Earlier, we saw that the tone ratio 24 is the tenth overtone and corresponds to Malkuth in the analogy between the ten Sephiroth & 22 Paths of the Tree of Life and the first ten overtones and 22 partials of the Pythagorean musical scale. This number is at the centre of the fourth face of the Tetrahedral Lambda, a position which corresponds to Malkuth in the analogy between the tetractys and the Tree of Life. The numbers in the Tetrahedral Lambda are not tone ratios. Instead, their ratios are tone ratios. The numbers at the centres of the four tetractyses are 6, 8, 12 & 24. They define the tonic (6/6=1), perfect fourth (8/6=4/3), first octave (12/6=2) & second octave (24/6=4). What is the meaning of this? It is that both the Greater Perfect System and the seven musical scales are defined by the 15 notes spanning two octaves. 15 (the number of YAH, the Godname of Chokmah) is the sum of the four integers along the leading edge of the tetrahedron:

1 + 2 + 4 + 8 = 15.

The sum of the 20 integers is 350, which is the number of notes & intervals in every ten octaves of a 8-note scale. The sum of the integers 1, 8 & 27 at the corners of the Lambda Tetractys is 36, which is the number of intervals between the eight notes in a scale, including the unit intervals between the notes and themselves.

These examples serve to show how the archetypal Tetrahedral Lambda embodies numbers that determine not only the tone ratios of the Pythagorean musical scale but also the intervals in one scale and its ten octaves.

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