Pendular Motion and Harmony

Abstract

Buoyancy and drag are fundamentally different forces, and hence affect falling bodies differently. The former depends on the ratio of the densities of the medium and the falling object; the latter depends on the tenacity, stickiness, or viscosity of the medium. Galileo’s recognition of this distinction was earned—at least in part—by carefully examining the motion of swinging pendulums. These observations also led him to the striking observation that the period of a pendulum depends neither on the mass of the pendulum, nor on the angle through which it swings, but only on the length of the pendulum string itself. In the reading selection that follows, Salviati, Simplicio and Sagredo continue their previous discussion of pendular motion, but now with the aim of answering a seemingly unrelated question: why is it that certain combinations of sounds are pleasing to the ear, while others are not? For Galileo, whose father was a skilled musician and composer, the motion of a swinging pendulum provided a key insight into the nature of harmony.

The effect of the fifth is to produce a tickling of the ear drum such that its softness is modified with sprightliness, giving at the same moment the impression of a gentle kiss and of a bite.

—Galileo Galilei