These, then, are the four kinds of royalty. First the monarchy of the heroic ages; this was exercised over voluntary subjects, but limited to certain functions; the king was a general and a judge, and had the control of religion The second is that of the barbarians, which is a hereditary despotic government in accordance with law. A third is the power of the so-called Aesynmete or Dictator; this is an elective tyranny. The fourth is the Lacedaemonian, which is in fact a generalship, hereditary and perpetual.
The line has magnitude in one way, the plane in two ways, and the solid in three ways, and beyond these there is no other magnitude because the three are all.
Emotions of any kind are produced by melody and rhythm; therefore by music a man becomes accustomed to feeling the right emotions; music has thus the power to form character, and the various kinds of music based on various modes may be distinguished by their effects on character.