Day 242: The Math of Music

Day 242: The Math of Music, originally uploaded by susanvg.

In the 2009/365 photo group on Flickr, the theme for this month is mathematics. You may ask what the math is behind this image. If you look at the bottom two recorders, their relationship is 2:1 The length of the alto recorder is twice that of the sopranino. What is the musical relationship? They are exactly one octave apart. Similarly with the top two recorders, a soprano and a tenor, the length of the soprano is 1/2 of the tenor and it is one octave higher. If students were to look at this image, it would be good to think about why a smaller recorder plays at a higher pitch. Is this true about other instruments? Can the students make instruments to demonstrate this principle?

Music is full of mathematical ideas - the length of notes (whole notes, half notes, quarter notes...), the relationship of a time signature (2/4, 3/4, 6/8..), repeated patterns of notes and on and on. It's a great place to see real life applications of mathematics in all its beauty.