(This is an excerpt from Chapter 11 of my book, The Next Octave.)
“The experience of the fifth as a spiritual experience
was the first to be lost to humanity.” –Rudolf Steiner
Ideally, music and economics are driven by the power of 2, but regulated by the power of 3. We do not, however, live in an ideal world.
In music, the perfect 5th is the most stable interval after the octave. This implies it is, admittedly, less stable than the octave and that’s because the perfect 5th interval, not being generated by the power of 2, is less grounded in this density of the material world. Because doubling drives the energy of physical reality, the octave’s harmonic consonance becomes an expression of grounded, material stability.
In contrast, the 5th is generated by the power of 3 and is more closely aligned to the spiritual or next octave. A perfect 5th is based on the ratio of 3:2 or 3/2, which encodes the concept of triality over duality. We can expand this ratio to better see its proportions by stating that 3 is to 2 as 9 is to 6 (3:2 :: 9:6). These four numbers feature prominently in the Mobius Circuit; after the number 2 generates the wings inside the circuit, the 3, 6, and 9 next come into play. Recall that the numbers 3-6-9 remained untouched by the circuit’s iterative doubling. This fact sets these numbers apart from 1-2-4-8-7-5 in a profound way. Though the system functions by doubling, it’s regulated or controlled by tripling: “The 3, 9, and 6 always occur together,” writes Rodin, “with the 9 as the control.”
To generate the lines connecting 3-6-9, we start by tripling the 3 to 9 and drawing a dotted line between them. (Note that we do not start with 1, nor do we triple 1 to 3, as there is no line connecting the 1 with 3.) The number 9 can be seen as a perfect 5th off the tonic of 3, as the interval is defined by the power of 3 (a 5th is the tonic x 3). The 9 tripled, however, is 27, which reduces back to 9 (2 + 7). Any power of multiplication used on 9 will reduce that number back to itself, so we’ll have to start again with the 6. The 6 tripled is 18 and 1 + 8 = 9, so we’ll draw another dotted line from 6 up to 9. These dotted lines form a lambda.
In contrast to the mirrored, dualistic pairs generated by doubling is the spiritual 9 on top of the circuit. “The 9 demonstrates the omni dimension,” Rodin writes, “which is the higher dimensional flux emanation called Spirit that always occurs within the center of the magnetic field lines… It is the singularity or the primal point of unity… It is complete, revealing perfection, and has no parity because it always equals itself.”2
A line dropping down from the 9 to intersect the midpoint of the two wings vertically intersects each hypo-thetical line connecting the mirrored pairs at a right angle of 90 degrees. Rodin refers to the line drawn down from 9 through the circle’s center as the vortex axis. It functions as a mean or mese for the circuit, a middle point between the numerical polar extremes. The number 9 can be seen as a control, lining up the other numbers into their mirrored flanks, into dualities Plato called “extremes,” that are controlled and reconciled by the meson function of the 9.
When we apply the power of 2 to the numbers 3-6-9, however, we see two behavioral patterns emerge. The number 9, consecutively doubled, generates products that always reduce back to the value of 9. The 9 remains constant. But the numbers 3 and 6, consecutively doubled, form a dualistic oscillation of values back and forth between 3 – 6 – 3 – 6 – 3 – 6, etc.:
3 doubled = 6
6 doubled = 3 (12, or 1 + 2 = 3)
12 doubled = 6 (24, or 2 + 4 = 6)
24 doubled = 3 (48, or 4 + 8 = 12, 1 + 2 = 3)
48 doubled = 6 (96, or 9 + 6 = 15, 1 + 5 = 6)
96 doubled = 3 (192, or 1 + 9 + 2 = 12, 1 + 2 = 3)
This oscillation continues to infinity, but the values produced by doubling 3 and 6 are locked and unascendant. The energy between them travels only horizontally, unable to break that plane or escape its mathematical loop. So the power of 2 produces both a constant at the apex (9) and a lower, locked oscillation between odd and even (3-6). These two behavioral patterns tell us that within the circuit’s system of 3-6-9, the powers of 2 and 3 coexist together.
A reconciliation of the powers of 2 and 3 is somewhat unexpected. Richard Cohn earlier explained, as have countless others, that these mathematical powers are mutually exclusive, primarily because 2 is even and 3 is odd. Two is the way of the octave while 3 is the way of the 5th and ne’er the twain shall meet… but they do meet, forming a creative tension that’s resolved by the governing power of 3.
A similar result occurs in economics when we plug the triad of supply, demand, and exchange into the circuit. Just as a coupled oscillation is formed between 3 and 6 via the power of 2, the same oscillation is occurs between demand and exchange when we remove the control of supply:
The unascendant oscillation between demand and exchange is the definition of debt: making an exchange based only on the desire of demand, and failing to pay for that purchase with a previous supply. But when supply controls the process as a triad, through the apex position of 9, debt is removed from the system and the coupled oscillation becomes a tripled circuit of energy flow.
This is how the economic process is supposed to function: both demand and the exchange are sustainably regulated, governed, or limited by how much supply is avail-able for any given transaction. This prevents over-consumption and runaway inflation of both the money supply and prices.
Through the apex position we generate economic flow, the release of energy locked in oscillation between demand and exchange and its movement up into a triangular cycle. It represents a transcendence of duality, three over two, where a point between the dichotomous extremes occupies the ascendant mese.