The Synergetic Temperament System
The coordination between the whole system, its parts or frequencies, and a common nuclear core or source is through the procedure of division of 12 into the number of nodal points found in the outer-shells of the various frequency-edged modulations of the vector equilibrium. In other words, all cycles per second values, when multiplied by 12, (the number of directions through which sound or energy is propagated), are equal to the number of nodes found in the outer-shells of the various frequency-edged modulation of the vector equilibrium, or of a sphere created through the interaction of four great circles.
Physically speaking, it is a coordination between equidistantly spaced pulsating spheres in their state of greatest compression and greatest tension. Irrespective of the frequency-edged modulations, all totally compressed spheres have the same value of force located or centralized in the region of their innermost core, while at the same time, individually, each is of unique nodal value or force when in its state of greatest expansion or tension.
The coordination between the system, its parts, and a common nuclear core is established through the mathematical procedure of division of an energy system's or sound's potential nuclear energy and direction, found in its outer-shell. Three-dimensionally, nuclear potential energy is of zero excitation or zero speed but it has a factor or 12 potential directions for propagation illustrated through the closest-packing of spheres as described above.
Energy systems are of varying energy and direction but they have the same velocity value at the level of their innermost nuclear core. All energy systems have a field of possibilities or a propagative field or a vibratory field or a space which can be described by the number of nodal points found in their respective outer-shells.
Thus, the coordination of the frequencies and a common nuclear source within the synergetic temperament system is through the division of the nuclear potential energy, its motion and direction, which is common to all frequencies, into the space of field of propagation of the various frequencies which is defined by the number of points found in their outer-shells.
Proof of this coordination between the frequencies themselves and between the frequencies and a common nuclear source, in terms of the change of motion and direction between the adjacent shells of frequencies and the first frequency and adjacent shells of frequencies and the first frequency and the common nuclear core, can be mathematically established through determination of an acceleration rate. In other words, the shells of the adjacent frequencies progressively increase in excitation, frequency, direction and space at a rate of 1.666... cycles per second per second or at a ratio of 3:5.
While the acceleration rate, in measurement of the rate of change in motion and direction between the adjacent shells within the system, remains constant, the intervalic ratios between the adjacent frequencies do not adhere to the same behavior. The intervalic ratio relationships between the frequencies within the system progressively diminish in size. For example, where the intervalic ratio between the first and second tones of the system, respectively 21 cps and 30.1666 cps, is of a value of 1.4365079, the intervalic ratio between the last two tones, 3967.66 cps and 4083.5 cps is of a value of 1.0291943.
This phenomenon seems to conform to the same behavior found in the intervalic ratios found between adjacent whole numbers. For example, the intervalic ratio between 1 and 2 is 2, but the intervalic ratios between the higher adjacent whole numbers progressively diminish toward 1 but never obtains unity. In the synergetic temperament system, the energetic behavior between adjacent frequencies remains constant while at the same time; the frequencies progressively increase in value thus diminishing their sequentially adjacent intervalic ratios.
A - Ratio
In the same manner that the intervalic ratios between whole numbers progressively diminish, so do the intervalic ratios of the frequencies in the synergetic temperament system progressively decrease in size but never obtains the value of unity.
© 2006 Kenneth Hemmerick