Popular scientific lectures

nds. It is difficult to portray the delight which one experiences in running over the leaves of these volumes. One sees as an actual spectator almost the

It is astonishing how extraordinarily near Sauveur was to the view which Helmh

scientific research, and that he had invested the new science with the name of "acoustics." On five successive

e the union of "simplicity with multiplicity." Precisely as Euler[136] did a number of years later, he regards a consonance as more perfect according as the ratio of its vibrational rates is expressed in smaller whole numbers, because the smaller these whole numbers are the oftener the vibrations of the two tones coi

e vibrations in a second. By diminishing its length then in a given proportion we obtain a proportionately augmented rate of vibration. But this procedure appears too uncertain to Sauveur, and he employs for his purpose the beats (battemens), which were known to the organ-makers of his day, and which he correctly explains as due to the alternate coincidence and non-coincidence of the same vibrational phases of differently pitched notes.[137] At every coincidence there is a swelling of the sound, and hence the number of beats per second will be equal to the difference o

ch Sauveur took for the highest audible limit. The author's delight at his successful enumeration of the "imperceptible vibrations" is unmistakably asserted here, and it is justified when we reflect that to-day even Sauveur's principle, slightly

much easier to handle than pipes in such investigations, and

ation of the overtones (sons harmoniques) belonging to its fundamental note (son fondamental) thus rendered visible. For the clumsy bridge the more convenient feather or brush was soon substituted. . While engaged in these investigations Sauveur also observed the sympathetic vibration of a string induced by the excitation of a second one in unison with it. He also discovered that the overtone of a string can respond to another string tuned to its note. He even went further and discovered that on exciting one string the overtone which it has in common with another, differently pitched string can be produced on that other; for example, on strin

when less than six occurred in a second. Larger numbers were not distinctly perceptible and gave rise accordingly to no disturbance

sound, and it may be held with much plausibility that the reason w

s not beat in the other. Consequently it is called an imperfect consonance. It is very easy by the principles of M. Sauveur, here established, to ascertain what chords beat and in what octaves, above or below the fixed note. If this hypothesis be correct, it will disclose the true source of the rules o

e seen, however, that according to his view all distant intervals must necessarily be consonances and all near intervals dissonances. He also overlo

s. Being himself essentially involved in the old view of Sauveur, which is usually attributed to Euler, he yet a

fect consonances which beat because the succession of their short cycles[146] is periodically confused and interrupte

is of a different kind from the smoother beats and undulations of tempered consonances; because we can alter the rate of the latter by altering the temperament, but not of the former, the consona

rcing beats of high and loud sounds, which make imperfect consonances with one another. And yet a few slow

the investigations had been continued on the basis of Sauveur's idea, these additional roughnesses would have

een Sauveur's and Helmholtz's

tes of vibration is indeed a mathematical characteristic of consonance as well as a physical condition thereof, for the reason that the coincidence of the overtones as also their further physical and physiological consequences is connected

that very slow beats are not a cause of disturbance, and Helmholtz found a much higher number (33) for the maximum of disturbance. Finally, Sauveur did not consider that although the number of beats increases with the recession from unison, yet their strength is diminished. On the basis of the principle of specific energies and of the laws of sympathetic vibration the new theory finds that two atmospheric motions of like amplitude but different periods, a sin(rt) and a

g how near Sauveur's errors were to the truth, it behooves us to exercise some caution a

uties of a Beethoven sonata are not easily effaced on a poorly tuned piano; they scarcely suffer more than a Raphael drawing executed in rough unfinished strokes. The positive physiologico-psychological characteristic which distinguishes one harmony from another is not given by the beats. Nor is this characteristic to be found in the fact that, for example, in

uli to the single sound-sensing organs, in which case the beats would be totally eliminated. Unfortunately such an experiment can hardly be regarded as practicable.