one-frequency vectory equilibrium

The Synergetic Temperament System

Kenneth Hemmerick

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The most fundamental ingredient of communication is the phenomenon of the common experience. It is the definition of this most basic experience that enables an idea, emotion or integrity to be transmitted from one to another. It is within this common experience through which expression and impression are realized. The definition of an experience necessitates first a common experience.

In language, the common experience is the alphabetical progression of sound. In art, it is the array of colour found on the artist's palette. In music, the common experience is the pitch/frequency modulation or progression of sound. It is called temperament, which is the system of adjustment of the intervals between the tones of an instrument of fixed intonation.

Individually, each component within these various common denominators is of very little meaning but combined, they synergetically form a medium through which the message is relayed. The message is the common experience and the common experience is defined by the medium.

Each and every medium is of unique expressive and impressive orientation thus confining the definition of an experience, idea or integrity within the parameters of its medium's structure. The expression and impression of an experience is of purely subjective matter with the definition of the experience being the object itself. The object of the experience is hence defined by the range and scope of the subjects' immediate and ultimate environments.

The purpose of this writing is to theoretically define a system of temperament or common experience in music in terms of the design and behavior of a 3-dimensional wave formation. It describes the tempering of sound in such a manner for sound is propagated through the environment in the manner of a pulsating sphere. It defines both the musical medium and message within the boundaries of a 3-dimensional structure.

The ideas and integrities within this essay have been realized through an intuitional reasoning with the aid of 3-dimensional models. The use of models in this manner have served to take the design of a sound wave formation off of a 2-dimensional surface and to give it 3-dimensional space.

It is through these models that this theory of system of temperament is developed. This conceptualization describes the phenomena of tempered sound in terms of geometric relationship rather than consonance and dissonance. It describes the relationship between the components within its structure as a whole system with an innermost (lowest) and outer-most (highest) frequency which together define the system's boundaries. Conventional theories of temperament structure sound in terms of the octaval relationship. However, the system's conceptualization defines the equalization of temperament not through intervalic relationship but rather in terms of the rate of change of the motion and direction between the individual frequencies.

Finally and most fundamental to the theory of the system is the conceptualization of a state of least excitation of sound in which sound finds its energetic source. It is conceived that from within this state sound finds its source of propagation regardless of frequency, amplitude, duration and form. This state of least excitation is conceived to lie within the system's structure at its innermost point and is the system's common denominator from which the co-ordination or tempering of the sound within it is established.

There are areas in the complex phenomenon of the sounding of sound, which this writing does not address. The objective of this article is to describe to the reader in simple terms; a three-dimensional system of temperament design on the basis of the structure of a three-dimensional wave formation. Too many fields of discussion would only serve to confuse the issues at hand. For this reason they have been purposefully avoided.

Kenneth Hemmerick


The Synergetic Temperament System is a mathematical co-ordination of sound. The co-ordination exists between; first, the frequencies within and without the system, second, the individual frequencies within the system itself and third, the whole system, its frequencies and a common nuclear source. The synergetic temperament system is a system of adjustment of the intervals between the tones of an instrument of fixed intonation.

The basic scientific principle on which the theory of the system is formulated, simply stated, is that sound is propagated through the environment in the manner of a pulsating sphere. The synergetic temperament system is conceived in terms of being a 3-dimensionally-integrated network of sound described by the formation of equidistantly spaced pulsating spheres lying one within and without another with a common nuclear core at its innermost point.

The synergetic temperament system is a coordination between the sound within and without the system. The sound without the system is that which is outside of the frequency range of the system. Tonal space defines the vast multitude of longitudinal vibrations, regardless of frequency, amplitude, duration and form. It encompasses sound, which is outside of human perception, normally limited to a frequency range between 16 cps to 10,000 cps.

The synergetic temperament system is a short section of the two million cycle-per-second-wide frequency spectrum of tonal space. It encloses and excloses a space within tonal space. It is a closed system. It is a tonal environment of unique quantitative and qualitative value determined by the frequencies within its structure and their inherent overtonal formation and interaction.

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© 2006 Kenneth Hemmerick