General Science by Bertha May Clark (best historical fiction books of all time TXT) π
[Illustration: FIG. 9.--Determining one of the fixed points of a thermometer.]
The Centigrade thermometer, in use in foreign countries and in all scientific work, is similar to the Fahrenheit except that the fixed points are marked 100Β° and 0Β°, and the interval between the points is divided into 100 equal parts instead of into 180.
The boiling point of
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263. The Pitch of a Note. By means of an apparatus called the siren, it is possible to calculate the number of vibrations producing any given musical note, such, for example, as middle C on the piano. If air is forced continuously against the disk as it rotates, a series of puffs will be heard (Fig. 177).
If the disk turns fast enough, the puffs blend into a musical sound, whose pitch rises higher and higher as the disk moves faster and faster, and produces more and more puffs each second.
FIG. 177.βA siren.
The instrument is so constructed that clockwork at the top registers the number of revolutions made by the disk in one second. The number of holes in the disk multiplied by the number of revolutions a second gives the number of puffs of air produced in one second. If we wish to find the number of vibrations which correspond to middle C on the piano, we increase the speed of the disk until the note given forth by the siren agrees with middle C as sounded on the piano, as nearly as the ear can judge; we then calculate the number of puffs of air which took place each second at that particular speed of the disk. In this way we find that middle C is due to about 256 vibrations per second; that is, a piano string must vibrate 256 times per second in order for the resultant note to be of pitch middle C. In a similar manner we determine the following frequencies:β
do re mi fa sol la si do C D E F G A B C 256 288 320 341 384 427 480 512The pitch of pianos, from the lowest bass note to the very highest treble, varies from 27 to about 3500 vibrations per second. No human voice, however, has so great a range of tone; the highest soprano notes of women correspond to but 1000 vibrations a second, and the deepest bass of men falls but to 80 vibrations a second.
While the human voice is limited in its production of sound,βrarely falling below 80 vibrations a second and rarely exceeding 1000 vibrations a second,βthe ear is by no means limited to that range in hearing. The chirrup of a sparrow, the shrill sound of a cricket, and the piercing shrieks of a locomotive are due to far greater frequencies, the number of vibrations at times equaling 38,000 per second or more.
264. The Musical Scale. When we talk, the pitch of the voice changes constantly and adds variety and beauty to conversation; a speaker whose tone, or pitch, remains too constant is monotonous and dull, no matter how brilliant his thoughts may be.
While the pitch of the voice changes constantly, the changes are normally gradual and slight, and the different tones merge into each other imperceptibly. In music, however, there is a well-defined interval between even consecutive notes; for example, in the musical scale, middle C (do) with 256 vibrations is followed by D (re) with 288 vibrations, and the interval between these notes is sharp and well marked, even to an untrained ear. The interval between two notes is defined as the ratio of the frequencies; hence, the interval between C and D (do and re) is 288/256, or 9/8. Referring to Section 263, we see that the interval between C and E is 320/256, or 5/4, and the interval between C and C' is 512/256, or 2; the interval between any note and its octave is 2.
The successive notes in one octave of the musical scale are related as follows:β
Keys of C C D E F G A B C' No. of vibrations per sec. 256 288 320 341 384 427 480 512 Interval 9/8 5/4 4/3 3/2 5/3 15/8 2The intervals of F and A are not strictly 4/3 and 5/3, but are nearly so; if F made 341.3 vibrations per second instead of 341; and if A made 426.6 instead of 427, then the intervals would be exactly 4/3 and 5/3. Since the real difference is so slight, we can assume the simpler ratios without appreciable error.
Any eight notes whose frequencies are in the ratio of 9/8, 5/4, etc., will when played in succession give the familiar musical scale; for example, the deepest bass voice starts a musical scale whose notes have the frequencies 80, 90, 100, 107, 120, 133, 150, 160, but the intervals here are identical with those of a higher scale; the interval between C and D, 80 and 90, is 9/8, just as it was before when the frequencies were much greater; that is, 256 and 288. In singing "Home, Sweet Home," for example, a bass voice may start with a note vibrating only 132 times a second; while a tenor may start at a higher pitch, with a note vibrating 198 times per second, and a soprano would probably take a much higher range still, with an initial frequency of 528 vibrations per second. But no matter where the voices start, the intervals are always identical. The air as sung by the bass voice would be represented by A. The air as sung by the tenor voice would be represented by B. The air as sung by the soprano voice would be represented by C.
CHAPTER XXVIII MUSICAL INSTRUMENTS265. Musical instruments maybe divided into three groups according to the different ways in which their tones are produced:β
First. The stringed instruments in which sound is produced by the vibration of stretched strings, as in the piano, violin, guitar, mandolin.
Second. The wind instruments in which sound is produced by the vibrations of definite columns of air, as in the organ, flute, cornet, trombone.
Third. The percussion instruments, in which sound is produced by the motion of stretched membranes, as in the drum, or by the motion of metal disks, as in the tambourines and cymbals.
266. Stringed Instruments. If the lid of a piano is opened, numerous wires are seen within; some long, some short, some coarse, some fine. Beneath each wire is a small felt hammer connected with the keys in such a way that when a key is pressed, a string is struck by a hammer and is thrown into vibration, thereby producing a tone.
If we press the lowest key, that is, the key giving forth the lowest pitch, we see that the longest wire is struck and set into vibration; if we press the highest key, that is, the key giving the highest pitch, we see that the shortest wire is struck. In addition, it is seen that the short wires which produce the high tones are fine, while the long wires which produce the low tones are coarse. The shorter and finer the wire, the higher the pitch of the tone produced. The longer and coarser the wire, the lower the pitch of the tone produced.
FIG. 179.βPiano wires seen from the back.
The constant striking of the hammers against the strings stretches and loosens them and alters their pitch; for this reason each string is fastened to a screw which can be turned so as to tighten the string or to loosen it if necessary. The tuning of the piano is the adjustment of the strings so that each shall produce a tone of the right pitch. When the strings are tightened, the pitch rises; when the strings are loosened, the pitch falls.
What has been said of the piano applies as well to the violin, guitar, and mandolin. In the latter instruments the strings are few in number, generally four, as against eighty-eight in the piano; the hammer of the piano is replaced in the violin by the bow, and in the guitar by the fingers; varying pitches on any one string are obtained by sliding a finger of the left hand along the wire, and thus altering its length.
Frequent tuning is necessary, because the fine adjustments are easily disturbed. The piano is the best protected of all the stringed instruments, being inclosed by a heavy framework, even when in use.
FIG. 180.βFront view of an open piano.
267. Strings and their Tones. Fasten a violin string to a wooden frame or box, as shown in Figure 181, stretching it by means of some convenient weight; then lay a yardstick along the box in order that the lengths may be determined accurately. If the stretched string is plucked with the fingers or bowed with the violin bow, a clear musical sound of definite pitch will be produced. Now divide the string into two equal parts by inserting the bridge midway between the two ends; and pluck either half as before. The note given forth is of a decidedly higher pitch, and if by means of the siren we compare the pitches in the two cases, we find that the note sounded by the half wire is the octave of the note sounded by the entire wire; the frequency has been doubled by halving the length. If now the bridge is placed so that the string is divided into two unequal portions such as 1:3 and 2:3, and the shorter portion is plucked, the pitch will be still higher; the shorter the length plucked, the higher the pitch produced. This movable bridge corresponds to the finger of the violinist; the finger slides back and forth along the string, thus changing the length of the bowed portion and producing variations in pitch.
If there were but one string, only one pitch could be sounded at any one time; the additional strings of the violin allow of the simultaneous production of several tones.
268. The Freedom of a String. Some stringed instruments give forth tones which are clear and sweet, but withal thin and lacking in richness and fullness. The tones sounded by two different strings may agree in pitch and loudness and yet produce quite different effects on the ear, because in one case the tone may be much more pleasing than in the other. The explanation of this is, that a string may vibrate in a number of different ways.
FIG. 182.βOnly one half of the string is bowed, but both halves vibrate.
Touch the middle of a wire with the finger or a pencil (Fig. 182), thus separating it into two portions and draw a violin bow across the center of either half. Only one half of the entire string is struck, but the motion of this half is imparted to the other half and throws it into similar motion, and if a tiny A-shaped piece of paper or rider is placed upon the unbowed half, it is hurled off.
FIG. 183.βThe string vibrates in three portions.
If the wire is touched at a distance of one third its length and a bow is drawn across the middle of the smaller portion, the string will vibrate in three parts; we cannot always see these various motions in different parts of the string, but we know of their existence through the action of the riders.
Similarly, touching the wire one fourth of its length from an end makes it vibrate in four segments; touching it one fifth of its length makes it vibrate in five segments.
In the first case, the string vibrated as a whole string and also as two strings of half the length; hence, three tones must have been given out, one tone due to the entire string and two tones due to the segments. But we saw in Section 267 that halving the length of a string doubles the pitch of the resulting tone, and produces the octave of the original tone; hence
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