simple science

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Simple Science

261. Noise and Music
When the rapid motions which produce sound are irregular, we hear noise; when the motions are regular and definite, we have a musical tone; the rattling of carriage wheels on stones, the roar of waves, the rustling of leaves are noise, not music. In all these illustrations we have rapid but irregular motion; no two stones strike the wheel in exactly the same way, no two waves produce pulses in the air of exactly the same character, no two leaves rustle in precisely the same way. The disturbances which reach the ear from carriage, waves, and leaves are irregular both in time and strength, and irritate the ear, causing the sensation which we call noise.

The tuning fork is musical. Here we have rapid, regular motion; vibrations follow each other at perfectly definite intervals, and the air disturbance produced by one vibration is exactly like the disturbance produced by a later vibration. The sound waves which reach the ear are regular in time and kind and strength, and we call the sensation music.

To produce noise a body must vibrate in such a way as to give short, quick shocks to the air; to produce music a body must not only impart short, quick shocks to the air, but must impart these shocks with unerring regularity and strength. A flickering light irritates the eye; a flickering sound or noise irritates the ear; both are painful because of the sudden and abrupt changes in effect which they cause, the former on the eye, the latter on the ear.

The only thing essential for the production of a musical sound is that the waves which reach the ear shall be rapid and regular; it is immaterial how these waves are produced. If a toothed wheel is mounted and slowly rotated, and a stiff card is held against the teeth of the wheel, a distinct tap is heard every time the card strikes the wheel. But if the wheel is rotated rapidly, the ear ceases to hear the various taps and recognizes a deep continuous musical tone. The blending of the individual taps, occurring at regular intervals, has produced a sustained musical tone. A similar result is obtained if a card is drawn slowly and then rapidly over the teeth of a comb.

That musical tones are due to a succession of regularly timed impulses is shown most clearly by means of a rotating disk on which are cut two sets of holes, the outer set equally spaced, and the inner set unequally spaced .

If, while the disk is rotating rapidly, a tube is held over the outside row and air is blown through the tube, a sustained musical tone will be heard. If, however, the tube is held, during the rotation of the disk, over the inner row of unequally spaced holes, the musical tone disappears, and a series of noises take its place. In the first case, the separate puffs of air followed each other regularly and blended into one tone; in the second case, the separate puffs of air followed each other at uncertain and irregular intervals and the result was noise.

Sound possesses a musical quality only when the waves or pulses follow each other at absolutely regular intervals.

FIG. - A rotating disk.
262. The Effect of the Rapidity of Motion on the Musical Tone Produced
If the disk is rotated so slowly that less than about 16 puffs are produced in one second, only separate puffs are heard, and a musical tone is lacking; if, on the other hand, the disk is rotated in such a way that 16 puffs or more are produced in one second, the separate puffs will blend together to produce a continuous musical note of very low pitch. If the speed of the disk is increased so that the puffs become more frequent, the pitch of the resulting note rises; and at very high speeds the notes produced become so shrill and piercing as to be disagreeable to the ear. If the speed of the disk is lessened, the pitch falls correspondingly; and if the speed again becomes so low that less than 16 puffs are formed per second, the sustained sound disappears and a series of intermittent noises is produced.
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 .

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.

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. The 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, - rarely falling below 80 vibrations a second and rarely exceeding 1000 vibrations a second, - the 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.

FIG. - A siren.
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 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.

FIG. - A song as sung by three voices of different pitch.
265. Musical instruments
Musical Instruments:
Musical instruments maybe divided into three groups according to the different ways in which their tones are produced: -

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
Musical 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.

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. - Piano wires seen from the back.

FIG. - Front view of an open piano.
267. Strings and their Tones
Musical Instruments:
Fasten a violin string to a wooden frame or box, as shown in Figure, 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.

FIG. - The length of a string influences the pitch.
268. The Freedom of a String
Musical Instruments:
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.

Touch the middle of a wire with the finger or a pencil, 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.

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 a string vibrating as in Figure 183 gives forth three tones, one of which is the fundamental tone of the string, and two of which are the octave of the fundamental tone. Hence, the vibrating string produces two sensations, that of the fundamental note and of its octave.

When a string is plucked in the middle without being held, it vibrates simply as a whole, and gives forth but one note; this is called the fundamental. If the string is made to vibrate in two parts, it gives forth two notes, the fundamental, and a note one octave higher than the fundamental; this is called the first overtone. When the string is made to move as in Figure, three distinct motions are called forth, the motion of the entire string, the motion of the portion plucked, and the motion of the remaining unplucked portion of the string. Here, naturally, different tones arise, corresponding to the different modes of vibration. The note produced by the vibration of one third of the original string is called the second overtone.

The above experiments show that a string is able to vibrate in a number of different ways at the same time, and to emit simultaneously a number of different tones; also that the resulting complex sound consists of the fundamental and one or more overtones, and that the number of overtones present depends upon how and where the string is plucked.

FIG. - Only one half of the string is bowed, but both halves vibrate.

FIG. - The string vibrates in three portions.

FIG. - When a string vibrates as a whole, it gives out the fundamental note.
269. The Value of Overtones
Musical Instruments:
The presence of overtones determines the quality of the sound produced. If the string vibrates as a whole merely, the tone given out is simple, and seems dull and characterless. If, on the other hand, it vibrates in such a way that overtones are present, the tone given forth is full and rich and the sensation is pleasing. A tuning fork cannot vibrate in more than one way, and hence has no overtones, and its tone, while clear and sweet, is far less pleasing than the same note produced by a violin or piano. The untrained ear is not conscious of overtones and recognizes only the strong dominant fundamental. The overtones blend in with the fundamental and are so inconspicuously present that we do not realize their existence; it is only when they are absent that we become aware of the beauty which they add to the music. A song played on tuning forks instead of on strings would be lifeless and unsatisfying because of the absence of overtones.

It is not necessary to hold finger or pencil at the points 1:3, 1:4, etc., in order to cause the string to vibrate in various ways; if a string is merely plucked or bowed at those places, the result will be the same. It is important to remember that no matter where a string of definite length is bowed, the note most distinctly heard will be the fundamental; but the quality of the emitted tone will vary with the bowing. For example, if a string is bowed in the middle, the effect will be far less pleasing than though it were bowed near the end. In the piano, the hammers are arranged so as to strike near one end of the string, at a distance of about 1:7 to 1:9; and hence a large number of overtones combine to reŽnforce and enrich the fundamental tone.

FIG. - A string can vibrate in a number of different ways simultaneously, and can produce different notes simultaneously.
270. The Individuality of Instruments
Musical Instruments:
It has been shown that a piano string when struck by a hammer, or a violin string when bowed, or a mandolin string when plucked, vibrates not only as a whole, but also in segments, and as a result gives forth not a simple tone, as we are accustomed to think, but a very complex tone consisting of the fundamental and one or more overtones. If the string whose fundamental note is lower C (128 vibrations per second) is thrown into vibration, the tone produced may contain, in addition to the prominent fundamental, any one or more of the following overtones: C', G'', C'', E'', C''', etc.

The number of overtones actually present depends upon a variety of circumstances: in the piano, it depends largely upon the location of the hammer; in the violin, upon the place and manner of bowing. Mechanical differences in construction account for prominent and numerous overtones in some instruments and for feeble and few overtones in others. The oboe, for example, is so constructed that only the high overtones are present, and hence the sound gives a "pungent" effect; the clarinet is so constructed that the even-numbered overtones are killed, and the presence of only odd-numbered overtones gives individuality to the instrument. In these two instruments we have vibrating air columns instead of vibrating strings, but the laws which govern vibrating strings are applicable to vibrating columns of air, as we shall see later. It is really the presence or absence of overtones which enables us to distinguish the note of the piano from that of the violin, flute, or clarinet. If overtones could be eliminated, then middle C, or any other note on the piano, would be indistinguishable from that same note sounded on any other instrument. The fundamental note in every instrument is the same, but the overtones vary with the instrument and lend individuality to each. The presence of high overtones in the oboe and the presence of odd-numbered overtones in the clarinet enable us to distinguish without fail the sounds given out by these instruments.

The richness and individuality of an instrument are due, not only to the overtones which accompany the fundamental, but also to the "forced" vibrations of the inclosing case, or of the sounding board. If a vibrating tuning fork is held in the hand, the sound will be inaudible except to those quite near; if, however, the base of the fork is held against the table, the sound is greatly intensified and becomes plainly audible throughout the room.

The vibrations of the fork are transmitted to the table top and throw it into vibrations similar to its own, and these additional vibrations intensify the original sound. Any fork, no matter what its frequency, can force the surface of the table into vibration, and hence the sound of any fork will be intensified by contact with a table or box.

This is equally true of strings; if stretched between two posts and bowed, the sound given out by a string is feeble, but if stretched over a sounding board, as in the piano, or over a wooden shell, as in the violin, the sound is intensified. Any note of the instrument will force the sounding body to vibrate, thus reŽnforcing the volume of sound, but some tones, or modes of vibration, do this more easily than others, and while the sounding board or shell always responds, it responds in varying degree. Here again we have not only enrichment of sound but also individuality of instruments.

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