distance. It is used by firemen and by mariners, as shown in Fig. 112.

By means of the speaking trumpet. the voice of the captain can be heard above the noise of the winds and waves in a tempest. According to Father KIRCHER, ALEXANDER THE GREAT employed a speaking trumpet in commanding his armies.

The effect of the speaking trumpet has been explained by successive reflections of sound-waves from the scnorous material of which the instrument is composed, by virtue of which the voice is transmitted only in the direction of the tube.

But the fact is, that sound is transmitted in all directions, which would indicate that its effect should be attributed to a reinforcement of the voice by the vibration of the column of air contained in the trumpet, according to the principle that sound is reinforced by an auxiliary vibrating body.

The Ear Trumpet.

160. The EAR TRUMPET is a trumpet employed by persons whose hearing is defective, as shown in Fig. 113.

It is simply the speaking trumpet reversed. It serves to collect and concentrate the sound-waves, which are thus enabled to produce a more powerful impression on the drum of the ear. The shape of the ear in man and in animals is such as to perform the function of the trumpet.

Difference between a Musical Sound and a Noise.

161. A MUSICAL SOUND results from a succession of vibrations of equal duration. Such vibrations are called isochronal.

(160.) What is an Ear Trumpet? How does it differ from the speaking trumpet? What is its use? (161.) What is a Musical Sound?

169

NOISE results from a single impulse, or from a succession of vibrations of unequal duration. Thus, the crack of a whip, the discharge of a pistol, the rattling of thunder, or the roar of the waves of the ocean, are destitute of musical value, and are simply noises.

Pitch of Sounds.-Music.

162. The PITCH of a musical sound depends upon the frequency of the vibrations. Those sounds which result from very rapid vibrations, are called acute, whilst those which arise from very slow vibrations, are called grave.

The terms acute and grave are relative; thus, a given sound may be acute with respect to a second, whilst it is grave with respect to a third; thus, a sound which corresponds to 160 vibrations, is acute with respect to one corresponding to 80 vibrations, and grave with respect to one corresponding to 320 vibrations per second. A well arranged and happy combination of grave and acute sounds according to the principles of harmony, constitutes music.

Limits of perceptible Sounds.

163. M. SAVART investigated the subject of sound with respect to the number of vibrations, corresponding to the most grave and acute sounds perceptible by the human ear, by means of an apparatus devised for that purpose.

As the result of his investigations, he concluded that the gravest perceptible sound was produced by 16 vibrations per second, and the most acute by 48,000 vibrations per second. Allowing 1090 feet as the velocity of sound, we find for the length of the waves, corresponding to the gravest sounds, 68 feet, and for the length corresponding to the most acute sounds, a little more than a quarter of an inch.

What is a Noise? 162. What does Pitch depend upon? What is an acute sound? A grave one? Illustrate by examples. gated the limits of audible sounds? Give the results of his investigation. What is music? (163.) Who investi8

The limits of sounds employed in music are much narrower, especially in singing. SAVART gives for the gravest sounds of the male voice, 190 vibrations per second, and for the female voice, 572. For the most acute sounds of the male voice he gives 678 vibrations per second, and for the female voice, 1606.

Two sounds, corresponding to the same number of vibrations per second, are in unison.

Musical Scale.-Gamut.

164. The ear not only distinguishes between giveń sounds-which is most grave, and which is most acute-but it also appreciates the relations between the number of vibra tions corresponding to each. We can not recognize whether for one sound the number of vibrations is precisely two, three, or four times as great as for another, but when the number of vibrations corresponding to two successive or simultaneous sounds have to each other a simple ratio, these sounds excite an agreeable impression, which varies with the relation between the two sounds.

From this principle there results a series of sounds characterized by relations which have their origin in the nature of our mental organization, and which constitute what is called a Musical Scale.

In this scale sounds recur in the same order in groups of seven. Each group constitutes what is called a Gamut of seven notes, known by the names, ut, re, mi, fa, sol, la, si. The first six of these names are the first syllables of the first six verses of the hymn that is chanted at Rome at the feast of St. John. The name, si, has been given more recently to the seventh note. The notes are more generally called by the first letters of the alphabet, A, B, C, &c.

The word gamut comes from the name gamma, the third letter of the Greek alphabet, because GUIDO D'AREZZO, who first represented

What are the limite in singing? When are sounds in unison! (164) What is a Musical Scale? What is a Gamut? Why so called? Name the notes of the gamut.

the notes by points placed upon parallel lines, designated these lines by letters, choosing the letter gamma to designate the first line.

Intervals.-Accords.

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165. An INTERVAL is the relation between two sounds, that is, between the number of vibrations corresponding to those sounds.

The interval between two suceessive notes is called a second, thus, the interval between ut and re is a second, as is the interval between re and mi, mi and fa, and so on.

If the interval between two notes comprises one, two, three, four, five, or six notes, this interval is called a third, fourth, fifth, sixth, seventh, eighth, or octave. For example, the interval between ut and mi, is a third, that between ut and fa, a fourth, or quarter, and so on. Finally, the interval between the ut of one gamut, and the ut of the next succeeding gamut, is an octave.

The coexistence of several sounds is called an accord. When the ear can distinguish, without fatigue, the relation between two sounds, which is the case when this relation is simple, the coexistence of these sounds is called a consonance; when the ear is painfully affected by the coexistence, it is called a dissonance.

The most simple accord is the unison, in which the number of vibrations are equal; then comes the octave, in which the number of vibrations, corresponding to one sound, is double that corresponding to the other; then the fifth, in which the numbers are as 3 to 2; then the fourth, in which the numbers are as 4 to 3; and finally the third, in which the ratio is that of 5 to 4.

When the numbers of vibrations corresponding to three simultaneous sounds, are as 4, 5, and 6, the combination is called a perfect accord. For example, the notes ut, mi, sol, form a perfect accord, as

What is the simWhat is a perfect

(165.) What is an Interval? What is a third, fourth, fifth, sixth, seventh, octave? What is an Accord? A Consonance? A Dissonance? plest accord? The next simplest? Next three in order? accord? Example.