(1) Loudness, (2) Pitch, (3) Quality, timbre or klang, as the Germans call it.
Loudness depends upon the amount of energy expended in producing the sound. If I rub a tuning-fork with a well-rosined bow, I set it in vibration by the resistance offered to the rosined hair; and if while it is vibrating I again apply the bow, thus expending more energy, the note produced is louder. Repeating the action several times, the width of excursion of the prongs of the tuning-fork is increased. This I can demonstrate, not merely by the loudness of the sound which can be heard, but by sight; for if a small mirror be fixed on one of the prongs and a beam of light be cast upon the mirror, the light being again reflected on to the screen, you will see the spot of light dance up and down, and the more energetically the tuning-fork is bowed the greater is the amplitude of the oscillation of the spot of light. The duration of the time occupied is the same in traversing a longer as in traversing a shorter space, as is the case of the swinging pendulum. The vibrating prongs of the tuning-fork throw the air into vibrations which are conveyed to the ear and produce the sensation of sound. The duration of time occupied in the vibrations of the tuning-fork is therefore independent of the space passed over. The greater or less energy expended does not influence the duration of time occupied by the vibration; it only influences the amplitude of the vibration.
The second quality of musical sounds is the pitch, and the pitch depends upon the number of vibrations that a sounding body makes in each second of time. The most unmusical ear can distinguish a high note from a low one, even when the interval is not great. Low notes are characterised by a relatively small number of vibrations, and as the pitch rises so the number of vibrations increase. This can be proved in many ways. Take, for example, two tuning-forks of different size: the shorter produces a considerably higher pitched note than the longer one. If a mirror be attached to one of the prongs of each fork, and a beam of light be cast upon each mirror successively and then reflected in a revolving mirror, the oscillating spot of light is converted into a series of waves; and if the waves obtained by reflecting the light from the mirror of the smaller one be counted and compared with those reflected from the mirror attached to the larger fork, it will be found that the number of waves reflected from the smaller fork is proportionally to the difference in the pitch more numerous than the waves reflected from the larger. The air is thrown into corresponding periodic vibrations according to the rate of vibration of the sound-producing body.