epogdoon (plural not attested) (mathematics, Ancient Greece, rare) A number equal to another plus an eighth thereof; a number 1.125 times another.
Keely
Scale of the Forces in Octaves
"First octave (unity of sound) is approximately the lowest frequency capable of producing waves of rarefaction and condensation in the air. The atomic aggregate oscillating at this pitch can be experimentally determined, and the aggregate vibrating at a pitch one octave higher will have a mass lying between 1/8 and the cube root of the mass of the first mentioned aggregate; the exact relation under varying conditions of gravity, magnetic saturation, and pressure, can be determined only by accurate measurements. But assuming a body of a size represented by x, with a pitch represented by 1024 per second, then a pitch of 2048 per second will be produced by a body having a volume of some mean between 1/8 of x and the cube root of x. By accurately determining the pitch of a volume of any metallic sphere capable of oscillating at the pitch of, e.g., the eleventh octave of sonity (1024 per second), under normal conditions of gravity, pressure, magnetism, and then successively diminishing its size by 1/8 of itself, we get the successive octaves of pitches higher and higher in period-frequency until we pass the domain of sonity and enter the domain of sono-thermity. The point where the one form of energy merges into the other lies approximately at the twenty-first octave, and this pitch also marks the point where the air is no longer capable of vibrating at that pitch in waves of transverse form. The first gamut of 21 1/2 octaves consists of three forms; viz. sonity, sound, and sonism. The following is a tabulation of the pitches of sonity in octaves from one vibration per second to where the next form of energy commences." [Keely, from Dashed Against the Rock] See Law of Force
See Also
diapason
diapente
diatessaron
Scale of the Forces in Octaves