A pendulum swings to and fro. On the left side is the Negative side or pole. On the right side is the Positive side or pole. When swinging to the right the action is positive until the swing begins to come back to the center or Neutral point. During the swing back to the center the positive polarity takes on a Negative modulation because Negative polarization is a "center seeking" force whereas the Positive is an expanding force. The same holds true but in reverse for the Negative half of the pendulum's swing.
"When the lengths of four pendulums are 1, 1/4, 1/9, and 1/25, their relative motions are 1, 2, 3, and 5; and when 5 is counted for the highest, the oscillations of these four pendulums will meet at one." [Scientific Basis and Build of Music, page 16]
"The numbers which express the motions of these twenty-five quantities have among themselves nineteen different ratios, or rates of meeting; and when these ratios are represented by the oscillations of twenty-five pendulums, at the number of 64 for the highest one, they will all have finished their periods, and meet at one for a new series. This is an illustration, in the low silence of pendulum-oscillations, of what constitutes the System of musical vibration in the much higher region of vibrating strings and other elastic bodies, and determines the number of undeveloped sounds which form the harmonious halo of one sound, more or less faintly heard, or altogether eluding our dull mortal ears; and which determines the number of sounds which, when developed, constitute the System of musical sounds." [Scientific Basis and Build of Music, page 16]
"Things are not always what they seem. Common sense, so very valuable in every-day life, goes but a very little way in science. Common sense could not have told that, when a uniform body is suspended at one end and oscillated as a pendulum, the oscillations would be the same if suspended at one-third from the end. Much less could common sense have told that suspension at a point between these two points, namely, at two-thirds of this one-third from the end, would give the highest rate of speed of oscillation of which the body is capable, a point which we shall call the center of Velocity." [Scientific Basis and Build of Music, page 18]
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]
"the other, like as we also reckon the vibrations of a pendulum." Holden adds that Dr. Smith, in his Harmonics, reckons the complete vibration to be double of this. Lees, in his Acoustics, says- "The travel of a vibrating elastic body from one extreme to the opposite and back again is called a vibration. Continental writers define a vibration to be the travel of a vibrating body from one extreme position to the opposite. This corresponds to our definition of the oscillation of a pendulum." [Scientific Basis and Build of Music, page 23]
"The time period of a pendulum with a moveable weight is most easily ascertained by experiment and not by calculation. Theoretically, in the case of a "simple" pendulum - that is, an imaginary pendulum without weight except at the bob - the period of oscillation varies inversely as the square root of the length, i.e., if the length be increased four-fold, the time period will be one half what it was before. A simple pendulum does not however, exist practically, and though the law above ennunciated may serve to give a general idea of the lengths corresponding to different time periods, these are really only to be arrived at with accuracy by trial." Harmonic Vibrations and Vibration Figures, page 37
"The pendulum which swings one way has its invisible counterpart which swings the other way. This drawing illustrates a sun at the crest of its wave which will eventually be voided by its counterpart, awaiting at its trough, and reborn again from the same point. See Fig. 66." [Atomic Suicide, page 257]