To how many sad hearts did he come like an angel, with the rich tones of his voice waking harmonics of hope, where before there had been despair and silence?
The long vault has a certain keynote of its own, which, when firmly struck, excites harmonics, including tones of incredible depth and sweetness.
He showed, both by analysis and by synthesis, that quality depends on the order, number and intensity of the overtones or harmonics that may, and usually do, enter into the structure of a musical tone.
It may be imagined further that, when he established himself at the Academy, his first care was to draw up a scheme of education, including arithmetic, geometry (plane and solid), astronomy, harmonics and dialectic, and that it was not until he had arranged for the carrying out of this programme that he devoted himself to the special functions of professor of philosophy.
Aristotle also formed his Peripatetic school into a kind of college with common meals under a president (6tpxcov) changing every ten days; while the philosopher himself delivered lectures, in which his practice, as his pupil Aristoxenus tells us (Harmonics, ii.