"As every mass consists of vibrations in thirds, balanced in harmonic equilibrium without cancellation or diminution of energy, it stands therefore in harmonic relation to every other mass. All forms of matter and of motion are thus interrelated and interchangeable. Through resonance, increasing this sympathy, we can control the states of matter." [MASS ACTION]
Keely was first and foremost a musician. He saw the universe and all it contains as musical constructs thus he expressed the truths he found in musical terms. Music is organized vibration and oscillation. Unorganized vibration and oscillation is just noise. For instance a Keely Sixth is the dissipative (entropic) side of the equation and depending on its state or degree of dissipation may be placed along the MINUS side of Russell's scale at -1, -2, or -3. Likewise a Keely Third is the concentrating (syntropic) side of the equation and depending on its state or degree of concentration may be placed along the PLUS side of Russell's scale at +1, +2, or +3. Basically, a western musical octave is composed of two (not identical) thirds and a fourth or four thirds (depending who you ask) going up in frequency to the octave position.
In standard music theory the INVERSE of a third is a called a SIXTH - so increase by thirds and decrease by sixths, conceptually speaking. Whether this holds arithmetically has not yet been worked out (08/24/08). Keely's Ninths corresponds to Russell's Zero Point of the Infinite Octave which he says does not figure into numeration and activities. This concentrating and dissipating action is shown in Russell's painting below represented by the actions of focalizing and defocalizing lens. The large lens in the center is, at its vertical center line, pure Vacuum or pure potential of full neutrality-in-inertia. This point has what appears to be infinite density because at this point all impinging energies from the center is received, regenerated and returned much as an echo is an impacting sound received, regenerated and returned to its source.