corresponds to a given ratio (say, 3:2, or two-thirds the
length of the undivided string), move the bridge into place,
and then pluck the resulting partial length (the two-thirds
length) to hear if the predicted interval sounds (the
perfect fifth). The other way is for the students to move
the bridge around under the string, plucking and listening
at each point, until they reach what sounds like a given
interval and then use a meter stick to determine the ratio
into which the string has been divided. The octave is
especially interesting because of its simplicity and
familiarity. Knowing that its ratio is 2:1, students can
divide a string exactly in half without ever using a
visual measuring device. All they have to do is listen
for the division that sings the octave.
This simple Pythagorean experiment is a real
treat for students, who invariably experience amazement at
the mathematical grounding of music in nature. The
experience helps their learning in a number of ways. It
makes them realize that the musical intervals and the scale
acquire a precise definition only through the power of
mathematics (ratios); that the practical problem of tuning a
stringed instrument like a guitar or a piano is a
mathematical problem of getting different ratios to fit with
one another in a consistent scale; and that the tuning they
have inherited (the 12-toned equal temperament in which an
octave is divided into 12 equal half-steps) is the product
of a rich, complex history marked by incredible ingenuity
and laborious effort.
Music Shapes Us
Even apart from this profound connection with
mathematics, music is pre-eminent among the arts for the
order and clarity, the sharply defined character, of its
elements. Music moves us, sometimes to overpowering emotion.
It does so through well-defined structures, through an order
of tones and rhythms. It is not the mere sound of drums but
their rhythmic beating that stirs us. Here we come upon the
central paradox of music, the paradox that defines music as
a worthy object of sustained intellectual wonder: Music is
the union of the rational and irrational, of order and
feeling.
Ultimately, by shaping feeling, music shapes
the whole human being. For a proper understanding of this,
we turn to the ancient Greeks, for whom music, far from
being morally neutral, played a decisive role in moral
education. Aristotle’s Politics ends with an
extensive discussion of the proper moral and political uses
of music and the effect of music on the souls of citizens.
In the Republic, Plato draws our attention to the
power music has over the young. He places special emphasis
on the danger of music. The severity of his critique
underscores what we, in our effort to excuse or defend
music, often fail to acknowledge: that music is a great
power and, like any great power, can be used for great good
or great evil. Why is music so emotionally powerful, far
more powerful than the visual arts? Plato provides a
possible answer. In the Republic, he calls upbringing
in music “most sovereign” because rhythm and concord “most
of all sink down into the inmost part of the soul and cling
to her most vigorously.” In experiencing music, we do not
behold from a distance but drink in and incorporate. Some
forms of music, so Plato claims, are conducive to
orderliness of soul and the love of grace and beauty; others
indulge the baser passions and feed the lust for disorder
and self-indulgence. Studying music as a liberal art gives
students the opportunity to consider the possibility that
Plato is right—that music is not limited to taste and
enjoyment, but has a powerful influence on who we are and
whether we are ennobled or debased.*
This leads me to the observation that we are
shaped not only by music, but also by our opinions about
music. It is all the more important to revisit the
connection between music and moral education in a culture
like ours, steeped as it is in self-indulgence and
vulgarity. The study of music as a liberal art gives
students an extended opportunity to scrutinize their
opinions—and to confront the causes and effects of their
passions.
Cultivating Musical Taste
By studying music, we want to cultivate our
students’ taste, encourage their appreciation of beauty. But
what is this beauty? Why do we say that an aria from
Mozart’s Magic Flute or a movement from Beethoven’s
Ninth Symphony is beautiful? Although a complete
definition of beauty is beyond the scope of this essay, I
will venture a few remarks on this topic.
I begin with the old saying, “Beauty is in
the eye of the beholder” (or the ear of the listener).
This saying is both obviously true and obviously false. True
because beauty exists only in relation to a responsive
subject: It must appear beautiful to someone. False because
merely thinking that something is beautiful does not make it
so—judgments of beauty are not relative. Thinking that they
are confuses judgments of mere subjective liking with
judgments of aesthetic taste, which always claim to be
objective and universal. After all, beauty is not the same
as pleasure. Just as beautiful things do not always
immediately please, pleasures are not always beautiful. We
can take pleasure in something ugly and base. Beauty is not
a feeling in a human subject but a quality we perceive in an
object. The perception comes first, then the emotional
response. Beauty can take us by surprise. It strikes,
pierces, even transforms us. This would not be possible if
beauty came from us. Beauty educates us by taking us outside
ourselves. It compels us to transcend self-interest and
self-feeling. We do not merely behold beauty, but look up to
it. In appreciating beauty, we admire that which deserves to
be admired. To cultivate taste is therefore to cultivate
judgment. Beauty, in short, is in the eye of the educated
beholder.
Moreover, the beauty of a great musical work
is not always immediately evident. Sometimes it takes time,
and training, to realize that it is beautiful. Students
often say that a piece they did not like at first became one
of their favorites with repeated experience of it. Their
taste changed, not because they got used to something they
didn’t like, but because an inherent quality eventually
became apparent to them. There is an ancient Greek saying:
“Beautiful things are difficult.” This is true to our
experience of beauty, which sometimes comes to us only if we
make an effort to go to it.
In order for beauty to be admired, it must
first be recognized. As discussed in the previous section,
there is a long tradition that connects beauty and order,
especially mathematical order. The musician and
mathematician Edward Rothstein, in his book Emblems of
the Mind, shows how mathematical relations underlie the
beautiful in music. He writes: “A composition is a
construction of patterns and proportions, resembling an
argument in mathematics.” Relations like symmetry and
various sorts of proportion are, in fact, evident in the
works of the great composers.
But mathematics, though beautiful in its own
right, cannot fully explain the beauty of music. By itself,
it cannot explain our response to a Mozart aria or a
Beethoven symphony. Why do these pieces continue to attract
listeners who become familiar with them all around the
world, not just in the West? These pieces seem not to have
been written for one country, people, or time. They are
universal and belong to everyone. They strike us with their
amazing wholeness and perfection. Everything seems to fit
and cohere in a carefully worked out scheme. The orderliness
is not merely correct but inspired. With time and effort,
most of us can detect the layers of order and the balance of
forces at work in these pieces: the architecture of the
whole. We can detect how tensions build and are sustained,
and how they are satisfyingly resolved. We can even learn to
identify the technical means by which these effects are
produced. We hear how a theme is announced and then
developed, how it seems to take on a life of its own,
occasionally even seeming to spin out of control only to be
brought back into the economy of the musical whole.
Beautiful music pleases and sometimes
challenges us with its intelligence, depth, and complexity.
It does not please for the moment, but invites endless
re-experience and return. The more we listen, the more we
hear. And the more we study the music, the more reason we
have to find it beautiful. Music unfolds in time and
exhibits a delightful play of forces or tensions. In music,
the question of beauty comes down largely to this perception
of how musical forces conspire to form a whole.†
These forces or tensions are at work in the familiar major
and minor scales, and in the chords of harmony. Great
musical works exploit these tensions to the fullest. That is
why they are both maximally ordered and emotionally potent,
why, as we say, they are beautiful.
Learning from a Simple
Melody: Scarborough Fair
Music education that aims at real knowledge
requires careful attention to the elements of music: tones,
time-values, intervals, etc. Students must learn to read
music and correctly identify notes on a staff. Soon after
this “basic training,” they should look closely at how the
elements conspire to form significant musical wholes. These
wholes need not be impressive compositions by well-known
composers like Bach and Mozart—they demand way too much all
at once. A better way to begin is with a folk song.
Scarborough Fair, the very old folk
song made popular by Simon and Garfunkel in the ’60s, is a
good example of a beautiful, simple melody that lends itself
to close analysis. With the right guidance and materials,
even the most musically naïve students can begin to engage
in a deep and thorough analysis of this haunting melody.
One of the problems in getting students to
think about music is that it comes to us too easily. It
seems to be right there for our immediate pleasure. Music
does not, by itself, raise questions. One way to generate
questions is with a series of “experiments.” Play the melody
on the piano several times and have the students sing along.
Then change one note and get the students to state, to the
best of their ability, how they think the melody has changed
in sound and “feel.” Do this with different notes in the
melody and examine each change in turn. At each point, ask,
“What happened? What was the effect of the change?” Changing
a note in a melody—in effect, disrupting a familiar whole—is
also a good way to get students to become aware that there
is a whole. What is right sounding about a melody comes to
light when we cause it to stray from its intended path and
sound “wrong.” Students then begin to realize that the
melody consists of carefully made choices, and that a change
in one part is a change in the whole. Such experiments
become even more revealing when we alter the melody’s
rhythm.
Next, students should explore the connection
between the notes of the melody and the words. To do
this thoroughly, they should have access to the complete
text (whose story is very sad). Does the sound of the melody
fit the meaning of the words? What do the words gain in
being sung? Does the melody make certain words stand out?
How does the rhythm affect the mood of the song, the meaning
of the words, and the story they tell?
Finally, students can compose a variation of
Scarborough Fair, perhaps with their own lyrics. In
this exercise (which I have found works beautifully in
class), students learn, through direct experience, that
composition involves revision: that certain musical choices
don’t work, that some work better than others, and, more
generally, that a piece of music (like a piece of writing)
can be improved.
A simple, familiar folk song is a musical
education in itself. The examination of simple melodies
encourages students to give reasons for what they feel. This
liberates them from the erroneous and stultifying opinion
that a response to beauty is based solely on subjective
feeling (that beauty is “relative”) or habit (that we hear
musical events as we do only because we’ve heard them
repeatedly). It reveals, in highly specific ways, that human
feeling is complex, that our emotional response to beautiful
sound is grounded in a remarkably precise, if usually
unconscious, perception of order. Similarly, examination of
simple melodies reinforces the trust that analysis, however
abstract it may seem at first, can lead us back to our
musical experience with renewed wonder, a keener sense for
the details of a beautiful whole, and a more intense and
discerning pleasure. By analyzing Scarborough Fair,
we get a better idea of what to listen for in this melody.
We also come to understand it better and, as a result,
appreciate it even more. To borrow from Elizabeth Barrett
Browning’s famous poem, it is like being able to “count the
ways” in which we love someone.
Music As a Liberating Art
The study of music has several goals. One of
them is to improve, through education, students’ aesthetic
taste: to introduce them to truly great music in an effort
to beget a love for all things graceful and well formed. As
a music teacher, I hope that the study of music begets in my
students a habit of searching for the causes and details of
beautiful things, and that the love of beauty will nourish
the love of knowledge and truth. As students’ intellects are
opened to the power of music, I hope they will strive to
imitate in their day-to-day lives the musical virtues of
harmoniousness, proportion, good timing, appropriate
flexibility or grace, and “striking the right note” in
thought, speech, feeling, and action.
Music, as I noted earlier, is one of the
traditional liberal arts. It liberates us from vulgarity,
intellectual rigidity, and the tyranny of unexamined,
popular opinions about music and beauty. Music does this by
encouraging human fellowship (in singing), by inspiring a
love of beauty that transcends the mere gratification of
desire, by making us more attentive to the elements and
causes of our emotional response to beauty, and by
compelling us to test conventional opinions against the
standard of our own experience.
Music, alas, is the neglected Muse of
educational programs across the board, from kindergarten to
college. One reason for this is a failure to perceive the
importance of music in the education of the young and in
human life generally. Another is the tendency to regard
music as a “soft” subject—there for the sake of amusement or
a vague sort of “music appreciation.” Yet another is the
opinion that music is not basic to our human nature, but is
the prerogative of a trained or gifted elite—something that
only those with the potential to be professional musicians
need study. I have endeavored to show that none of these is
true.
If studied as a liberal art (i.e., in order
for the student to become more inquisitive and reflective
and more aware of music’s power) rather than as a fine art
(i.e., in order for the student to become a musician), music
gets students to look beyond surface distinctions in order
to seek out deep, underlying harmonies or bonds between
things apparently remote. In the breadth of its domain, in
its union of the mathematical and the poetic, and in its
involvement of the whole human being (body, heart, and
mind), music is an essential liberating art.
* It is interesting to note that the Greek
word for beautiful (kalos) also means noblem just as the
word for ugly (aischros) also means base.
† For Discussion of the treatment of tones as forces, see
the Sense of Music by Victor Zuckerkandl, Princeton
University Press, 1959.
________________________________________
Peter Kalkavage has been a tutor at
St. John’s College in Annapolis, Md., since 1977. He is
director of the St. John’s Chorus, author of various
published essays on Plato, Dante, and Hegel, and has
produced an edition of Plato’s Timaeus for Focus
Philosophical Library. He is also author of two texts that
have been used in the St. John’s music program: On the
Measurement of Tones and Elements: A Workbook for Freshman
Music. This article is based on “The Neglected Muse:
Reflections on Music as a Liberating Art,” which he
wrote for Basic Education, vol. 47 (2).
© 2006 American Educator. Reprinted
with permission
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