# Ratios

If you halve a string, it sounds exactly an octave higher. Its frequency has doubled, so the two notes are in the ratio 2 to 1. This is the oldest idea in music theory: intervals are ratios of frequencies. The octave is 2:1, the fifth 3:2, the fourth 4:3 and the major third 5:4. To put one interval on top of another, you multiply their ratios. A fifth plus a fourth is 3/2 × 4/3 = 2, exactly an octave, and you can check this on any instrument.

Connects to:
- [The octave](https://mapideas.org/i/mu_octave)
- [The fifth](https://mapideas.org/i/mu_fifth)
- [Logarithms and cents](https://mapideas.org/i/mu_log)
- [Rhythm and polyrhythm](https://mapideas.org/i/mu_rhythm)
- [Harmony of the spheres](https://mapideas.org/i/mu_kepler)
- [Strings and pipes](https://mapideas.org/i/mu_string)
- [Music](https://mapideas.org/i/music)

Sources:
- [Wikipedia: Harmonic series (music)](https://en.wikipedia.org/wiki/Harmonic_series_(music))
- [What is music? Module 0, T1 ratios](https://sofiagallego.com/what-is-music/)

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