A Musician’s Fear and Loathing of Mathematics

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For Dr. Fidel Nemenzo

Many musicians fear Math.  We cringe at the mention of numeric equations, and scrunch our brows at the sight of mathematical symbols.  The irony of it all is that music is based on organized sound — patterns of all kinds.  Combined, they create a complicated cacophony of elements moving simultaneously.  Sound is measured, augmented and diminished in various ways, whether as frequencies or durations.  A competent pianist can sight-read a piece, easily computing distances of pitches and the length and quality of their resonance, concurrently for two hands.  His brain interprets the piece both horizontally and vertically, and simultaneously throws in extra-musical nuances like emotional interpretation.  But if given a mathematical equation that’s linear at best, this pianist will most likely run. 

Why is this?

When I was a child, despite my propensity for Music, I didn’t fear Math.  Indeed, as a very shy young girl who stared mostly at the ground, I used to count my steps and even the number of cement cracks my feet lands on.  I was fascinated by patterns and recognized them in the sounds I heard.   In fact, I wrote my first composition in color-coordinated numbers: with measured distances both in a horizontal (melody) and vertical (harmony) manner. I was five years old.

My fear of numbers began in grade school when my Math teacher corrected the way I added them up.  I remember being able to add figures easily but not, according to my teacher, in the “right” way.  I had my own unusual method of getting the sum of two quantities and it was not one that could be explained with ease so bear with me. 

I would think of the numbers as images that I break up much like this:

                                      equa.jpg

I tend to find the relationship between both figures, match them up, and identify their difference.  I can’t say that the illustration is an accurate representation of what I envision in my mind, and it’s possible that it doesn’t appear like it makes any sense, so it certainly demonstrates the thorny task of explaining to my teacher what the process entailed.  Her remarks embarrassed me in class and my love for Math wavered.  In first year high school, my algebra test paper was returned to me with encircled solutions and a glaring red question: “How did you get this?”  All week long I waited to be confronted with cheating during the exam.  It didn’t matter that I got the answers right: my method at arriving to it was different and, therefore, wrong.

Thus began my loathing for the subject.  Though I didn’t stop appreciating patterns in Music, I gradually stopped seeing the connection between my art and Math.  I started composing music seriously around this time and playing more complicated piano pieces.  Although I believed in my gift, I recognized my limitations in sight-reading and in notating my compositions.  Was it any accident or coincidence that my difficulties lay on interpreting symbols and visually representing musical patterns?  I think not.  As I look back, I now realize that my fear and loathing of Math have stunted my growth as a musician, especially in the area of logical organization.  I thrived in my early years as a composition student in College, but as my requirements grew in length and size, I could no longer rely on inspiration or plain will.  I needed to shift back to “hearing” sound as patterns and visualizing them in my head.

I took Robert Frost’s cue and walked the road less travelled.  My journey took me to the world of Theatre, Dance, and the other Fine Arts.  I gravitated into the realm of teaching, heard and finally answered its call.  My quest as a Music teacher was to put myself in my students’ shoes, as an actor would, and see music in their eyes.  My challenge was to introduce music, not as an entity so foreign to them, but as one to which they can relate.  I firmly believed that all in life is connected, and if so, I can find a way to bridge music to anything my students were interested in.  Having strongly-left brained students forced me to reconcile my fear and loathing of Math in order to reach them, and I revisited my “incorrect” methods in Mathematics and slowly began to appreciate their uniqueness.  As an educator, I am encouraged to regard my students as individuals with distinctive characteristics and needs; why, then, should I not value myself as one and welcome my different method of solving problems in Math?

Recently, a professor’s narrative about Math and its place in the world made me excited about it once again.  His desire to make it less formidable and more accessible to us was an invitation to love Math again, and to see that I am part of a universe of patterns, and therefore, am, myself, a mathematical blueprint.  And as he spoke about patterns everywhere, and how the Supreme Being must be a Mathematician, I couldn’t help but imagine new possibilities in Music and in Life, strengthening my belief that everything in life is connected in an unending and infinite design.  Near the end, he declared his hope that we leave the auditorium and see Math everywhere and in everything; and as I let myself out the room, I took in my surroundings in wonder as I had done as a child, and walked to my next class fully aware of my existence in a world that made sense. 

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17 thoughts on “A Musician’s Fear and Loathing of Mathematics

  1. kevmoore says:

    An interesting entry. As a professional musician of 30 years standing, I can attest to actively hating mathematics!
    I also neither can, nor have any desire to, sight read. I am self taught, and play by ear. Needless to say, I have come up against the snobbery of so-called “proper” musicians many times. I once depped in a 10 piece soul band on bass, with one night to listen to their rehearsal tape. When I declined to use the music placed in front of me, announcing “Soul music is from the heart, not a piece of paper, and anyway, its not rocket science!” I won few friends, but I like to think they were silenced by the end of the gig. But I’ve come to see the mathematical connection with the arts through my partner, who is a painter and a Doctor of Mathematics. She maintains maths runs through her paintings, and of course, it runs through music too. Like you, I just didnt like being forced to sit with a book full of Logorithms. It made zero sense to me. Still doesnt, but hey, I can play a mean guitar!

    Hello, Kevmoore. 🙂 When I was younger, I played by ear. I was quite good at it and could oido the music that I hear quite easily. Because of this innate ability, I didn’t place any relevance in sight-reading, and, in fact, abhorred it. However, one of our requirements as a composition major in college, though, is notation and so you could say I was forced to write my music down. In order to hone my writing skills, I had to train myself to sight-read. I don’t know about you, but I sweat bullets whenever I did, and stare at the score waiting for the symbols to make sense. The reason why I mentioned Math with regards to sight-reading is this: now that I have shifted the way I regard Math, the symbols seem to make more sense. Instead ot reading each note and counting leger lines, I think of chords or clusters as shapes placed in precise order on the staff. Eversince adapting this new way of interpreting the score, sight-reading has become easier.

    Although I now see value in sight-reading, I don’t think it’s the end-all of being a good musician. Think of it this way, people who play by ear can pick up musical nuances that can never be represented properly in paper. I believe we are more sensitive to sound and its connection to our emotions (or soul, if you will). I know incredible sight-readers who can play any score for the first time flawlessly, but I find them lacking in interpretation and soul.

    Thanks for dropping by and mentioning my blog to Miki. 🙂 Keep on rocking!

  2. Miki says:

    You have no idea how excited and touched I am to find your blog, and especially this entry! In fact it is my boyfriend, Kev Moore, a musician, who pointed it out to me.
    I am myself a painter, but primarly I am a mathematician. I fell in love with mathematics as I was a very small girl and I spent 40 years of my life deep within it. After a long, painful inner fight, I decided to leave mathematics for art. But my love for mathematics is as pure as it ever was.
    I had so much to say to your entry, and I recognized so many things!
    I studied mathematics and physics in France and in Germany to a very high level. While I was studying I met many maths students who loved music and practised it intensely. Most of the time it was classic music which they loved and played themselves classical instruments like violin and piano.Among students and teachers it was very well-known, that Maths and Music perfectly work together. So you see: perhaps musicians hate maths, but mathematicians love music!
    I was different. All these people never understood that my art was painting and not music! And though, for me painting is so close to mathematics, I approach it in the same way as I approached mathematical problems. In my website is written:
    “Miki´s painting is a reflection of her life: a permanent oscillation between light and shadow, lines and shapes, times and places, always looking for that equilibrium which she can only find in continuous movement, in the mysterious and the unknown. A life divided between two passions: mathematics and painting. The first as a supreme form of abstract art ruling her universe… The second as a way of cementing the beauty of that art”
    I think it is enough comment for now, but be sure, I will come back.
    Just a last idea; its´clear to me that Mathematics and classical music are kind of one and the same. But I have no doubts that any kind of music will find his twin in some mathematical theory.
    Yes, Kev Moore, even yours!

    Hello, Miki. 🙂 I’m sorry to get back to you just now. I also believe that ALL music will find its equivalent in math, not just classical music. As I mentioned, I took the long route back to Math by taking detours in other art forms: visual arts, dance, and theatre. In the end I came up with similarities amongst them like line, shape, time and space (the elements mentioned in your painting review). Funny, I didn’t connect those with Math until my professor mentioned them in his lecture. It dawned on me that I’ve been immersed in Math all this time and didn’t know it. Granted Music is NOT Math, but I’d like to think (and hope you agree) that maybe I just expressed it differently — through sound.

    Thanks for dropping by and for sharing. 🙂 I, too, was quite excited to read your comment, and hope that maybe we can continue this exchange of ideas about math and music.

  3. wpm1955 says:

    Hi Lizzie,

    I’m so glad to see you back (found your comment on Miki’s blog)! I was afraid you might not post any more, and I’ve always enjoyed your blog, and missed it recently!

    Madame Monet (aka Eileen, Elementary Teacher)
    Writing, Painting, Music, and Wine

    Yes, I’ve been very busy and I just didn’t have the focus I need to write. I also had some internet connection problems. I’ll try to keep writing and commenting. Thanks so much for dropping by! 🙂

  4. wpm1955 says:

    Dear Lizzie,

    Sorry this comment is off-topic, but I didn’t see how to email you. Someone just sent me this, and as a music teacher I think you’ll find it very interesting (on a city bus, it looks like in the United States somewhere).

    http://www.slide.com/r/thGZS46E1j9mYdOJY721DD8HwfOzlbQs

    Madame Monet

    Hi, Eileen! I clicked on the link and, although it did open, the ‘slide’ was blank. I’m curious. What is it supposed to be? 🙂

  5. Chris says:

    How true! Being a musician myself, I never remembered liking math at all. It’s funny at work, people seem to think that I’m good at math. Being in the art/tech field, my job requires equations and computations and all that robotic stuff. It barely dawned on me that the dots have always been connected. Like when playing or recording music, I sometimes find myself having to fit seven beats into an eight bar and make it sound like it’s played in 4/4. So I have to do the math, so to speak. As a graphic/web designer I also have to do a bunch of computations to make sense of all the puzzle pieces that when put together would make sense and look good when viewed from a distance. Math really does come with the territory of art. Thanks for a great post.

    🙂 Is it possible that we are or can be good at math but don’t know it? I think of math as a different language. If musical terms sound French to the non-musician, mathematical terms give us musicians a nosebleed because we can’t “decode” it. I remember flunking my first algebra test in high school because I just couldn’t get it. In order to pass the next test, I hit the books and gave myself drills everyday. Somewhere along the way something just clicked and — tadaa! — I got it. It’s like finding this invisible key to a complicated code.

    “Math does come with the territory of art.” Yes, I agree. Which comes first, though? Sometimes I wonder. 🙂

    Thanks for dropping by and for sharing, Chris.

  6. Chris says:

    Lizzie… you have a beautiful mind! Your students are the luckiest creatures. 🙂

    Coming from a math hater, I’m afraid I’d have to admit that musicians can possibly be good at math. Albeit the simpler variety. 🙂 And there’s no doubt that math comes before art. That is, if we’re talking science, of course. It is the true universal language that makes it possible for music/art to exist. My ego is bruised but… oh well!

    I’ll come back here and wait for more words of wisdom, if you don’t mind.

    I do not mind one bit, Chris. 🙂 (I don’t know about the “words of wisdom” and my “beautiful mind”, though.)

    Interesting. “… there’s no doubt that math comes before art.” I don’t deny that almost everything in this world can be explained using math and/or science, and I understand what you meant by math being the root of art. However, if a composer doesn’t consciously think of math or science in the process of writing a song, can you still say that that person’s art is a consequence of math or science? Many composers, even the ones whose music can be boxed by mathematical explanations, didn’t even think of math while composing it. Bach and his fugues, for example, with their precise melodies and measured complex harmonies. To him it was all about sound and creating it for the greater glory of his maker. But just because they can be explained and broken down by math, does it mean they are products of mathematics? 🙂 It’s sort of like the ever-famous Zen (?) question: if a tree falls in the forest and there’s no on there to hear it, does it make a sound?

    I wonder, then, if improving my math skills will strengthen my abilities as a musician. It’s possible. But will it make me a better one? I don’t know. I’m just rambling.

    Me head hurts. You’re making me think. 😛

    BTW, I’m signing in as “almacabel” from now on (explained in my latest entry). “Lizzie’s” just fine, though.

  7. Chris says:

    Lizzie. I like Lizzie. Can I call you Lizzie? Please? Alma makes me feel like I’m calling myself by my last name. 🙂

    Anyhow, don’t think too much, though! That’s not such a musician thing to do. 🙂

    I don’t believe that Mr. Bach intentionally wrote complex music for the sake of being complex… as in simply desiring to blow people’s minds by his genius. If he did, then I am mightily disappointed by this fraudulent act.

    Anyhow, IMHO, I don’t think musicians should concern themselves too much with math. It just takes away from the soul of their music. When I write or perform, I don’t count. I feel. That’s why I believe in honest mistakes. When I play guitar, the strings will squeal everytime I switch from one chord to another. It may not sound like it belongs with the music but the scientific truth is that it’s just the way things work whether you like it or not. So you accept. And you make it a rule rather than the exception. Sometimes when you cry, you don’t want to but you do anyway because you can’t help it. You don’t go, well it’s the third time today that I cried so I’ve reached my quota and won’t cry again until tomorrow.

    My math inclinations come from my being in the technical field. I am a sound engineer as well. And in order to present my music in the best possible light, out of neccesity, I have to consider proper adjustments of acoustical properties. This means I am burdened by having to count decibels, measure sonic frequencies and things that don’t have anything to do with the heart and soul of the music itself. 🙂

    Math, to me, should never have to interfere with music itself. It should be built-in and all measured up perfectly. Much like a roller coaster ride. If you’re not queasy, you don’t make computations of whether or not the structure will hold. You trust. And you enjoy the ride. With your arms in the air even! Same with music. No need to intellectualize. If you’re inspired and the feelings are strong… simply go full speed ahead. I say, hit that note with reckless abandon!

    By the way, have you seen the movie Dead Poets Society?

    Carpe diem! It’s my artistic motto. Just thought I’d share. 🙂

    … And thank you for sharing! 🙂 I really appreciate it, Chris.

    Yes, Lizzie’s fine since it’s one of the names I’m called. Your last name is unusual. Does it translate to ‘Joseph’s soul’?

    “Anyhow, don’t think too much, though! That’s not such a musician thing to do.” — I know you were kidding so I won’t react to this. 😛

    There are some composers who have intentionally turned to math as a foundation for their music. They created certain musical systems based on pitch intervals and used them as matrices. I don’t think their works lost any of their musicality, but maybe that’s just me and my atonal-loving ears. 😀

    http://en.wikipedia.org/wiki/Music_and_mathematics

    I’m not entirely disagreeing with you. There are people who use formulas to create music. Notice I don’t call them composers. They find the patterns in existing songs and repackage them to sound different. If you know how to listen well, you will hear that it’s merely a clone of a hit song. However, I think that if your mind has the capacity for it (being both strongly left- and right-brained), then maybe harnessing mathematical concepts in order to compose will work for you. Math then would be a tool for making music, just as your choice of instruments or use of musical elements would be.

    I may not be math-smart but I see the beauty in patterns and symmetry. I think math has soul. How can it not if everything in the world, beautiful or otherwise, can be explained by math?

    Yes, I have seen Dead Poet’s Society. Many times, in fact. It’s one of my favorite movies and Robin William’s character is the teacher I always wanted to be. 😀 Carpe Diem!

  8. Chris says:

    Hi Lizzie… thanks for not taking things the wrong way. Sometimes this kind of conversation can lead to senseless arguments. To be honest, half the time, I don’t even know what I’m talking about. Ha! :0 That’s quite a revelation. And I hate it when I sound philosophical. Maybe I’m just trying to defend, not my point of view, but my feelings. My art has always been about feelings. No articulations. Just feelings. Because I don’t see anything right or wrong about it. It’s just what it is.

    Nuff said, though. 🙂

    I thought of you and Dead Poets Society at the same time. There’s a parallel. And yes, it’s one of my all-time favorites as well.

    I think we’re just having a conversation, and a very interesting one at that. 😀 No worries. I hope you didn’t think I was being argumentative, though. It’s just me thinking out aloud, the way I usually do when conversing with people. I used to have this group of close friends and we would meet over a cup of coffee and just talk from sundown to sun-up. Notice I said, “I used to..”. They’re AWOL and I miss them; but, hey, they have their lives to live.

    I feel very flattered that you thought of Dead Poet’s Society with regards to me. It makes me want to sound my barbaric yawp over the roofs of the world. 😀 Thanks, Chris!

  9. Chris says:

    I forgot to mention… yes, Alma Jose means soul of Joseph. An American friend had to reveal that to me sometime ago. I had no clue. 🙂

    Heehee. I knew it. 😀

  10. […] this entry started as a response to Dino Manrique (a.k.a. noid) and his comment on my post, “A Musician’s Fear and Loathing of Mathematics” which I posted on his website, […]

  11. kevmoore says:

    Miki and I revisited Dead Poets Society recently. What a powerful movie! I yelled at the overbearing Father, I cried at the show of solidarity for Willaims’character. Great stuff. Just wanted to wish you, and indeed all your students a Merry Christmas. I’ve written a special Christmas song for all our blog visitors. You can check it out on Cafe Crem

    I reacted the very same way, Kev. I love that movies! Thank you for your well wishes! I, too, wish you and your loved ones a MAGICAL MUSICAL CHRISTMAS! Thank you for the song! I will check it out presently. 😀

  12. -It was interesting to read that your “problem” with maths started with your teacher. While living in Holland, I read in the newspaper a letter that claimed that 60% of “intelligent” kids were underachieving. I can believe this -and I’m afraid that it comes as a direct result of the way (under financial preassure) teaching has developed as a profession.

    In my experience -it is (in theory and practice) often very difficult to tell the difference between an “above average” and a “below average” intelligence. This is because in both cases these is a deviation from the “norm”. A good teacher needs to understand their subject fully -and thus can recognise the “thought” behind a question (or misunderstanding). A bad teacher can only check to see if the answer corresponds with the one given in the book -and cannot evaluate the reason for any deviation.

    With regard to Maths and Art/Music, I agree entirely that these are all about “pattern”. Maths and art (and perhaps “pattern”) are also fundamentally all about “relationships” and the consequences of defining relationships. Once again, the problem is probably caused by bad teaching (although it is also a fundamental problem within western culture). At school we all learn Pythagoras’ theorem -however, he was a mystic and not a practical person in the contemporary (mathematical) way….. All of early mathematics (and much of science, including chemistry) has a philosophical/religious (non-christian) background. Western culture is fundamentally schizoid -and needs to be healed.

    Incidentally, your “addition” method sounds most interesting. I’m personally interested in different “number bases” and relating them to concepts of space…. I’m actually working (slowly) on a java programme involving such concepts -which one day will be published on my website……

    Hi, Trevor. 🙂 I’m sorry to have responded to this only now. It was a chaotic couple of weeks. 🙂

    I’ve just been reading Ayn Rand’s The Return of the Primitive where she claims that many schools today (mainly the progressive ones) are responsible for stifling the intelligence and creativity of students. Although there really are terrible teachers whose attitudes and teaching styles wreak havoc on students’ minds, the educational system is partly responsible, too, in limiting the abilities and capabilities of learners.

    Often I think students have a point when they ask why they have to study something when they’re not going to use it in the future anyway. But reading what you said about patterns made me think just now: instead of teaching each subject as a separate entity to be learned, what if we teach Patterns as a concept then connect it to disciplines such as music and the other arts, math, geography, etc.? Maybe this way, students can see the relevance of their subjects in school.

    “Incidentally, your “addition” method sounds most interesting.” — My thoughts exactly, especially since I can’t quite explain it! 🙂 Relating music with space is another thing I’m beginning to get caught up with, especially after I visited Fatima’s blog. Maybe after this obsession with math and music, I’ll chew on that idea. 🙂

    More power to you and your java programme! Thanks for sharing. 🙂

  13. Rebekah says:

    After reading your story I felt a slight bit envious. You see – as a musician (singer/pianist) I have envied people that are good at maths. I an very strong in English and History myself but not maths, I often try my hardest to make sense out of numbers and symbols and wished I was good at maths.

    It takes me an awful long time to understand a mathematical concept and in saying that I wish that I am good at maths.

    Well anyways, enough my my envying talk … hats off to you for providing such a thought provoking article.

  14. Soulessaint says:

    Oh my goodness, I came upon this by chance and I’m happy I did. I’m a pianist and I dread math more than Hanon exercises. I’ve actually had someone to tell me, “all musicians know math it shows in statistics”. I had to correct her on that statment. She was bent on believing I was an expert in math and since I wasn’t to her, “I’m not a true musician”. I didn’t argue with her, but advised her to do more research and not to go by what society says. I continue to have a love hate relationship with math, but gradually I’m growing patience with it. Well, trying to. Good day

    • Liz says:

      Thank you for the comment and I’m sorry for not replying right away.

      I know a few musicians adept in math, and know more who hate it. You see, the second half of my statement tells you what I believe: that our ability (or lack thereof) in math is based on deep-seated negative feelings towards it. Not because we, as musicians, are programmed to be bad at it. Many of us think differently from the left-brained people who are naturally skillful in math. Unfortunately, many of our past math teachers were these left-brainies and they couldn’t relate to our problem. Maybe we just need a different method.

      Cheers!

      • Soulessaint says:

        Indeed! Thank you so much for your reply. Hopefully, we can keep in contact. I’m definitely returning to review your articles. Good day

        My pleasure. You are always welcome. Best regards!

  15. Huang says:

    Hi I’m so very glad to find your post! I have often been puzzled why people say that musically inclined people are good at maths. Although I am not a professional musician, I am more ‘musical’ than most of my peers. On the other hand I am quite hopeless at maths. When I finally could bid maths lessons goodbye upon entering university, my elation at being free from the clutches of maths was beyond words. (I’m from Singapore and here, you have to do maths till you leave junior college.)

    As a young child I could play on the piano songs I heard on TV, with both hands. Nobody taught me which chords I should use, they just seemed to flow. I’m not sure if I have perfect pitch, probably not, but close. I wish I had continued learning music, but well, life’s not perfect.

    The interesting thing is that I used to love maths when I was young. In fact I always looked forward to holiday homework, I loved doing the problems. But things took a sudden twist when I went to secondary school. While I scored 98% in my final maths examination in primary school, mostly I either failed terribly or only managed to scrape through in secondary school. It was worse when I went to junior college. I had decided to give myself up, but was saved by a very caring maths teacher. I was hating everybody and everything related to maths, and only continued going for class because my tutor was a wonderful person, I didn’t want to make things difficult for him. There I was sulking at my desk because I simply could not make sense of anything, yet instead of questioning me for doing nothing, he gently asked how I was doing. And in that instant I decided I would hang on till graduation, just to repay his kindness. Even today I still tear up when I think of how his kindness pulled me up from total despair.

    By the way, maths wasn’t always a chore, I loved drawing graphs and diagrams, and always wondered why my classmates’ drawings were so terribly messy and ugly. But they got the answers, while I had no clue what I was supposed to do.

    I remember reading somewhere that musically inclined people tend to do well in rudimentary maths, but badly at complex maths. I don’t know how true this is but it happens to be so in my case. There was an abacus craze around the time I graduated from university, and I eagerly signed up for a course. I did very well, but dropped out of class because I thought the teacher was too slow! It was not challenging enough for me. Weird, since I’m supposed to be bad at maths. My guess is that arithmetic is great fun for people like me, but conceptual theories are too dry and tough to chew.

    I wonder if there is any correlation somewhere (I think there is), but I am also better than many people in learning new languages. Some people tell me it’s hard to learn a new language, much less several. But to me the more languages you know, the easier it gets, because you see more patterns. I seem to get such patterns more easily than most of my friends. So many patterns all over the place – sound patterns, grammar patterns, and what have you. And I love reading aloud, it’s like singing to me. Listening to native speakers and learning to speak like them is like learning new songs.

    On the other hand, I can’t make sense of patterns in maps, if there is any to begin with. I need to turn the map round and round to find the right direction. Despite having turned the map round a few times, I still get lost most of the time. I take my hat off to taxi drivers, I really find it amazing that they can find the way around. I had a friend who had a very good sense of direction, he said the map was in his mind, he could see the whole layout in his mind. I found that unbelievable, while he often marvelled at my ‘hearing’ different tones in my mind.

    So sorry for the rambling! Not sure if there’s anything useful in my comment, sure hope there is, but anyway, thanks again for the lovely post!

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