# Logarithms and cents

Since intervals combine by multiplying, it is hard to compare their sizes directly. Logarithms help, because they turn multiplication into addition. Musicians use a logarithmic unit called the cent. An octave is 1200 cents and each semitone of the piano is exactly 100. A pure fifth, ratio 3:2, is about 702 cents, and the piano's fifth is 700, so they differ by two cents, a fiftieth of a semitone. Most listeners only start to notice differences of around five to ten cents.

Connects to:
- [Ratios](https://mapideas.org/i/mu_ratio)
- [The cochlea](https://mapideas.org/i/mu_cochlea)
- [Continued fractions](https://mapideas.org/i/mu_contfrac)
- [Notation](https://mapideas.org/i/mu_notation)
- [Maqām and makam](https://mapideas.org/i/mu_maqam)

Sources:
- [Wikipedia: Cent (music)](https://en.wikipedia.org/wiki/Cent_(music))
- [What is music? Module 0, T2 logarithms and the converter](https://sofiagallego.com/what-is-music/)

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