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first comparison and combination of quantities

Ramsay = wave amplitude, swing of a pendulum.

Ramsay
"While Mr. Ramsay was meditating on these teachings of the great mathematician, Euler, and studying these notes and their vibrations, he was led to discover that the order of quantities above F, when taken below B, constitutes the Minor System. This was the discovery of the Law of Duality in Music. This Law of Duality in Mr. Ramsay's hands asserts an importance not second even to the Law of Mathematical Ratios which rules in the genesis of the notes." [Scientific Basis and Build of Music, page 8]

"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


amplitude
Distance
first comparison and combination of motions
first comparison and combination of quantities
first condition in the first ratio
first condition in the third ratio
first condition of the second ratio
key to motion
Law of Motion
laws of motion
Laws of Music
laws of oscillatory and vibratory motions
laws of quantities and motions
laws of vibratory motion
Mode
Motion
movement
Newton Laws of Motion
Newton Third Law of Motion
Number
Period
quantities and motions
Ratio
Relativity
second comparison and combination of the three primary ratios
theory of relativity
third comparison and combination of the three primary ratios
three primary ratios
Time
Variable

Created by Dale Pond. Last Modification: Monday March 15, 2021 04:32:15 MDT by Dale Pond.