Sunday, August 30, 2009

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.


  1. Wonderful connection between the instruments length and their musical characteristics. I am in no way musical, but I do understand the way you have explained this concept and am pleased to have learned something new today. Thanks for that.

  2. Wow - a 2 for one lesson! Love the woods on these instruments.

  3. My math professor friend is always pointing out the 'music' to math - great connections.

  4. There are so many musicians who are good at math...are you one of them?
    My husband is great with calculations, but can't tap out two consistent measures of 4/4 time. Music is my thing, math...not so much.
    Our son...great at both. There is such a connection between the music and math...I wonder why more people aren't gifted with both talents?