Parallel (Simon Singh): Musical Mathematics
It is extraordinary that so much of the universe can be explained using mathematical equations. Indeed, it is often said that mathematics is the language of the universe. It is certainly the language of science.
In this clip, from a documentary in the American Nova series, the jazz musician Esperanza Spalding explains how maths is also at the heart of music. Pay attention to the way that numbers relate to musical intervals (an octave, a fifth and a fourth).
1. What ratio in lengths describe a fourth?
4:4
4:3
4:2
4:1
1:4
2. Pythagoras is said to have noticed the relationship between mathematics and music. According to Pythagoras, the universe is based on numbers, but only whole numbers and their ratios. So, when one of his followers discovered a different type of number, Pythagoras executed him. What sort of number did the follower discover? You might need to do some googling to get the answer.
Hint: Pythagoras acted irrationally when he executed the follower.
Negative numbers
Zero
2
∞
Fractions
Quaternions