Posted by: Alexandre Borovik | May 1, 2008

## Fractions

My old friend Owl sent me the following quote :

I realized that reading a piano piece is much like solving a math problem. Each note has a beat which is a fraction of a whole bar, and the sum of the notes’ beats in a bar should equal the numerator in the so called “time signature”, the fraction indicated on the left most side of the staff. (A staff is a series of bars.) The denominator in the time signature specifies the kind of note which would receive ONE beat. Thus, a time signature of 2/4 means that a quarter note (1/4) would have one beat, and each bar would have two beats; an eighth note (1/8) would receive a half-beat, and the bar may have as many as four eighth notes, or a combination of one quarter note and two eighth notes, and so on and so forth. Whew! Beethoven must have been a good mathematician!

## Responses

1. To contemporary musicians, of course, Beethoven’s music is at kindergarten level! You need to try the piano music of mid 20th century composers such as Iannis Xenakis to be really challenged arithmetically — 13 notes against 9 against 17 against 5, written across three or more staves (instead of the traditional one stave for each hand), with time signatures (the 4/4 part) changing every bar, and all to be played at high speed.

2. I learned sheet music (on the piano) at the same time as we did fractions in school. The timing was very good, and I’m certain that the reason I got more familiar with the fractions then many of my classmates was because the piano sessions gave me some practice in it.
Actually, thinking about it, the people in my class taking music after school seemed to do better with it.

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