Strict logic and order
This section should prove useful for the following reasons : 1. the mathematical structures will be used in the synthetic
structure of each musical dimension ; 2. these mathematical structures are perfect examples of the hierarchy manifested in
generative structure, in which order completely dominates the development and in which there is no liberty, no exceptions,
and everything is assembled with strict logic and rigor ; since generative structures will also apply to the development of
each musical dimension, it seems important and pertinent to study and appreciate these numerological models and to stimulate
our capacity of scientific intuition never neglecting the fact that -
The Numerical Structure of Addition-Subtraction has its own color.
The Numerical Structure of Multiplication-Division also has its own color.
The Numerical Structure of Power-Root has its own color as well.
These colors are essential to the understanding of Qualitative Mathematics.
A Numerical Structure is made up of :
(a) a point of departure, preferably but not necessarily the central point of the system ;
(b) an increment, the most fundamental and simple being the smallest integer ;
(c) a procedure which determines the operation of the increment.