Description and Construction
The portacle is formed using a phase-space transform from the dynamics present within the voice and breath (or whatever other dynamic stimulus we choose to use - the only prerequisite is that we use a vector which changes in phase over time). The portacle forms one component toward the beginning of an optical chain which is used to populate the toroidal space. When a transform is performed, there is a function known as a "window" that is typically used to condition the data for processing.
With waveform processing, for example, windowing usually involves superimposition of some manner of envelope - usually just a ramp function to smooth out the beginning and end - to eliminate transients at the outer extents of a vector. With optical processing, the window is essentially a two dimensional aperture that's used to condition the outer edges of a beam of light. The portacle used in the harmonic resolution algorithm most closely resembles the latter.
Phase-space can be thought of as the intensity of rotational change between one moment and the next (in the temporal domain) and one frequency and the next (in the spectral domain). Both of these factor into the construction of the portacle window, which is a snapshot of the phase-space generated by the dynamic outward expression of the voiced individual.
Because of the utilization of the deltas present in phase-space, rather than time or frequency, the "details" of the original stimulus employed become transparent in the process (thus the "break in relativity" from the properties and characteristics of the original voice sample). This is how we're able to achieve "domain independence" from the data-gathering technique used to derive one's essence for the remainder of the processing transform.
The "holes" in the portacle are essentially square. Because the portacle is precisely the same resolution as the eventual matrix, there's no issue with "edge frequency". Since our transform allows a smooth bridge between the analog and digital domains, we are immune to quantization loss provided we adhere to the conditions of the transform.
The portacle, as we've already defined, represents the pure essence of the individual. However, in order to generate the matrices - and everything else that is "sourced" from them - we need to "shine" a pure, coherent source of harmony through it. In this manner, we arrive at the optimization of that essence which is embodied within the portacle. Thus, it's not so much a matter of "redistribution" as it is one of "harmonization". If the individuals themselves possessed a pure, intrinsic and coherent source of harmony, we would have a state of "dominant outward radiance" - and they would be performing the role of our harmonic reference for themselves and that / those which surrounded them.
Thus, the fifth-column data represents the achievable state if one had a pure harmonic power source within, and the fourth column is the difference between the present state and what is possible through harmonic reinforcement. In "working" the matrices or "assembling" the aural rendering, one can essentially gather the roadmap that will take them from the first column to the fifth column...and the details of this journey are embodied within the fourth column.
The Portacle is similar in structure to a pinhole mask, but it is a simple Cartesian plane - rather than a circle - where the horizontal axis embodies the Real and the vertical axis the Imaginary. The data, however, is derived from the circular register into which the parameters of the voicing partials are loaded. What is unique about the Cartesian plane used is that it is configured as a "reciprocal space". In other words, it's center point is what we would perceive as the outer edge, and the sides and corners are the innermost parts. Another way to look at this is with respect to gravity, where the greatest intensity in the reciprocal space would be at the edges, and it would be measurably non-existent at the center. Thus, diffusion would "scatter" into a central, coherent form.
Rather than beginning at some point - such as the Origin - and spiralling outward, the reciprocal space is loaded "all at once" (thus the intensive need for parallel vector processing). Frequency is not regarded in the construction of the Portacle, but Magnitude forms the density of the elements in the "particle cloud" and Phase provides the wavelength. This is one of the key reasons the transform remains domain-independent, and can utilize any form of dynamic stimulus. Once the "cloud" has been set within the plane, diffusion begins. The more organized particles of greater density diffuse outward from the center, while the more chaotic ones with minimal density collect toward the center. Thus, the Portacle is formed.
Thus, to simplify:
1) The Portacle is similar in structure to a pinhole mask, and is formed from a Cartesian plane of reciprocal space. The real and imaginary partials from the voicing - their parameters having been loaded into a circular register - comprise a "particle cloud" which is projected into this plane, where a partial's magnitude becomes a particle's density and its phase becomes the wavelength. The organized particles of greater density gravitate toward the perimeter of the plane while the chaotic ones of lesser dense congregate at the center.
The Portacle is used as an optical filter to shine coherent light through. Rather than having a simple screen to receive the pattern, we have toroidal space. The torus is filled with the values of light falling on that surface. These values at each point result, however, from the combined effects of all the "holes" in the Portacle, as each spreads its individual effect across the entire surface of the torus.
The Portacle forms a sort of "optical filter" through which a collimated body of harmonic partials are passed. These partials embody a complete algorithmic and harmonic series compressed into a single point, all at the maximal normalized magnitude of unity. The "radiance" of this point is expanded and collimated - the results being very similar to a coherent light source - before being routed through the Portacle. The "filtered" partials are then condensed back into a point and focused upon the zero-dimensional vortex thread at the center of a dynamically-torsioning torus (this ensures that the whole of toroidal space comes in contact with the focal point). Upon completion of a single cycle, the torus is fully populated with the Portacle-conditioned partials.
A compressed, zero-dimensional body of algorithmic partials - formed of a complete harmonic series at unity gain - is collimated into a "beam" to pass through the Portacle "filter". The conditioned partials, having taken on the essence of the Portacle, are then focused back into a zero-dimensional point precisely at the vortex thread at the center of a flowing torus. After one complete cycle of flow, the whole of toroidal space becomes populated with these partials.
An algorithm then "unfolds" the torus, which is then presented as the Matrix. The "unfolded" torus embodies the complex chromaphase matrix. The other matrices - imaginary magnitude, imaginary chromaphase, real magnitude, real chromaphase and complex magnitude - are then derived from the seed complex chromaphase matrix for analysis and display.
The matrices shown represent the pure imaginary, real and complex partials. The values of the 1st column are derived from the real matrices, the values of the 5th column are derived from the complex matrices, and the values in the 4th column represent the resolution of the real into the complex through the complete integration of the imaginary. There used to be a column to the left of the real one (presently the 1st) which was derived from the imaginary matrix, but this was eliminated because the values and percentages were always "0.000...".
The two discreet channels of the aural rendering are representative of the imaginary and real matrices, respectively. Thus, the reassembly of the two is best embodied within the data of the 4th column on the Spectral Essence Data Page.
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