Beat (acoustics)

“ The lower beat is heard most distinctly when the number is less than half the frequency of the lower primary, and the upper when the number is greater. The beats we have been considering are produced when two notes are sounded slightly differing in frequency, or at all events their frequencies are not so great as those of two notes separated by a musical interval, such as an octave or a fifth. ”

“ When a composition begins upon the weak beat (e.g., the fourth beat of a four-pulse measure) , the preceding strong beat itself, together with the back-stroke accompanying it, is often given as the preparation for the actual initial beat. In case this is done the conductor must guard against making this preliminary strong beat so prominent as to cause the performers to mistake it for the actual signal to begin. ”

“ In music a beat means a regularly recurrent swelling caused by the reinforcement of a sound and this is set up by the interference of sound waves which have slightly different periods of vibration as, for instance, when two tones take place that are not quite in tune with each other. This, then, is the principle of the heterodyne, or beat, receptor. ”

“ It is possible by means of beats to measure the sensitiveness of the ear by determining the smallest difference in pitch that may give rise to a beat. In no part of the scale can a difference smaller than 0.2 vibration per second be distinguished. The sensitiveness varies with pitch. ”

“ Musical sound, or tone, is produced by regular vibrations, and differs from mere noise whose vibrations are irregular and confused. The pitch of a musical tone rises in proportion with the rapidity of the vibrations that produce it. Tones may be perceived by the human ear ranging from about sixteen vibrations in a second to nearly forty thousand, more than eleven octaves. Only about seven octaves are used in music. The science of acoustics is full of interesting facts of this kind, and is of profound value to any one who would gain an insight into the structure of music. ”

“ As the pressure is increased, the air, passing through the holes, assumes a rhythmical beat, which soon becomes metamorphosed into musical notes. It is evident, therefore, that, by means of this instrument, the number of vibrations which produce a definite tone can be measured with absolute accuracy by any one who has an ear capable of appreciating a musical note. ”

“ It will be seen, from the above facts in connection with the study of the table of vibration numbers in Lesson XIII, that all fifths do not beat alike. The lower the vibration number, the slower the beats. If, at a certain point, a fifth beats once per second, the fifth taken an octave higher will beat twice; and the intervening fifths will beat from a little more than once, up to nearly twice per second, as they approach the higher fifth. Vibrations per second double with each octave, and so do beats. ”

“ When, therefore, a whole tone lies below any note marked for a beat, an accidental sharp is to be supposed on that lower note, except that A is seldom thus sharpened in a beat. The beat is, therefore, the reverse of the shake, (but without the turn,) and is made generally at the distance of a semitone below ; and all the notes, excepting C and F, re-quire the note below to be sharped for the beat. ”

“ Even in actual modern dance tunes of the best kind the impulse to add something independent to the fundamental rhythm is found in such devices as tying over the [Pg xlii] last note of a group of three in a valse to the strong beat of the succeeding rhythmic group, while the essential rhythm is maintained by the bass or other instruments of the accompaniment, and composers have even successfully devised such attractive ingenuities as the effect of three long beats being superimposed on two groups of the three lesser beats of the established rhythm. ”

“ Since all sound is caused by vibration, acoustics may be defined as the science which treats of the phenomena of sound-producing vibration.
2. All sound (as stated above) is produced by vibration of some sort: strike a tuning-fork against the top of a table and see the vibrations which cause the tone, or, if the fork is a small one and the vibrations cannot be seen, hold it against the edge of a sheet of paper and hear the blows it strikes; or, watch one of the lowest strings of the piano after striking the key a sharp blow ”

“ It ought to be familiar to every student of acoustics. The sound produced by the striking or twanging of a single string (on a monochord) is called the tonic, and also, from its position as the lowest note, the bass. If we divide this string in half, we will obtain a series of vibrations producing a sound the same in character, but, so to speak, doubly high in pitch. This sound is named the octave, because it is the eighth note in our common diatonic scale. If we divide the string into three parts, the result will be a sound called the large fifth ”

“ Now that we have made ourselves acquainted with overtones and beats, we may proceed to the answer of our main question, Why do certain relations of pitch produce pleasant sounds, consonances, others unpleasant sounds, dissonances? It will be readily seen that all the unpleasant effects of simultaneous sound-combinations are the result of beats produced by those combinations. Beats are the only sin, the sole evil of music. Consonance is the coalescence of sounds without appreciable beats. ”

“ In the heterodyne, or beat method, separate sustained oscillations, that are just about as strong as those of the incoming waves, are set up in the receiving circuits and their frequency is just a little higher or a little lower than those that are set up by the waves received from the distant transmitter. The result is that these oscillations of different frequencies interfere and reinforce each other when beats are produced, the period of which is slow enough to be heard in the headphones, hence the incoming signals can be heard only when waves from the sending station are being received. ”

“ But the tremendous currents above us, which sweep along the vast masses of vapor, are noiseless until they touch the earth, and some little trifling eddies are made in their lower sweep by hills and trees and houses. It is then only noise. The ear requires yet smaller waves of air to experience the sensation of tone. The lowest note of a piano has barely enough of it to give a definite idea. As the waves become shorter, the ear begins to be pleasantly affected, and the realm of music is reached. ”

“ The cure for the trouble is brought about by the introduction of materials such as carpets, tapestries, and the like, which act as absorbers of sound and reduce the time of reverberation.
When music is played in an auditorium with a prolonged reverberation, the tones following one another blend and produce the same effect as that of a piano when played with the loud pedal in use. A reverberation is more advantageous for music than for speech, since the prolongation and blending of the musical tones is desired, but the mixing of the words in a speech is a distinct disadvantage. ”

“ While studying beats Sauveur makes the remark that they are displeasing to the ear. He held the beats were distinctly audible only when less than six occurred in a second. Larger numbers were not distinctly perceptible and gave rise accordingly to no disturbance. He then attempts to reduce the difference between consonance and dissonance to a question of beats. Let us hear his own words. [141]
"Beats are unpleasing to the ear because of the unevenness of the sound, and it may be held with much plausibility that the reason why octaves are so pleasing is that we never hear their beats. ”

“ Not only so, but the amplitude of vibration in the one will determine the amplitude of vibration in the other, for the intensity of the induced current is determined by the amplitude of the inducing vibration, and the amplitude of the vibration at the receiving end depends upon the intensity of the attractive impulses. When we sing into a piano, certain of the strings of the instrument are set in vibration sympathetically by the action of the voice with different degrees of amplitude, and a sound, which is an approximation to the vowel uttered, is produced from the piano. ”

“ The air column in the tube of the French horn, and the sounding-board of the pianoforte develop the vibrations caused by the lips and strings into musical tones pleasing to the ear. The tuning-fork alone can scarcely be heard, while the induced vibrations it sets up through properly adjusted resonance may be audible far away.
The vocal cords alone cannot make music any more than can the lips of the cornet player apart from his instrument. The tone produced by the vibrations alone of the two very small vocal bands must, in the nature of things, be very feeble. ”

“ We are now prepared to realize the error of the common notion that loudness of tone is due entirely to increase of breath pressure on the vocal cords. Simple experiments with the tuning-fork have shown that while the volume of sound it gives forth is due in part to the amplitude of its vibrations, its loudness is chiefly due to the character of the resonance provided for it.
The larger the resonance chamber the greater is its reinforcing capacity. The largest air chamber in the body is the chest, which serves not only as a wind-chest, but as a resonance chamber. ”

“ If there is no regular recurrence of waves, it is a noise. The rapidity of these regular beats determines the pitch of tones. That quality or timbre by which one sound is distinguished from another of the same pitch and intensity is due to the different complications of waves in the air; the ability to discriminate the various waves in the vibrating air is, therefore, the condition of our finding music in it; for every wave has its period, and what we call a noise is a complication of notes too complex for our organs or our attention to decipher. ”

“ Let us first consider the result of combining the reflected wave train with an incident wave train of the form
(3)
The result will be a beat phenomenon which can be represented (apart from additive factors) by
(4)
If had been a constant then the constant beat frequency can be determined by counting the number of waves in a specified interval of time . ”

“ 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 [279] must not only impart short, quick shocks to the air, but must impart these shocks with unerring regularity and strength. ”

“ What really passes out from the source is merely a rhythmical motion of the air particles, manifesting themselves as changes in pressure, spreading out in ever-widening spheres through the atmosphere. The order of these compressions is different for every sound. The musical sounds of an orchestra embody a different set of vibrations for each note of each particular instrument. If the fluctuations in pressure of a sound wave are irregular and non-periodic, the sound is called a noise; if they are cyclic, and follow a regular and sufficiently rapid periodic lag, the sound is musical. ”

“ Tones, or musical sounds,93 are produced by isochronous or equal-timed vibrations; thus C of the first octave is produced by 256 vibrations a second, and if this tone is prolonged the vibration rate will continue uniformly the same. Noises, on the other hand, are produced by vibrations which have no uniformity of vibration rate. The ear's sensibility to pitch extends over about seven octaves. The seven-octave piano goes down to 27-1/2 vibrations and reaches up to 3,500 vibrations. ”

“ With the musical sound given out by these vibrating strings must inevitably be mixed the dull and unmusical sound of the blow that set them vibrating. The trained ear will detect not only the thud of the hammer against the string, but that of the finger against the key, and that of the key itself upon its base. The study of touch and tone upon the piano is the study of the combination and the control of these two elements of sound, the one musical, the other unmusical. ”

“ The resonance-chambers influence volume also. A tone is augmented by resonance.
The larynx bears certain resemblances to both stringed and wind instruments, but it is really unique (sui generis) . The vibrations of the vocal bands are caused solely by the expiratory current of air, which is more or less held back by the cords, owing to their approximation, so that the greater the obstruction the stronger must the blast of air be, other things being equal, and the result increase in pitch. The problem Nature had to solve is very complex. ”

“ Our churches and theatres are yet much too large, though we do not need pipes or speaking tubes. If we rub our moistened finger along the edge of a drink-big glass, or draw a bow across the strings of a violin, we can in both cases procure sounds which remain undiminished in intensity as long as the operation by which they are excited is continued. If we strike two bells, one of lead, and the other of brass, the sound of the former is feeble and momentary, compared with that of the latter ; so we see, that, though bodies all sound, yet the sounds produced are not all alike. ”