Music and Mathematics

Music is essentially about time, about the way a note or a beat picks up on those that went before and sets up those that will come after.

A metronome responds to this essential temporality.  It produces a rigid beat to which a musician can refer in order to hold firmly to the temporal “skeleton” of the piece being played: the metronome defines the core temporal flow that organizes the timing of the notes and the beats in the tune.

The metronome marks out the “time” of the piece, but it does it very abstractly and rigidly, very “mathematically.”  There is also another time of the piece, a concrete time.

When one is truly playing (or listening) to a piece of music, one does not count “1, 2, 3, 4” in one’s head to know where the beats fall.  Instead, one feels the beats: the rhythm is in the music, not imposed upon it, and one feels the time by getting into the music, not by going outside it to an independently defined number line.

And what happens when one plays “by feel” rather than by listening to the metronome?  Sometimes the music speeds up; sometimes it slows down.  The time, that is, is wrong from the point of view of the metronome, but the time is right from the point of view of the living experience of the music itself.  The music “breathes” with its own internal pulse, more like a living being than like a machine.

There is counting in music, and so there is math in music–indeed, it is hard to imagine music without number.  Music, however, offers something more than mathematics: in many respects, it is the ways in which it is not math that are what most make music valuable.

First, music is responding to the living pulse of the piece.  To respond to something living is much more demanding than counting.  It requires flexibility and openness, and the resourcefulness to pull together a unique and unanticipated “answer” to the question posed by the musical situation.

Mathematics and music, in additional to their intrinsic worth, are also both important educationally.  Education in mathematics, in addition to offering valuable practical skills, also opens us to the world of the “intelligible”–the structures that lie behind what is immediately perceptible: mathematical education shows us the permanent structures, the “rules,” to which all things answer.  Musical education, on the other hand, offers almost the opposite.  It educates us into creativity and imagination: into responding precisely in the absence of fixed rule.

Music also introduces us to beauty, the experience of an irreducible worth of a non-replaceable, non-universalizable, particular, concrete thing.  It alerts us to the singular worth of the irreducible specificities of our living reality.

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  1. ömer
    Posted October 26, 2011 at 2:30 pm | Permalink

    Thanks for this post, John. I am curious about your thoughts on the sequence of math and music in education. For, aside from their similarities and differences, music and math have often been viewed as one somehow leading to the other (most particularly in Plato, for instance the mathematical studies in book VII leading to harmonics). Obviously, children are attuned to music through their bodily motions (dancing) and through language (singing), long before than they learn to count; on the other hand, they are also aware of the difference between more and less before formal math education.

    So, when the child learns math, she is introduced to a new paradigm of truth: as you were saying, she gets introduced to a notion of truth that is precisely not the one she was implicitly familiar with in dancing and singing. In a way, she learns that what was “right” before is “wrong” from another stance.

    Thanks again for the post, and greeting from Istanbul!

    • JohnR
      Posted October 26, 2011 at 4:33 pm | Permalink

      With both music and mathematics we need to distinguish our innate attunement to these kinds of means and the formalized study of them. As you say, children both move to music and distinguish more from less, and I think the “sciences” of mathematics and music are the disciplined developments of the possibilities for meaning that are initially revealed to us in these primitive experiences. (And this suggests, among other things, that we can turn to these primitive experiences as a permanent source for revitalizing–indeed, revolutionizing–our established sciences and practices of mathematics and music.) I don’t immediately have an opinion about the sequence in which we study these things (though I do generally believe that cultivating creativity–in music, drawing, playing, etc.–is the best foundation for growth). I think your point is important, though, through being introduced to the ways of mathematics, the child can learn that what was “right” according to the ways of music can now seem “wrong,” (just as my post suggested that an introduction to the ways of music can lead one to see that what is mathematically “right” can now seem “wrong”). What I see here is the recognition that coping with the demands of our experience will always require of us that we negotiate the conflicting demands of discipline and creative spontaneity, of abstract regularity and concrete specificity, etc. It is important, in other words, to learn that each value on its own is only one-side of meaning.

  2. ömer
    Posted October 27, 2011 at 5:27 pm | Permalink

    This is very helpful, thanks.

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The Toronto Seminar

I am deeply committed to the idea that philosophy is a cooperative activity and an inherently fulfilling one. For this reason, I encourage activities of philosophical study in which, through conversation, a community develops in which each participant experiences her or his thinking to be elevated beyond the level she or he could achieve alone, and in which study and social life are closely interwoven.

Since 2003, I have run an annual summer seminar in philosophy. Each year, roughly 25 invited participants-primarily faculty members and Ph.D. students from universities across North America-gather for roughly one week of intense, group study of a major text from the history of philosophy. Participants meet twice daily for sessions of highly focused discussion of the text and the issues it raises. When not studying in preparation for the meetings, seminar participants also socialize together, generally taking advantage of Toronto's outstanding, multicultural dining opportunities, and taking part in Toronto's vibrant and varied live music scene. Participants in these seminars consistently have the experience of growth in their conversation and conceptual abilities, and typically leave with a transformed sense of the nature and possibilities of philosophy.

Throughout the year, I also often lead smaller private seminars, specially oriented to graduate students, on various texts and topics in the history of philosophy.

Music, along with the other creative arts, is one of the most profound ways in which people express and define the distinctive character of human life. Composing, performing, and listening to music are some of the most fulfilling of our experiences. Listening offers us the opportunity for the sensuous pleasure of listening and moving (in dance), for emotional self-expression, and for bonding with others in shared enthusiasm. Performing brings with it the demands and rewards of communication and cooperation-with band-members and with audience-and supports the development and deployment of highly-refined bodily and expressive skills. Composing can be a powerful intellectual and cultural practice, offering one a route into participating in the rich historical and multicultural traditions of musical expression. Engaging with music, like engaging with philosophy, touches us in every dimension-bodily, emotional, intellectual, interpersonal, cultural, spiritual-of our experience.

My own personal path into music has involved me in the study of jazz music in particular, and since 2005 I have performed regularly in Toronto as a guitarist with my own band, the John Russon Quartet. The band (with the outstanding musicians Nick Fraser, Mike Milligan, and Chris Gale on drums, bass, and saxophone respectively, and, on special occasions, with Tom Richards joining us on trombone) performs my original compositions, as well as interpreting the standard tunes of the jazz repertoire and experimenting with free improvisation. We have just (August 2011) gone into the studio to record our first CD, and it should be available in a few months. It has also been, and continues to be, a major project of mine to develop a community of jazz enthusiasts who will carry on the tradition of appreciating live musical performance in general and jazz music in particular in this age in which recording, downloading, and dj-ing have come to define "music" for most people.

I think of both philosophy and music as communal practices first and foremost, and I regularly try to design community activities involving either or both. Currently, I am organizing one series in downtown Toronto.

"Story and Song Night" is a once-a-month event in which a speaker narrates one of the great stories from the world's religious traditions. Stories are among the oldest and most basic of our ways of telling ourselves and each other who we are as people, and the ancient stories that have been handed down for generations remain powerful and provocative resources for thinking about ourselves and our lives. On the fourth Tuesday of each month, a speaker narrates a story she or he has found personally meaningful, and this is followed first by group discussion and then by a set of live music performed by some of the best of Toronto's musicians. The event is hosted by Naco Gallery Cafe (1665 Dundas St. W.).