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
"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
2.19 - Male-Father and Female-Mother Forces
9.9 - Sympathy or Harmony Between Harmonics or Overtones
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
Page last modified on Monday 17 of September, 2012 05:31:38 MDT