Ramsay
Musical sounds are usually caused in the ear by certain vibrations of the surrounding air, which originate from solid bodies in a state of vibration from some force exerted upon them. Vibrations of the air require to attain a certain rate of speed before they become audible to the human ear; and they require to have certain ratios of rate of rapidity in order to constitute that beautiful host of sounds which constitutes the music of mankind. These musical vibrations may arise in the air from a vibrating organ pipe, or a vibrating tuning fork, or a bell, or a sounding glass, or a strand of wire or gut-string, or other rhythmically vibrating body; but to explain and define the nature of a musical vibration from the action upon it of an elastic string is to explain and define it for all. But before defining what a vibration of a string is, let us hear what others have said about it. Charles Child Spencer, Treatise on Music, p. 6, says- "It is customary in calculating the ratios of vibration of musical strings, and which answer to the waves of the atmosphere, to reckon by double vibrations, so that instead of saying there are 32 single vibrations in the lowest sound, C, writers on this branch of music say there are 16 double vibrations in this sound. This method of calculation, therefore, gives 256 vibrations for the fourth Octave C." Playfair, in his Outlines of Natural Philosophy, p. 282, says- "It is usual to reckon the vibrations of a string different from those of a pendulum; the passage from the highest point on one side to the highest point on the other is reckoned a vibration of a pendulum; the passage from the farthest distance on one side to the farthest distance on the other and back again to its first position, is the accounted a vibration of a musical string. It is properly a double vibration." Holden, in his Rational System of Music, says- "Mr. Emerson reckons the complete vibration the time in which a sounding string moves from one side to [Scientific Basis and Build of Music, page 22]
are always when they have returned to the side from which they were started. The Pendulographer, also, when writing the beautiful pictures which the musical ratios make when a pen is placed under the control of the pendulums, always finds his figure to begin again when the pendulums have finished their period, and have come for a fresh start to the side from which the period began. This confirms our author's definition of an oscillation of a pendulum. Fig. 3 is an illustration of the correct definition of a Musical Vibration, as also given in this work. Although the definition of an oscillation is not identical with that of a vibration, yet on account of their movement in the same ratios the one can be employed in illustration of the other as we have here done. Fig. 4 is a uniform rod suspended from the end as a pendulum; it will oscillate, of course, at a certain speed according to its length. In such a pendulum there are three centers related in an interesting way to the subject of Music in its three chords - subdominant, tonic, and dominant, which roots are F, C, and G. The center of gravity in the middle of the rod at 2, suspended at which the rod has no motion, corresponds to F, the root of the subdominant, in which there is the maximum of musical gravity. The center of oscillation at 3, which is one-third of the length of the rod from the end, is like the root of the tonic whose number is 3 in the genesis of the scale from F1. In this point of suspension the oscillations are the same as when suspended from the end at 1. The point at 9 is at a ninth from the center of oscillation. Our author discovered that, if suspended at this point, the pendulum had its highest rate of speed. Approaching the end, or approaching the center of oscillation from this point, the rate of speed decreases. Exactly at one-ninth from the center of oscillation, or two-ninths from the end, is this center of velocity, as Ramsay designated it; and it corresponds in some sort also to the root of the dominant G, which is 9 in the genesis of the scale from F1; its rate of vibration is nine times that of F1. The dominant chord is the one in which is the maximum of levity and motion in music. [Scientific Basis and Build of Music, page 105]
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