Pythagorean comma
![Pythagorean comma on C. Play . The note depicted as lower on the staff (B♯+++) is slightly higher in pitch (than C♮).](/Images/godic/202502/05/Pythagorean_comma_on_C0448.png")
![The Pythagorean comma shown as the gap (on the right side) which causes a 12-pointed star to fail to close, which star represents the Pythagorean scale; each line representing a just perfect fifth. That gap has a central angle of 7.038 degrees, which is 23.46% of 30 degrees.](/Images/godic/202502/05/PythagoreanTuningGeometric0448.png")
![Pythagorean comma as twelve justly tuned perfect fifths.](/Images/godic/202502/05/Pythagorean_comma0449.png")
![](/Images/godic/202502/05/Circle_of_fifths_unrolled,_pythagorean_comma.svg0449.png")
In musical tuning, the Pythagorean comma (or ditonic comma), named after the ancient mathematician and philosopher Pythagoras, is the small interval (or comma) existing in Pythagorean tuning between two enharmonically equivalent notes such as C and B♯ ( Play ), or D♭ and C♯. It is equal to the frequency ratio 531441:524288, or approximately 23.46 cents, roughly a quarter of a semitone (in between 75:74 and 74:73). The comma which musical temperaments often refer to tempering is the Pythagorean comma.