Hi Felix; I'm not sure why you would have problems as identifying sound , color and octants as a dimensional reality. Wiki has the following definition for dimension;
The second meaning of the term "dimension" in physics relates to the
nature of a measurable quantity. In general, physical measurements that must be expressed in
units of measurement, and quantities obtained by such measurements are
dimensionful. An example if a dimension is
length, abbreviated L, which is the dimension for measurements expressed in units of length, be they
meters,
nautical miles, or
lightyears. Another example is
time, abbreviated T, whether the measurement is expressed in
seconds or in
hours. Speed, which is the distance (length) travelled in a certain amount of time, is a dimensionful quantity that has the dimension LT−1 (meaning L/T). Acceleration, the change in speed per time unit, has dimension LT−2.
Surely color and sound and octants are quantifiable and are different sounds or shades or position. They are as real as L,W,H. Do Re Mi Fa So La Ti and then back to Do to start a new octave. 3 primary colors 3 secondary colors, white and black. Every 3 dimensional object has the octants of inner space. I think our reality DEMANDS these extra dimensions, otherwise we wouldn't have sight or sound and perhaps other things. Best, Pat P.S. If not part of our reality where does color and sound come from? My An Idea explains this as being those inner dimensions rolled up in our reality.