610.30 Structural Harmonics

610.31 The conceptual sequence in the left column of Fig. 610.20 illustrates the basic octave behavior of structural transformations. The first three figures tetra, octa, icosarepresent the positive outside-out set of primitive structural systems. Three equiangular triangles around each comer add to tetra; four around each comer add to octa; five around each corner add to icosa; but six 60-degree angles around each corner add to 360 degrees; ergo, produce an infinitely extendible plane; ergo, fail to return upon themselves embracingly to produce a system’s insideness and outsideness; ergo, thus act as the zerophase of maximum evolution changing to the involution phase of maximum nothingness. As the transformation sequence changes from divergent evolution to convergent involution, from five, then four, then three equiangular triangles around each corner, it thereby produces successively the inside-out icosa, octa, and tetra, until the convergent involutional contraction attains the phase of maximum nothingness. At the minimum zero bottom of the sequence the inside-out tetra revolves outside-out to minimum somethingness of tetravolume 1 as the transformation diverges expansively to the maximum vector-equilibrium somethingness of tetravolume 20, thereafter attaining maximum nothingness and evolution-to-involution conversion. (See Sec. 1033.)

610.32 At six-vector hexagonality we have the vector equilibrium at maximum zero evolution-to-involution conversion.

610.33 The minimum zero tetrahedron with which the series commences repeats itself beneath the bottom figure to permit the accomplishment of octave harmony at minimum zero conversion whose terminal nothingnesses accommodate the overlapping interlinkages of the octave terminals: thus do-re- mi-fa-sol-la-ti-do.