The origin of Holder's comma resides in the fact that the Ancient Greeks (or at least Boethius) believed that in the Pythagorean tuning the tone could be divided in nine commas, four of which forming the diatonic semitone and five the chromatic semitone. If all these commas are exactly of the same size, there results an octave of 5 tones + 2 diatonic semitones, 5 × 9 + 2 × 4 = 53 equal commas. Holder attributes the division of the octave in 53 equal parts to Nicholas Mercator, who would have named the 1/53 part of the octave the "artificial comma".