# The Pythagorean comma

Start on a note and go up by twelve pure fifths. You pass through all twelve notes of the piano and arrive near the starting note, seven octaves higher. But not exactly: you overshoot by about 23.5 cents, almost a quarter of a semitone. This small difference is the Pythagorean comma. Because of it, an instrument with fixed notes, like a piano or an organ, cannot have all its fifths and all its octaves perfectly pure at the same time.

Connects to:
- [The fifth](https://mapideas.org/i/mu_fifth)
- [Primes and commas](https://mapideas.org/i/mu_primes)
- [Temperament](https://mapideas.org/i/mu_temper)

Sources:
- [Wikipedia: Pythagorean comma](https://en.wikipedia.org/wiki/Pythagorean_comma)
- [What is music? Module 4, primes and commas](https://sofiagallego.com/what-is-music/)

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