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**Sacred geometrical basis of the 192 rising & 192
falling intervals between the notes in the 7 diatonic musical scales**

__First (6+6) enfolded polygons__The first (6+6) enfolded polygons of the inner Tree of
Life contain 386 yods when their (35+35) sectors are tetractyses. The topmost corners of the two hexagons coincide
with the lowest corners of the two hexagons enfolded in the inner form of the next higher Tree. The 384 yods

192 = 3 + 189

and

192′ = 3′ + 189′,

where "3" (the three white yods) denotes the tonic, octave & interval of an octave, "3′" (the three black yods) denotes the unit interval between a note and itself, the next lower octave with tone ratio ½ and the falling octave interval of ½, "189" denotes the 189 rising intervals below the octave between the notes of the seven musical scales and "189′" denotes their 189 falling intervals (reciprocals of the tone ratios of the rising intervals). See also #37 & #38.

__Inner Tree of Life__When divided into their (

__Sri Yantra__When turned into tetractyses, the

__ 64 hexagrams__I Ching (易經), the ancient Chinese system of divination, is a set of commentaries about
the

__5 Platonic solids__Suppose that the

Seven yods line tetractyses inside each sector. Each set of halves of the five Platonic solids
has 90 sectors with (90×7=**630**) such yods, where **630** is the number value of
*Seraphim*, the Order of Angels assigned to Geburah. There remain
(1890−**1260**=**630**) yods surrounding their axes that are distributed in both halves
of all the Platonic solids. This **630**:**630**:**630** division is
analogous to what was discovered in #37 for the 189 intervals below the octave between the notes in
the seven scales. They were found there to divide into 63 notes & intervals, their 63 inversions and 63
intervals without their accompanying inversions. This triple division is what manifests in the table of
**64** hexagrams as the three rows of lines & broken lines in each trigram. The
**21**:42 division in the set of 63 intervals and in the set of their inversions corresponds to the
division of the 90 sectors in each set of half-Platonic solids into the 30 sectors of the faces of the
half-tetrahedron, half-octahedron & half-cube and the 60 sectors of the half-icosahedron &
half-dodecahedron because the number of yods lining tetractyses in the faces of the former = 30×7 = 210 =
**21**×10 and the number of yods lining tetractyses in faces of the latter = 60×7 = 420 =
42×10.

Here are five sacred geometries that embody the holistic parameter 384 characterising holistic
systems (see also here). Their *spatial* bifurcation into two halves, one the
mirror image of the other, expresses the distinction between the rising and falling intervals between two
musical notes. The 192 geometrical elements that compose each half are the counterparts of the 192
rising/falling intervals between the notes in the seven diatonic scales. These geometries demonstrate the
*sacred* *geometrical basis of the seven diatonic scales, which constitute a holistic
system.* See also #60 in **Wonders of
correspondences**. The 192:192 division that is displayed by holistic systems is discussed in
**The holistic pattern**.

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