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unit of quantities

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]

"In the third comparison and combination of the three primary ratios, 1/27 is the unit of quantities, and 9 is the unit of motions; and the same primes and the same process, again as before, will give the same relative quantities; and in this increasingly rapid range of oscillations the motions will be 9, 18, 27, and 45, compared with the original unit." [Scientific Basis and Build of Music, page 16]

See Also


approximation
cycles per second
DIRECT OBSERVATION UNRELIABLE
first comparison and combination of quantities
Frequency
Heisenberg uncertainty principle
laws of quantities and motions
Observation
order of quantities
Period
quantities and motions
quantities of strings
quantities
Ramsay - Duality in Quantities of Strings and Vibrations
relative quantities
three primary ratios
Time
unit
unit of quantities

Created by Dale Pond. Last Modification: Monday March 15, 2021 04:42:38 MDT by Dale Pond.