Category Archives: Math

Our Students, Their Brains


The idea for 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,

His comment

Imagination and the Right Brain
Submitted by noid on December 12, 2007 – 4:17pm.
An example of our school system’s — and our society’s’ for that matter — over-emphasis on left-brained modes of learning. That’s why creatives/right-brained individuals often feel left out or marginalized. The ironic thing though is that right brain/intuition is indispensable to genius. More than a handful of quotes, for example, have been attributed to Albert Einstein regarding the importance of the imagination:
I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.
Logic will get you from A to B. Imagination will take you everywhere.
To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science.
I, myself, am just finding this out. Am now more fascinated with math and science than I ever was in school, knowing that these fields can actually be approached from a more artistic perspective. Long live the right brain! 🙂

I agree with your observation about the focus of society and schools on left-brain modes of learning.  Math and science do exist in the realm of logic but every new theory and invention was born of creativity and ‘thinking out of the box’, possible only by way of the right brain.

What if we switch it around? Can we say that it’s possible that the arts can be approached in a more logical perspective?  Certainly, music can be analyzed structurally and this requires logical skills.  There is, in fact, a subject called “Forms and Analysis” where a piece is dissected by measuring harmonic and melodic pitch intervals and, by using certain systems (like the diatonic system — major and minor, for example), predicting the music’s movement in relation to the tonic (or where it originated).  It’s almost mathematical, this analysis. One can argue that music can be regarded logically “after the fact”, once it already exists; but what of the composers who intentionally employ mathematical concepts into their music, just as he would elements like timbre or dynamics?    

I’ve met musicians of all sorts. That many are strongly right-brained comes as no surprise.  They use intuition to create or interpret music, and are more likely to be innovative in their approach.  But there are also quite a few, composers and performance artists alike, who are strongly left-brained.  Not surprisingly, they’re the ones who excel in the analysis of musical form.  They sight-read music faster, are able to interpret musical symbols more efficiently.  However, one sort lacks what the other has: which could explain why ‘Forms and Analysis’, a subject where only a few breeze through and the others come out of crawling, is one of the most dreaded at the U.P. College of Music; and why not all performance artists, no matter how superb their technique, are said to have ‘heart’. 

Of course, the happy exception would be the musicians who have balanced right and left brains.  Possibly, they have a thicker corpus callosum which enable a more efficient communication between both hemispheres.  They have the capability and the ability to find the medium between creative and logical thinking.  As composers, they can go beyond existing structures and find unusual ways of expressing sound while still consciously aware of form and all its elements.  As performance artists, they are sticklers for what’s written on the score, but are able to bring a new dimension to the music by way of intuition.  One could say, probably, that these musicians know the rules and choose to break them, or more precisely, venture from them.   

As an educator with these observations in mind, I would probably be more careful in judging a music student’s or musician’s logical or creative abilities.   Too quickly, music teachers would label a certain student “bobo” (stupid) for not being able to quickly grasp musical concepts whose understanding require logical thinking, or “parang bato” (like a stone) for purely interpreting a piece as written, with nary a touch of feeling or personal interpretation.   Different brains means different capabilities.  In fact, musicians born with a balanced brain could have been easily programmed to lean heavily towards only one hemisphere had they been trained to do so by a music teacher who, say, forced them to stick to reading notes and never to play by ear (oido); or by one that constantly ignored a student’s inquiry about certain musical symbols and encouraged them instead to improvise. 

If  teachers are always encouraged to regard their students as individuals, then it follows that how their students think is just as important as what they think.  We must not rely on impressions or the usual clichés (all musicians are right-brained) and be quick to dismiss or give up.  Instead, we must be creative in finding new avenues of teaching in order to rouse our students’ less utilized brain hemispheres.  Observation, care, and a genuine concern for our students’ thinking process will ensure a deeper understanding and holistic response to music.

A Brave New World


I teach piano and voice at Center for Movement and Music, a performance arts school connected to the Associated Board of the Royal Schools of Music.  With the yearly assessment coming up, we were all deep in the grind of preparing our students.  Recently, on her way to work, one of our senior piano teachers met an accident just a few blocks away from school.  A speeding truck swerved to avoid another vehicle hitting her just a split second after she managed to push a young girl out of the way.  She died a few hours later without having regained consciousness.  She was in her 60’s, probably.  I never asked, and now I wish I had during one of our jeepney rides home after teaching.

The tragic news has jolted me into a state of uncertainty.  When I was young, though I thought of death constantly, I believed it could never touch me.  Death was for the old.  When I was 15, 35 seemed very old.  Now I’m 35 and I don’t feel old at all, but I know the possibility of dying, suddenly or in slow pain, draws nearer and nearer.  I’m not being maudlin.  It’s a fact that the older I get, the closer I am to being fertilizer. 

Which brings me to these random thoughts.  They all boil down to making some kind of dent in life’s ever-droning mechanism before my death.  I’ve always believed that I am in this world for a purpose that transcends the physical realm.  Seriously, are we just here to eat, sh*t, procreate, eke out a living, buy stuff, consume, and do all the other mundane things we human beings do in order to survive and have a semblance of a life?  I think not.  Ever since my 35th birthday, when I realized it was my 5th 7th year walking the earth (therefore, I believed, special), an urgent voice has been nagging — nay, hounding — my thoughts:

It’s time to do what you came here to do.

The only snag, and it’s oh-so-simple, is that my mind, which right now is a complicated web of ideas and feelings gathered in my 35 years, is trying to synthesize everything into one clear and solid statement that could possibly answer the question, “What is it that I came here to do?”

a.k.a. “Why am I here?”

a.k.a. “What is my purpose in life?”

And maybe, a.k.a. “What is the meaning of life?”

Since I know my oftentimes destructive propensity for perfection and know better, I am allowing my web of consciousness (and unconsciousness) to consolidate in its own time.  In the meantime, the inkling of a greater purpose in life is enough to sustain hope in my soul and push me to think of my future in relation to the cosmic scheme of mortals.  If you know me well, you would fall off your chair upon hearing this because I have never considered my future seriously or savored the meat of it as others do.  The customary job or school application question, “How do you see yourself in 10 years?”, I answer without much regard or sincerity because I don’t have the capacity to look ahead.  I live in the present; I always have and have never seen this as a flaw on my part.  However, this new strong desire to help and to give requires a steady gaze into the future and a complex world of possibilities. 

There is a battle ahead and I need to get ready.

While I wait for clarity, I have come up with a tentative list of tasks based on new interests and old passions.

Go back to my roots and compose.

I am a composer. 

Even before my life as a pianist, I have thought, felt, and lived as one ever since I was 5 years old.  In college, personal and emotional issues made me doubt my essence and I refused to call myself one since then.  I didn’t lose the ability to compose and could come up with a song or a piece if pushed, but you can relate the process to a person who cooks and calls it a ‘meal’, instead of his ‘creation’ or ‘masterpiece’ as a chef would. 

Recently, though, I have started composing again: a piece for piano trio and solo mezzo-soprano.  I can hear the music in my head again, and have rediscovered the unfazed attitude only real composers have, the one that enable us to say, “I will write it the way I want”, without apologies or doubt.  Thirteen years of limbo after, the accidental return to my roots was a consequence of a shift in the way I perceived the world, but the final nudge came from, mushy I know, a secret unrequited love (which will remain so).  I will continue composing long after my heart is healed, though, and this time, instead of hiding my works in yellowing notebooks, bravely find a venue for my music.    

Raise the Academe’s regard for Music.

The University of the Philippines is the most enlightened of all academic institutions, in my opinion.  Still, I know many of its administrators and faculty deem Music as a superfluous course.  Our college may be the first they turn for distraction or entertainment during important official functions, but I doubt if many of them view its students as intellectuals, or as vital members of society.   I make these claims from the experience of having professors say disparaging remarks about music students even before I got to fill in my classcard, and of hearing some of my classmates’ assumption that I will not perform as well as they do just because I’m not taking up business administration or engineering (or whatever course they believe is better than Music.)   

I’m not bitter.  We, music students, bear some fault.  We cut classes to attend rehearsals or gigs.  We hand in late papers because of late nights and a mind barren from exhaustion.  We stutter during recitations because many of us aren’t wired to be verbally articulate, and would probably express ourselves best through non-verbal sounds.  Our presence is hardly felt inside the classroom because many of us, despite our brave onstage face, are introspective and shy. 

But then, there are really those who think we’re just a bunch of frivolous stage-whores without intellectual depth or substance. 

This unfair regard for musicians and, more importantly, the pure excitement I feel at the thought of it, is pushing me to find ways to connect other disciplines, like Math and Science, with Music.  It’s hardly innovative or revolutionary, and, admittedly, it’s more for me and my need to respond wholly yet succinctly to people who snidely ask, “What is Music for?” or assert that it has no value in this world. 

It’s just me wanting to slap the haughtiness from their heads.

Well, mostly.

After the sting from the slap, I want to see their eyes light up with a new appreciation for Music.

Take my MA and my PhD.

Possible course for my MA:  Art Studies.

PhD: Education.

Be braver in standing up for what I believe in.

For starters, to ensure that everything I write here I declare instead of whisper, I have changed my public wordpress name from the “lizzie5apple” to “almacabel”, my real name.  No pseudonym from which to hide behind any longer.     

Baby steps, everyone.  Baby steps.

A Musician’s Fear and Loathing of Mathematics


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:


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.