The row

Due to the lack of any true precedent for the construction of a perfectly symmetrical matrix of this kind, determining the position of each unit in the prime row was initially very much an exercise in trial and error. The discovery of the 9-unit row was the result of this process, and from this emerged the foundation for the 2-dimensional matrix, and ultimately the 3-dimensional cube. Many, many efforts were made to duplicate the symmetry found within this 9-unit structure using other numeric values, but none could produce comparable results.

This is the prime row:

The Prime Row

As I will explain in The Matrix section, unit 8 is the primary axis around which the model is constructed, but for the purpose of analysis, let us disregard this for a minute and instead concentrate on understanding how the row itself is organized.

The Prime Row Structure

Because of the distinctly non-linear structure of the matrix, it is best to read the row from the center (unit 5) to the edge in both directions at once, instead of reading it from left to right. Unit 5 is one of two secondary axes, but in the prime row (P8) it is the fulcrum around which the other units are organized. The row, therefore, can be constructed by simply inverting the specific progression of addition and subraction in either direction from unit 5:

5 (+4) = 9; 5 (-4) = 1; 9 (-3) = 6; 1 (+3) = 4, etc.
If, for a moment, we ignore the visual logic of this row, and focus only on the numeric properties contained within the row, they can be understood thus:
1. The sum of the numeric values of the units with identical relative positions to unit 5 - 1 and 9, 4 and 6, 3 and 7, 8 and 2 - is equal to 10;

2. The sum of the numeric values of each of three groups of three units - 834, 159, and 672 - is equal to 15;

3. The sum of the numeric values of all the units in the row is equal to 45;

4. Any of the totals from 1, 2, or 3 above, when divided by the number of units added together, is always equal to 5:

8 + 2 = 10 and 10 / 2 = 5;

6 + 7 + 2 = 15 and 15 / 3 = 5;

9 units added together = 45 and 45 / 9 = 5.

When these simple calculations are performed on other rows in the matrix, there are some inconsistencies that are not found here. It is the absence of these inconsistencies which underscores the significance of this row (P8) as the foundation of the matrix.

Of considerable interest in this row is the presence of three groups of three units - or cells - whose importance becomes more apparent during the analysis of the matrix itself. It will be seen that these cells form both the structural and compositional backbone of the entire matrix.

Audio

Cell Audio Clip
834
159
672

The following section analyzes the arrangement of these rows for the construction of the 2-dimensional matrix.


The Cube Matrix: The evolution and analysis of a compositional model.
©2009 Emlyn Ellis Addison. All rights reserved