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invisible point

Ramsay
But let us proceed with our development, for we need another fifth, a lower one, a subdominant for our minor scale. Well, let us divide A5 by 3 and we have D1 2/3, the root of the lowest fifth; and if we divide A5 by 5 we have for our middle to this fifth F1, and this is F just as we find it at the major start, and identical in quantity in both major and minor. But let us examine the D1 2/3. It is not easy to compare D1 2/3 with D27 of the major; let us bring it up a few octaves by multiplying by 2. This will not alter its quantity, but simply give us the same quantity in a higher octave, in which we may more easily compare it with the major D1 2/3 multiplied by 2 is 3 1/3; multiplied again by 2 is 6 2/3; once more by 2 it is 13 1/3; and once more by 2 it is 26 2/3. Now we can compare it with D27 of the major, and we find this strange fact, that it is a little lower than the major D. The two D's are at the center of the dual system, but the center of the system is neither in the one D nor in the other, but as an invisible point between them, like the center of gravity in a double star; for the minor D is pushed a little below the center, and the major D is pushed a little above the center of the two modes of the system. [Scientific Basis and Build of Music, page 32]

See Also


13.31 - Polarization Points
associative point
cathode dividing point
center
center point balance equilibrium fulcrum
centering point
centering point of stillness
centering points of rest
central point
extended points of rest
focalizing point
fulcrum
interetheric point
isoelectric point
point
point of focalization
point of stillness
point of suspension
Points of rest
scalar
sequence of points of stillness
shafts made up of many points
still point
Triple Point
two points of stillness
white invisible still point
Zero Point
zero points of stillness

Created by Dale Pond. Last Modification: Monday October 5, 2020 05:18:40 MDT by Dale Pond.