# Primes and commas

Every whole number can be written as a product of prime numbers in only one way: 12 is 2 × 2 × 3 and nothing else. This simple fact has a musical consequence. Octaves are built from the number 2 and fifths from the number 3. However many fifths you stack, you get powers of 3, and these can never equal a power of 2. So a chain of pure fifths never lands exactly on an octave, and every tuning has a small leftover, which musicians call a comma.

Connects to:
- [The Pythagorean comma](https://mapideas.org/i/mu_comma)

Sources:
- [Wikipedia: Pythagorean comma](https://en.wikipedia.org/wiki/Pythagorean_comma)
- [What is music? Module 4, why pure fifths can never close the circle](https://sofiagallego.com/what-is-music/)

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