The Synergetic Temperament System

Kenneth Hemmerick

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Tonal Space

Tonal space can be conceived as being a space comprised of shells of pulsating spheres lying one within and without another with each shell being of specific frequency or pulsations per second. As sound is propagated through the environment in the manner of a pulsating sphere, then the space in which it finds its origins and completion must also conform to the design of this behavior.

Tonal space is a 3-dimensional bounded continuous expansion. It is bounded as it lies within the spaces of other frequency modulations but at the same tine it is a continuous expansion lying within the all-expanding phenomenon of universe. It is 3-dimensional for the events within it are of spherical structure.

A point is an abstraction that has no size, shape or extension. It can define the position of an event in space, which, in a 3-dimensional coordinate system, can be located through the description of three coordinates. A sphere, on the other hand, can geometrically represent the position, size or dimension of an event within a x,y,z coordination for it does not lack the intangible characteristics of an abstraction; it has size, shape and dimension.

An event in space, whether sonic or otherwise, must be energetic. Without motion an event in space can not be defined. Energy is motion and the motion of energy through space always has direction. Vectors are symbols used to describe the motion and direction of energy. An energetic event has frequency or vibration. A vibration can be measured in terms of the field of its propagation, which through its very nature, takes up space, which in turn can be measured in terms of size, shape or dimension.

All energetic events, regardless of their manifestation, have one common property, which can be described in terms of excitation. Within the field of the vibration of an energetic event lie sub-fields of varying excitation. This excitation is progressive with the greatest excitation found in the outer-shell of the vibratory field and with the field of least excitation found within the event at its innermost point. All energetic events must be at one point of the same degree of excitation, zero excitation, for all energetic events have the common property of an energetic nuclear source which is of least excitation.

Tonal space can therefore be conceptualized in terms of being a collection or agglomeration of spheres (points) of uniform size lying in a closest-packed manner with each sphere being an idealized model of a field of energy at a level or quantum of last or zero excitation.

To further the conceptualization of tonal space in this manner, tonal space can be considered to be an agglomeration of closest-packed spheres which each sphere having a unique x,y,z coordination. The position of a sound in tonal space is thus defined by its nuclear sphere. The shells of spheres created through the procedure of closest-packed layering, progressively describes the space enclosed by the vibration or frequency of the sound.

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© 2006 Kenneth Hemmerick