With his Generator, which was invented for the purpose of multiplication of vibrations, he secured higher frequencies by disturbance of equilibrium of mediums of different specific gravities, air as one, water as the other.

In the disintegration of water in his "Liberator" he produced the "etheric order of ozone." This he is said to have used in a "carbon register" to produce a high vibratory circuit that proved sufficient to break up cohesion, which he states is simply molecular magnetism. At that time he used, in molecular dissociation, one tuning fork of 620 per second, setting chords on the first octave, in atomic separation, two forks, one of 620 and one of 630, setting chords on the second octave, and in etheric separation used three forks, one of 620, one of 630 and one of 12,000, setting chords on the third octave.

"*When a chord is transmitted through a sectional transmitting wire, the "molecular triple" (intermolecule) is carried along sympathetically by the induced differentiation and in turn excites high affinity with the "polar terrestrial stream." This "polar terrestrial" is triune in character and requires a triune sympathizer, which is satisfied by the structure of the Trexar the differentiated sectional wire of silver, gold and platinum.*"

Frequency multiplication by Trexnonar (Trexar with nine nodes) transmission proceeds by means of inducted corpuscular oscillations within the Trexar itself. On sounding the "introductory ninths" (normal oscillation being 20,000 per second and the vibrational molecular range 1/3 their diameter) Keely states his procedure as follows: He tapped a "Chladni resonating disk" (probably producing a discordant series of sounds) and thereby multiplied the normal Trexar vibration 20,000 per second to 180,000 or 9 times normal. (The three nodes are as: 3:6:9, accelerating by (^{9}/_{3})^{2} or 9 times.) Should we start with a gold node over the platinum section, which is last, the multiplication will be 9 X 9 or 81 times, or 1,620,000 per second. Shifting the gold node to the extreme end or at the far end of the platinum section, will hold the frequency at 1,620,000 per second, with transmitted chord of B third octave.

To induce rotary action on the neutral center indicator, when focalizing on a disk through a soft steel attractor, requires transmissive multiplication of the triple triple or complete chords in three octaves, with the gold node over the extreme section, or 156,057,552,198,220,000 corpuscular oscillations per second. This causes the indicator to revolve 110 times per second and represents multiplication of the transmissive chord by only one gold node.

Using the second node of platinum together with the gold node coming first, both over the last section, raises this frequency to the 81st power, or 156,057,552,198,220,000^{81} or infinitely beyond computation.

Keely states he induced 123 revolutions per minute on a neutral indicator, which "represented billions and billions of vibrations per second."

He states that on sounding the "harmonic thirds" as an introductory impulse, the molecular vibration is increased in the Trexar from a normal frequency of 20,000 per second to 100,000,000. On the enharmonic sixths, the molecular vibrational frequency becomes 300,000,000. On the diatonic ninths it becomes 900,000,000 and on the dominant etheric sixths, becomes 8,100,000,000. On the interetheric ninths this frequency becomes 24,300,000,000, all of which he states can be demonstrated and represented by sound colors.