Note 63 — § 37. Epilogue—Speech and Song.

The two schools distinguished by Plato seem to be those which were afterwards known as the harmonikoi or Aristoxeneans, and the mathêmatikoi, who carried on the tradition of Pythagoras. The harmonikoi regarded a musical interval as a quantity which could be measured directly by the ear, without reference to the numerical ratio upon which it might be based. They practically adopted the system of equal temperament. The mathêmatikoi sought for ratios, but by experiment 'among the consonances which are heard,' as Plato says. Hence they failed equally with those whose method never rose above the facts of sense.