In parallel use since antiquity, those two methods have produced considerable confusion. It is observed that the intervals of the diatonic tetrachord – the basis of the musical systems in ancient Greek, Byzantine and Eastern, in general, civilizations – are given, already since Pythagoras or Aristoxenos, different values, varying with the method of calculation. Similar discrepancies occur between the values given to the intervals by Chrysanthos from Madytos and the 1881 Committee of the Constantinople Patriarchate.

The division of the octave into 53 units (the tetrachord into 22), attributed to Mercator (17th c.) is the only one permitting a nearly perfect coincidence between the two methods. Adopted by the Turks, this method contributed to their coherent and lucid music theory. Besides, it indicates to the fact that the Pythagorean and the natural intervals have up to this date dominated the musical practice of the East.