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The seven diatonic scales, as the distinct authentic and plagal Church modes, are the historical basis of Western music. Their most ancient, known forms are the seven Mesopotamian heptachords. They constitute a holistic system, sharing the same universal pattern that is embodied in sacred geometries and which manifests in the 64 codons of human DNA. Their Tree of Life basis arises from the fact that there are 64 SLs in the ten Trees of Life representing the ten Sephiroth of the generic Tree of Life. When these SLs are each replaced by Trees, the 384 SLs above the lowest one up to Chesed of the 64th Tree consist of 64 triads of SLs in the upper set of 32 Trees and 64 triads in the lower set of 32 Trees. The three sets of 64 intervals (rising and falling), or, conversely, the 64 triplets of intervals, are their musical counterpart. The 64 pairs of intervals and their inversions correspond to the 64 SLs on each side pillar that embody the polar opposites of the cosmic duality of Yang & Yin. The counterpart in the I Ching table of the 64 pairs of triads of SLs is the group of 64 hexagrams, each being a pair of trigrams. In other words, to every one of the 384 SLs there corresponds a line or broken line. The fact that there are 10 Sephiroth is what groups the 384 lines and broken lines into 64 sets. The triadic relationship between Sephiroth — two polar opposites on the Pillars of Mercy & Judgement and their integrated balance on the Pillar of Equilibrium — is what groups them into trigrams. The fact that the six Sephiroth of Construction above Malkuth form two triads is what pairs trigrams into hexagrams and what pairs triplets of ascending intervals with triplets of descending intervals.
