Loading...
 

system of motions in pendulums


Ramsay = wave amplitude, swing of a pendulum.

"In the laws of quantities and motions there are three primary ratios from which the musical system of vibrations is developed.
Pendulums, from the slowness and continuance of their motions, are well adapted to give an ocular demonstration of the relative motions of each of these three primary ratios when compared and combined with the unity and with each other. The numbers 2 and 4 express the first condition in the first ratio; as, in falling bodies, when the times are 2 the distances are 4. In the case of two pendulums, when the length of the one is one fourth part of the other the motions are 1:2; and when two is counted for the upper one, the oscillations of these two pendulums will meet at one. The numbers 3 and 9 express the first condition of the second ratio; as, in falling bodies, when the times are 3 the distances are 9. In the case of two pendulums, when the length of the one is the ninth part of the other, the motions are 1:3; and when three is counted for the upper one, the oscillations of these two pendulums will meet at one. The numbers 5 and 25 express the first condition in the third ratio; as, in falling bodies, when the times are 5 the distances are 25. In the case of two pendulums, when the length of the one is twenty-fifth part of the other, the motions are 1:5; and when five is counted for the upper one, the oscillations of these two pendulums will meet at one.
In the system of motions in pendulums, the three primary ratios indicated in the foregoing paragraph, namely, 2:4, 3:9, and 5:25, are compared and combined with three different units. In their comparison, 1 is the unit of quantities, that is lengths, and 1 is the unit of motions. The numbers 1/4, 1/9, and 1/25, when taken together with 1 as unity, express the first comparison and combination of quantities; and the numbers 2, 3, and 5, taken together with 1 as unity, express the first comparison and combination of motions." [Scientific Basis and Build of Music, page 15]

See Also


cosmic pendulum
double compound pendulum
Figure 2.7 - Swinging Pendulum showing equal but opposed Polar States
Figure 8.9 - Four Fundamental Motions of a Pendulum
Harmonograph
Pendulograph
Ramsay - Pendulum Illustrations of Ratios
Ramsay - PLATE XXVIII - The Two Modes Notes Pendulums
Ramsay - PLATE XXX - Vibration Ratios and Pendulum Proportions
Ramsay - The New Way of Reckoning a Pendulum Oscillation
Ramsay - The Sharp and the Flat - Pendulum Illustration of Ratios
Sympathetic Oscillation
system of motions in pendulums
Distance
first condition in the first ratio
first condition of the second ratio
Motion
Number
Period
Ratio
theory of relativity
Time

Created by Dale Pond. Last Modification: Wednesday December 2, 2020 05:46:49 MST by Dale Pond.