In my last post about math I mentioned that I didn't think that math and music had much to do with one another, but now that I have spent the past week spending at least an hour a day on sixth-grade math (I'm 39% through the 6th grade over at the Khan Academy), I can honestly report that doing math and understanding what I am doing when I am doing it has a positive influence on the way I practice and the way I think when I'm playing.
I have had a physical aversion to math since the sixth grade. Part of the physicality of my aversion had, no doubt, to do with the fact that I had become near-sighted and had to strain to see the blackboard in my sixth-grade classroom. I struggled until I got glasses some time in the seventh grade, and by that time I chalked up my inability in math to pure inability. The eye strain was gone, but the residual brain strain of having missed developing significant skills remained.
That's about the time I started relying on my intuition. Intuition has done me well. Avoiding anything having to do with numbers and quantities allowed me to develop a startlingly high degree of intuition. But intuition doesn't help when you are counting measures rest, and the very numbers themselves give rise to confusion. As Stevens Hewitt so beautifully put it, "The most difficult part of playing the oboe (or by implication any other instrument) is knowing exactly when." Gradually learning to accept numbers as friends has helped me to keep my place when counting rests. I noticed the results in less than a week of doing sixth-grade math.
I notice tendencies in my math exercises that I notice in other parts of my life. I sometimes "see" numbers that are not there. I sometimes transpose numbers. I sometimes don't read the whole problem, and leave out the most important part. The problem of attention is easy to get around when there is not a correct answer that needs to be found.
My intuition has allowed me to estimate sizes and distances, and for the most part I have been very lucky. The times when I have not been lucky have caused me to waste a lot of time (and sometimes resources, like paper). There other day I needed to use Finale to convert a passage written in flats to one written in sharps. Normally I would guess at the size of the margins I would need, but this time I located the "ruler" feature in the program, and I used a physical ruler to measure the width I needed to match on the page. I grabbed the ruler before guessing. I trusted that the ruler would be right. I got the passage to fit perfectly. (And I could also actually play the passage, weeks after hitting my head against the previous notation.)
After spending time with graphing, I have started to think of the positions of my fingers on the fingerboard as points on a graph. I have started to think about the distances between my fingers just a little bit differently.
Perhaps the most revealing thing about doing sixth-grade math is the fact that there is a right answer to any problem I encounter. When I get that right answer I am as right as anyone else doing the same problem. I belong to a small community of "right-ness."
Speaking of math, it's time to do a few more problems.