see Etheric Elements, Subdivision
Generally speaking there are no enharmonic or inharmonic frequencies per se (excepting cases). As degree of harmonicity or enharmonicity is relative (relationship between two or more quantities) there are enharmonic relationships, ratios, chords or intervals.
A shortcut (general rule of thumb) to determining enharmonicity as opposed to harmony is if the number is divisible by 2 (with no remainder) it is considered harmonic but on the natural scale. All other divisions are some degree of enharmonic in relation to the harmonic.
In SVP or Keely's jargon, Harmonic, Dominant and Enharmonic refer to, respectively, Syntropic, Dominant and Dispersive or Entropic. Enharmonic may be considered as dispersive or entropic. [See 2.19 - Male-Father and Female-Mother Forces and Triune States of Matter and Energy]
"All the forces of nature, writes Keely, proceed from the one governing force; the source of all life, of all energy. These sympathetic flows, or streams of force, each consists of three currents, harmonic, enharmonic, and dominant; this classification governing all orders of positive and negative radiation." [Vibratory Physics - The Connecting Link between Mind and Matter] [See Laws of Being]
"Electricity is the result of three differentiated sympathetic flows, combining the celestial and terrestrial flows by an order of assimilation negatively attractive in its character. It is one of Nature's efforts to restore attractive differentiation. In analyzing this triple union in its vibratory philosophy, I find the highest order of perfection in this assimilative action of Nature. The whole condition is atomic, and is the introductory one which has an affinity for terrestrial centers, uniting magnetically with the polar stream; in other words, uniting with the polar stream by neutral affinity. The magnetic or electric forces of the earth are thus kept in stable equilibrium by this triune force, and the chords of this force may be expressed as 1st, the dominant, 2nd, the harmonic, and 3rd, the enharmonic. The value of each is, one to the other, in the rates of figures, true thirds. E flat- transmissive chord or dominant; A flat- harmonic; A double flat- enharmonic. The unition of the two prime thirds is so rapid, when the negative and the positive conditions reach a certain range of vibratory motion, as to be compared to an explosion. During this action the positive electric stream is liberated and immediately seeks its neutral terrestrial center, or center of highest attraction." [Vibratory Physics - The Connecting Link between Mind and Matter]
"In analyzing this triple union in its vibratory philosophy, I find the highest order of perfection in this assimilative action of Nature. The whole condition is atomic, and is the introductory one which has an affinity for terrestrial centres, uniting magnetically with the Polar stream, in other words, uniting with the Polar stream by neutral affinity. The magnetic or electric forces of the earth are thus kept in stable equilibrium by this triune force, and the chords of this force may be expressed as 1st, the dominant, 2nd, the harmonic, and 3rd, the enharmonic. The value of each is, one to the other, in the rates of figures, true thirds. Eb, - transmissive chord or dominant; Ab - harmonic; Abb - enharmonic. The unition of the two prime thirds is so rapid, when the negative and the positive conditions reach a certain range of vibratory motion, as to be compared to an explosion. During this action the positive electric stream is liberated, and immediately seeks its neutral terrestrial centre, or centre of highest attraction." [True Science]
"Keely has discovered and was the first to demonstrate that electricity has never been handled; that it is not merely a force or a form of energy, - that it is matter; and that what we call electricity, and have diverted for commercial use in electric lighting, is but one of the triune currents, harmonic, enharmonic, and diatonic, which are united in pure electricity; that the enharmonic current seems to be sympathetically and mysteriously associated with the dominant current; and that the dominant current can no more be brought under control than can the lightning itself. The diversion of the dominant current would mean destruction to any mechanical medium used for that purpose, and death to the operator. The intense heat evolved by the electric stream Keely attributes to the velocity of the triple subdivision at the point of dispersion, as each triple seeks its medium of affinity. Sudden unition induces the same effect; but demonstration shows that the concentration of this triple force is as free of percussion as is the breath of an infant against the atmosphere; for the three currents flow together as in one stream, in the mildest sympathetic way, while their discharge after concentration is, in comparison to their accumulation, as the tornado's force to the waft of the butterfly's wing. The enharmonic current of this triple stream, Keely thinks, carries with it the power of propulsion that induces disturbance of negative equilibrium; which disturbance is essential to the co-ordination of its flow, in completing the triune stream of electricity. When this fluid is discharged from the clouds, each triplet or third seeks its terrestrial concordant, there to remain until that supreme law which governs disturbance of equilibrium again induces sympathetic concordant concentration, continuing to pass through its evolutions, positively and negatively, until the solar forces are expended." [Keelys Contributions to Science]
"The sympathetic acoustic impulses are:
"the DOMINANT - a diatonic third -
"the HARMONIC - the connective "sixth" - and
"the ENHARMONIC - or diminished seventh - which Keely calls a ninth -
"inducing "infinite trajective velocity" or "neutral radiation" from neutral centers. [Snell Manuscript]
"If a violin string is bowed steadily, the frequencies of the partials of the resulting complex tone will be integral multiples of the lowest fundamental frequency, and the partials may properly be called harmonics. If, however, the same string is struck or plucked and then allowed to vibrate freely, the frequencies of the partials in the airborne sound and the frequencies of the corresponding modes of vibration are, in general, no longer exactly in the ratios of integers, and the partials and modes of vibration are inharmonic." [A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900]
""in concord"; relating to that genus or scale employing quarter tones; comprising a major third and two quarter tones also the difference between three conjunct major thirds and an octave (ratio of 125:128); relating to the difference in pitch that results from the exact tuning of a diatonic scale and its transposition into another key.
"In Greek music the enharmonic genus was the oldest of three ways of subdividing a tetrachord, the other two being the diatonic and the chromatic. In its original form it seems to have consisted simply of a major third with a semitone below, but in quite early times the semitone was divided into two quarter-tones, so that there were four notes in all, instead of three.
"The existence of these small intervals, which were in use until Hellenistic times, is evidence of the close association between Greek music and Oriental music.
"In modern acoustics the enharmonic diesis is the interval between an octave, i.e., 2/1; and the three major thirds, i.e., (5/4)3=125/64; B# is therefore flatter than C, and the interval is (2)/125/64=128/125.
"On keyboard instruments, however, B# and C are identical, and this has encouraged composers to use harmonic changes which exploit this identity, where D# becomes Eflat. Substitution of this kind is known as an enharmonic change. An enharmonic modulation is one which makes use of such a change to facilitate the progress from one key to another." [Collin's Music Encyclopedia; William Collins Sons, & Co., Ltd., London, 1959]
"One of the three genera of Greek music, the other two being the Diatonic and Chromatic. Having intervals less than a semitone, e.g., an enharmonic organ or harmonium is an instrument having more than twelve divisions in the octave, and capable, therefore, of producing two distinct sounds where, on the ordinary instrument, one only exists, as, for instance, G# and A flat, etc." [A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900]
Figure 14.01 - Overtones Developed Musically Showing Up as Isotopes along the Vertical Axis of this Chart
Law of Assimilation
Law of Cycles
Law of Harmonic Pitch
Law of Harmonic Vibrations
Triune States of Matter and Energy
2.19 - Male-Father and Female-Mother Forces
9.9 - Sympathy or Harmony Between Harmonics or Overtones
13.11 - Triple Currents and Streams