## The Synergetic Temperament System

#### Kenneth Hemmerick

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A sphere, regardless of its magnitude, is a geometric figure, which is in a state of equilibrium due to the fact that all radii within its structure are of equal value. In terms of dynamics, a sphere is balanced by the force that acts upon it, thereby causing it to maintain its integrity of form. In a sense, a sphere is an equilibrium of force or an equilibrium of vectors.

A straight-lined vector may exist in the abstract but in a practical framework this does not hold ground. The motion of energy through space is always geodesically inclined due to the pull of the most fundamental force of gravity. Therefore, the vector equilibrium can be considered to be of spherical representation in terms of being a configuration created through the intersection of four great circles in which their intersection produces the twelve major vertices of the vector equilibrium.

Fig. 5 One-frequency vector equilibrium and one-frequency vector equilibrium in spherical representation.

The closest-packing of spheres around a central sphere does not produce the supra-structure of a sphere, but that of a vector equilibrium. Regardless of the frequency-edged modulation of the vector equilibrium its structural design of 14 faces and 12 major vertices remains constant.

The greatest level of excitation of an energy system is found in its outer-shell. Energy systems are contained explosions and implosions. In terms of dynamics, energy systems are in a state of equilibrium of these two forces.

The number of points found in the outer-most shell of the various frequency-edged modulations of the vector equilibrium is representative of the level of excitation found within its structure. In a one frequency-edged modulation, the excitation level is at a value of 12. In a two frequency-edged module, the level of excitation is at 42 and so forth. The only factors that remain common in all frequency-edged modulations are first, the structural design and second, the number of directions through which the configuration is formulated.

The vector equilibrium is a coordinate system in the sense that the various sequential frequency-edged modules lie equidistantly spaced one within and without another with a common nuclear core found at its innermost point.

The 2-dimensional wave formation is also a coordinate system of equidistantly extended nodal points with an innermost node. As sound is propagated through the environment in the manner of a pulsating sphere, it seems logical to assume that the 2-dimensional wave formation is not adequate to describe it as a 3-dimensional event.

The synergetic temperament system is a coordination between the frequencies within its structure. This coordination finds its basis in the design of a 3-dimensional wave formation, which conforms to sound's omni-directional design and behavior. The vector equilibrium can be used to describe such a design and behavior.

Fig. 6 One-frequency 2-d and 3-d wave formations.

Fig. 7  Four intersecting hexagons equal one vector equilibrium. Combined these four hexagons are representative of the omni-directional propagation of sound. There exist 12 essential waves per wave formation (three waves per hexagon), as there are 12 directions in which the energy will travel to and from the wave's nuclear source.

Fig. 8 2-d wave formation and 3-d wave formation of two frequency per second. Note: This is a partial illustration only. Four intersecting hexagons equal one vector equilibrium or one 3-d wave formation.

Synergetic Temperament System Formula

The synergetic temperament system is a system of adjustment of the intervals between the tones of an instrument of fixed intonation where each tone is of a specific frequency in cycles per second. It is a system comprised of equidistantly spaced spherical shells or vector equilibriums of various sequential frequencies lying one within and without another with a common nuclear core or source.

In a 2-dimensional wave formation, the frequency-edged modulations is equal to the number of directions in which the energy will travel divided into the number of nodal points found outside of the innermost nodal point.

The nodal points found outside of the innermost node determines the level of excitation or field of propagation per second within its structure. In a 2-dimensional wave formation, frequency number is always equal to the same value in cycles per second.

In a 3-dimensional wave formation however, there are 12 directions in which the energy will flow to and from the innermost nodal point. If this number of directions is divided into the number of nodal points found in the outer-shells of the various frequency-edged modulations, which defines the field of propagation or level of excitation of the wave, a series of values are created, which when assigned to the wave formations are considered to be frequency values in cycles per second.

The formula used to describe such a procedure is:

#### T = 2 + (10) X F² ——————— 12

Simply stated, the frequency value (T) of a 3-dimensional wave formation, in the structure of the vector equilibrium, in cycles per second, is equal to the number of nodal points found in the outer-shells of the configuration divided by 12.

The coordination of the equidistantly-spaced frequencies within the synergetic system can be mathematically determined through the progressive sequence of their second order differences which yield a value of 1.666... cycles per second per second. This value is the system's acceleration rate, which describes the frequencies within the system. This value describes the whole system's movement and direction in terms of velocity through tonal space.

© 2006 Kenneth Hemmerick