# Continued fractions

A continued fraction is a method to find the simplest fractions that come closest to a given number. In music, the number to approximate is the size of the fifth measured in octaves, about 0.585. The method gives the fractions 3/5, 7/12, 24/41 and 31/53, each closer than the one before. The bottom number of each fraction is a number of equal notes per octave that contains a good fifth. Twelve is on the list, and it is the first one where the fifth is so close to pure that most people cannot hear the difference.

Connects to:
- [Twelve notes](https://mapideas.org/i/mu_twelve)
- [Logarithms and cents](https://mapideas.org/i/mu_log)

Sources:
- [Wikipedia: Equal temperament](https://en.wikipedia.org/wiki/Equal_temperament)
- [What is music? Module 5, running the continued fraction by hand](https://sofiagallego.com/what-is-music/)

Source: https://mapideas.org/i/mu_contfrac · open on the map: https://mapideas.org/#mu_contfrac