Sound, like light, is physically a wave motion, though the sound vibrations are very different from those of light. They travel 1,100 feet a second, instead of 186,000 miles a second. Their wave-length is measured in feet instead of in millionths of a millimeter, and their vibration frequencies are counted in tens, hundreds and thousands per second, instead of in millions of millions. But sound waves vary among themselves in the same three ways that we {229} noticed in light waves: in amplitude, in wave-length (or vibration rate), and in degree of mixture of different wave-lengths.

Difference of amplitude (or energy) of sound waves produces difference of loudness in auditory sensation, which thus corresponds to brightness in visual sensation. Sounds can be arranged in order of loudness, as visual sensations can be arranged in order of brightness, both being examples of intensity series such as can be arranged in any kind of sensation.

Difference of wave-length of sound waves produces difference in the pitch of auditory sensation, which thus corresponds to color in visual sensation. Pitch ranges from the lowest notes, produced by the longest audible waves, to the highest, produced by the shortest audible waves. It is customary, in the case of sound waves, to speak of vibration rate instead of wave-length, the two quantities being inversely proportional to each other (in the same conducting medium). The lowest audible sound is one of about sixteen vibrations per second, and the highest one of about 30,000 per second, while the waves to which the ear is most sensitive have a vibration rate of about 1,000 to 4,000 per second. The ear begins to lose sensitiveness as early as the age of thirty, and this loss is most noticeable at the upper limit, which declines slowly from this age on.

Middle C of the piano (or any instrument) has a vibration rate of about 260. Go up an octave from this and you double the number of vibrations per second; go down an octave and you halve the number of vibrations. Of any two notes that are an octave apart, the upper has twice the vibration rate of the lower. The whole range of audible notes, from 16 to 30,000 vibrations, thus amounts to about eleven octaves, of which music employs about eight octaves, finding little use for the upper and lower extremes of the {230} pitch series. The smallest step on the piano, called the "semitone", is one-twelfth of an octave; but it must not be supposed that this is the smallest difference that can be perceived. A large proportion of people can observe a difference of four vibrations, and keen ears a difference of less than one vibration; whereas the semitone, at middle C, is a step of about sixteen vibrations.

Mixture of different wave-lengths, which in light causes difference of saturation, may be said in sound to cause difference of purity. A "pure tone" is the sensation aroused by a stimulus consisting wholly of waves of the same length. Such a stimulus is almost unobtainable, because every sounding body gives off, along with its fundamental waves, other waves shorter than the fundamental and arousing tone sensations of higher pitch, called "overtones". A piano string which, vibrating as a whole, gives 260 vibrations per second (middle C), also vibrates at the same time in halves, thus giving 520 vibrations per second; in thirds, giving 780 per second; and in other smaller segments. The whole stimulus given off by middle C of the piano is thus a compound of fundamental and overtones; and the sensation aroused by this complex stimulus is not a "pure tone" but a blend of fundamental tone and overtones. By careful attention and training, we can "hear out" the separate overtones from the total blend; but ordinarily we take the blend as a unit (just as we take the taste of lemonade as a unit), and hear it simply as middle C of a particular quality, namely the piano quality. Another instrument will give a somewhat different combination of overtones in the stimulus, and that means a different quality of tone in our sensation. We do not ordinarily analyze these complex blends, but we distinguish one from another perfectly well, and thus can tell whether a piano or a cornet is playing. The difference between different instruments, which we have spoken of as a {231} difference in quality or purity of tone, is technically known as timbre; and the timbre of an instrument depends on the admixture of shorter waves with the fundamental vibration which gives the main pitch of a note.

Akin to the timbre of an instrument is the vowel produced by the human mouth in any particular position. Each vowel appears to consist, physically, of certain high notes produced by the resonance of the mouth cavity. In the position for "ah", the cavity gives a certain tone; in the position for "ee" it gives a higher tone. Meanwhile, the pitch of the voice, determined by the vibration of the vocal cords, may remain the same or vary in any way. The vowel tones differ from overtones in remaining the same without regard to the pitch of the fundamental tone that is being sung or spoken, whereas overtones move up or down along with their fundamental. The vowels, as auditory sensations, are excellent examples of blends, in that, though compounds, they usually remain unanalyzed and are taken simply as units. What has been said of the vowels applies also to the semi-vowels and continuing consonants, such as l, m, n, r, f, th, s and sh.

Other consonants are to be classed with the noises. Like a vowel, and like the timbre of an instrument, a noise is a blend of simple tones; but the fundamental tone in a noise-blend is not so preponderant as to give a clear pitch to the total sound, while the other tones present are often too brief or too unsteady to give a tonal effect.