Editing Twelfth root of two (section)

===Other tuning scales===
Other tuning scales use slightly different interval ratios:
* The [[Just intonation|just]] or [[Pythagorean tuning|Pythagorean]] perfect fifth is 3/2, and the difference between the equal tempered perfect fifth and the just is a [[grad (musical interval)|grad]], the twelfth root of the [[Pythagorean comma]] (<math display=inline>\sqrt[12]{531441/524288}</math>).
* The equal tempered [[Bohlen–Pierce scale]] uses the interval of the thirteenth root of three (<math display=inline>\sqrt[13]{3}</math>).
* Stockhausen's ''[[Studie II]]'' (1954) makes use of the twenty-fifth root of five (<math display=inline>\sqrt[25]{5}</math>), a compound major third divided into 5×5 parts.
* The [[delta scale]] is based on ≈<math display=inline>\sqrt[50]{3/2}</math>.
* The [[gamma scale]] is based on ≈<math display=inline>\sqrt[20]{3/2}</math>.
* The [[beta scale]] is based on ≈<math display=inline>\sqrt[11]{3/2}</math>.
* The [[alpha scale]] is based on ≈<math display=inline>\sqrt[9]{3/2}</math>.