When I was in elementary school lo those many years ago, there were a few years when I had trouble with math. I tried really hard, and spent a lot of time at home trying to get it, and practiced many strategies for understanding concepts and coming up with the right answer. Sometimes, after I had exerted great effort, I would come up with an answer, and be delighted to have done so. It never occurred to me to think about my answer to make sure it made sense. As a result, Johnny, after starting with five apples and eating two may have had 325 left on a few occasions. It took a patient teacher to point out the impossibility of my answer, no matter how much effort I had exerted. I could have used a little common sense to help me learn math. Eventually, having physical objects in front of me, and removing two from a collection of five led me to understand that Johnny must have had fewer apples after eating some than when he started, and that he had only three left after his snack. Seeing real objects made the abstract numbers meaningful.
The same applies to music. Last week, I taught a lesson on phrase structure. I had my students mark the phrases in printed music of “Jingle Bells.” I chose that song because I knew they all were familiar with it, and would be able to use their familiarity with the melody to find the phrase structure. I gave them four things to look for. I told them new phrases begin after relatively long notes or rests, when a rhythm pattern starts over, when there is a sudden change in dynamics or articulation, and that all of the phrases would be the same length. While most students were able to correctly using the phrase structure using these principles as guides, some misapplied them, and gave an analysis that made sense to them on paper, but not when I sang the song to them pausing at the places they claimed the phrases ended. “Oh what fun it is to” I sang. “Does that make sense, to pause there?” The student instantly recognized that it did not make sense, and quickly found the correct location of the end of the phrase while listening to the music, and was able to mark the phrase correctly in the printed music, showing that they did have enough reading skill to mark phrases in printed music.
It did not occur to the student to employ the strategy of singing this familiar song while following the notation in order to find where one phrase ends and the next begins. They trusted what they thought about what they saw without checking their answer against some common sense. “If I have marked the phrase correctly, if I pause at that point, it will sound right, like a pause belongs there.” Because the student did not or could not connect what was read with what was imagined or heard, what was read could not possibly make any sense.
This brings out a fundamental problem encountered in learning: the connecting of everyday experience with abstractions of them. Written symbols, whether musical notes or words of a language are not the things themselves, but abstractions of them. The word “chair” is not a chair, but refers to a physical object we know as a chair. I am sitting in a chair now as I write this, but the word “chair” is on my computer screen, not under me. In the same way, a note is a sound with a certain pitch and a certain duration. It is something I hear, and it is caused by a physical thing, a sound wave, activating my ear and sending electrical impulses to my brain. This note is in the air or in my imagination, but not on the printed page. That note, on the page, is an abstraction of the real note. Understanding the abstraction, the written representation, is a matter of connecting experience with what is written. When the two cannot be reconciled, then one is in error; either what is written does not accurately represent what I have heard, or if I am reading, I have heard or imagined something other than what is written. In order to accurately read music, we must be able to “check our work,” making sure that the two do indeed match.