The diagram displays the inner Tree of Life basis of the 189 rising intervals and 189 falling intervals below the octave between the notes in the seven diatonic scales. The 21 red corners outside the root edge of one set of the first six enfolded polygons denote the 21 notes. The 168 coloured yods in these polygons denote the 168 inversions & intervals. The eight white yods coincide with Sephiroth & Daath of the outer Tree of Life. The 189 coloured yods in the other set of six polygons denote the 189 falling intervals. Notice that one coloured yod in each set of 168 yods lies on the root edge. It may symbolize the lone interval 729/512, which is the only inversion that is unpaired (see the table on the previous page). If so, the other violet yod on the root edge denotes its falling counterpart, the interval 512/729.

The first (6+6) polygons enfolded in successive Trees of Life have 384 yods that are unshared with those in the next higher Tree. They include (24+24=48) corners of these polygons and (168+168=336) other yods. The 24 corners associated with each set of polygons comprise one white endpoint of the root edge, the white corner of the triangle outside it, the lowest corner of the hexagon and 21 other corners. The former three corners denote the tonic, the octave (2) and the rising interval of an octave. Their mirror images in the other set of polygons denote the unit interval (1), the next lower octave (½) and the descending interval of an octave (½). The musical division of 192 ascending intervals and 192 descending intervals between the notes of the seven types of musical scales corresponds to the two mirror-image halves of the 12 enfolded polygons, their (21+21=42) intrinsic corners unshared with the outer Tree of Life denoting the 21 ascending intervals and 21 descending intervals for the 21 notes up to that with tone ratio 1024/729. The divisions:

384 = 192 + 192,

where

192 = 24 + 168

and

24 = 3 + 21,

are characteristic of all sacred geometries, as is discussed in The holistic pattern. Examples are analyzed here. Here in the context of the inner Tree of Life is the true geometrisation of the intervals between the notes of the seven diatonic musical scales. Only this geometry is not ordinary geometry but sacred geometry (see page 41), for the inner Tree of Life is the "invisible half" of the outer Tree of Life known to Kabbalists for centuries. The holistic character of the seven diatonic scales (in their pure form — as opposed to their modern, equal-tempered version) is demonstrated by the fact that they conform to the geometry of the inner Tree of Life. 
 

<< Previous    1...   36  37  [38]  39  40  ...45    Next >>

Home