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Magazine of Advanced and Practical Esoteric Thought.
SOME OCCULT, PHENOMENA AND FORCES FROM
THE SCIENTIFIC STAND-POINT.
It is easily shown that the division into twelve harmonics is based upon natural phenomena, and that it is not an arbitrary distinction. That each one is also related to a definite physical and emotional effect, can be experimentally, as well as theoretically shown. It is not the absolute numerical value of the period-frequency of the given harmonic which determines its emotional effect, but its relative frequency, or ratio, to other harmonics of the fundamental tone.
There is a correspondence between the absolute numerical value of the tone, and its mental effects, but it belongs rather to the larger eras of mental unfoldment, than to any class of effects in the given era. For instance, there is a gradual rise in the pitch-frequency recognizable by the human ear, and there is a universal demand for music upon a little higher pitch than in former years.
It has been determined, for instance, that the standard for the concertpitch has been gradually rising during the past few centuries. Music of Mozart, Bach, and Beethoven should be rendered upon instruments tuned considerably lower than our modern organs and pianos.
In all the principal theatres and conservatories of Europe there has been, since their time, a gradual rise in the frequency of the accepted standard of concert-pitch.
In 1859 a French Commission was appointed to determine the uniform standard for middle A in the treble stave, and it was placed at 437.5 vibrations per second.
Since that time the accepted pitch has gradually been rising at a rate corresponding to about one semitone per century
In the earlier and simpler music of all peoples, there is a comparative absence of all of the higher pitches, and, as the music becomes more com plex, there is a gradual introduction of higher notes, which fact points to the unavoidable inference that there is some relation between a higher emotional culture, and the higher pitches of the musical gamut.
Under the influence of intensified emotion, a natural singer introduces the highest notes of the upper register, and the violinist resorts to the harmonics, or flute-notes of his instrument.
The most effective appeals of the impassioned orator, are delivered in a high-keyed tenor, and innumerable are the instances illustrative of the fact that the higher pitches belong to the intensified emotions. But the 92nd law of sound does not relate to this gradual rise in pitch. Each one of the harmonics of a fundamental tone is capable of producing a class of effects peculiar to itself, and distinctly different from the effects producible by any of the other eleven harmonics. As a rule, an emotional effect is the preliminary condition resulting from the action of tones upon the system; and these emotional effects produce a physical change in the circulatory system, a consequent increased oxidization of carbon and phosphorus, a rhythmical regulation of the bodily movements, - especially of the non-volitional, -and a complete adaptation of the organism for the maintenance, with the least possible exertion, of the emotional condition produced by the tones.
A combined action of the physical and emotional changes, results in the production of a mental state, and this mental state depends upon the fundamental harmonic, as modified by its associate harmonics. It is the object of culture in this direction to intensify this mental state, and to allow it to absorb the sum of the emotional and physical energies produced by the tones in bringing it about. It is during such moments that certain faculties of the mind become dominant, similar to the mesmeric condition; and if the related melodies and tones be maintained without discord, the Sambudhistic condition is easily produced. The majority of our emotions have, as yet, found no analogue in the intellect, but their existence indicates corresponding mental powers that are as yet undeveloped.
Music enables us to open the door leading to a new order of mind-powers, and in the secret sittings of the G.....R there are regular exercises, aided by tones and harmonics, for the production of these emotions, and the development therefrom, of higher states of reverie, abstraction, meditation, and Sambudhism.
The dominant harmonic referred to in the 92nd law, must bear concordant relations to the associated harmonics, for the production of all major tones, and of all emotions destitute of the element of pain. If one of the associate harmonics be not concordant with the base harmonic, the minor element of conflict and pain disturbs the continuity of the emotional, physical and mental effect. It is an element of disease.
NYAIKA's 93RD LAW OF SOUND. “When a given and particular one of the twelve possible harmonics of a fundamental tone characterizes and creates its corresponding definite emotional, mental, or physiological quality of that tone, the variations in degree and intensity of that emotional, or other quality, are produced by corresponding variations in the relative amplitude and volume of that dominant harmonic, as compared to that of the fundamental tone."
NYAIKA'S 94TH LAW OF SOUND. " When a dominant harmonic has characterized a tone, giving it a definite emotional quality belonging to a certian interval in the gamut of human emotions, then the other harmonics, bearing concordant ratios to the dominant harmonic, produce, by variations in their amplitude and volume,
corresponding changes in the shadings, or qualities of that particular class of emotions excited by the dominant harmonic."
In this connection it may be well to remark that, in the 92nd Law, the different dominant harmonics may correspond, in their definite emotional effects, to different, distinct colors; the relative variations thereof with reference to the fundamental tone mentioned in the 93rd Law, to variations in the intensity, or “ body," of these distinct colors; while the variations mentioned in the 94th Law, to the various shades of these colors, and to their variable tints, corresponding to the finer shades of sentiment and pathos connected with refined and cultivated emotions and feelings.
The above is also true of harmonic undertones, as well as of the harmonic overtones. These undertones are much lower in pitch than the fundamental tone, and they include within their scope, all there is of time,” and “ rhythm,” as well as their extension known as "motivigation,” “phrasing,” and “movement;” and this rhythmical beating of time and accentuation is governed by the laws just described.
An easy and instructive method of remembering the harmonic relations to the fundamental tone; and of understanding the normal, concordant relations between the harmonies themselves, is given here for the purpose of rendering more lucid the next Law of Sound.
NEW FACTS FROM OLD EXPERIMENTS. Imagine an elastic “string,” about one yard in length, in a state of tension between two supports. Slowly draw over it a rosined bow, and observe that it oscillates throughout its entire length. This gives the fundamental pitch of the string, and, for convenience, we will call its period-frequency 200. Continue to produce a tone by means of the bow, and touch the string midway between its two ends with a feather, or some light article, and observe that the string now oscillates in two segments, with a point of · relatively no oscillation in the centre where the feather touches the string.
Each one of these segments, or half-lengths of the string, oscillates at a frequency twice as great as that of the string oscillating throughout its entire length. A pitch an octave higher is thus produced. Remove the feather, and, if your ear has been well trained, you will hear both the octave, and the fundamental note. This octave is the the first harmonic (400) of the fundamental note (200), and is producible by the division of the string into two equal parts. To divide the string into three equal portions will produce the third harmonic. It can be done experimentally by touching the string with the feather at a point one-third of its length, while the bow is being drawn across its other end. If you have acquainted yourself with these facts by experiment, you will possess more accurate concepts than you can get by any description, and it will be quite obvious to you that the second and third harmonic of this kind cannot co-exist in the same string, since, if the string is divided into two segments, it cannot divide itself into three. Now as the second harmonic has an emotional and mental effect and correspondence different from that of the third, it follows that we have here the natural division of two emotional gamuts, the branching of a road into two different paths : one leading into flowery landscapes and fertile meads, - the other winding among desolate places, and solitary ruins. It is evident that the second and third harmonics give a duul aspect to all emotional, or tone-quality effects of tones. The first aspect consists of fundamental tones, accompanied by their octave as har
monics; the second aspect consists of fundamental tones, accompanied by their major fifths (above first octave) as their harmonics. From the first is eliminated the emotional effect of the third harmonic, and its multiples; and from the second is eliminated the second harmonic, and its multiples, and their emotional effects. The first aspect, (200), (400), and the second aspect, (200), (600), — the first being a string oscillating as a whole, and, at the same time, in two segments; the second oscillating as a whole, and, at the same time, in three segments. The first aspect extends to the higher harmonics, by each of the two segments dividing into either two or three additional segments: if into two segments, the emotional character of the first aspect is maintained, and the next harmonic of the first aspect will be 800 ; —that is, there will be four segments, each having a pitch of 800; two segments, each having a pitch of 400, and one string having a pitch of 200; —but if into three segments, the emotional character of the second aspect is combined with the first aspect, and the next harmonic of the first aspect, instead of being 800, will be 1200; – that is, there will be a string oscillating at 200, divided into two equal segments at 400, and each of these two segments will be divided into three segments each one of which oscillates 1200 times per second.
The division of the two segments of the first aspect into three segments each, causes it to partake of the qualities of the second aspect, because it throws the string into six segments, each segment having a pitch of 1200 vibrations, and this is the same result that is obtained in the second aspect, by dividing each of the three segments into two oscillating segments. The effects are not the same, however: in the first aspect the six segments are divided into two groups, while, in the second, they are divided into three groups, and this effectually enables the trained ear to detect the difference.
An obvious corollary of the above mentioned laws is, that, for the production of the finer shadings of tones corresponding to the finer senti- . ments, there must be a vocal instrument correspondingly complex. To produce variations in the amplitude of a dominant harmonic relative to the fundamental tone, there must be, in the vocal or instrumental structure, the capacity to vary the amplitude of the aliquot segments of the oscillating cord, ligament, or wire, without varying the amplitude of the fundamental oscillation; and also for varying the loudness of the remaining harmonics, relative to the dominant harmonic. To repeat:- the variations of the amplitude of the dominant harmonic relative to the fundamental tone, produce the different intensities and degrees of that kind of emotions characterized by that given harmonic; while the variations in the loudness of the remaining associated harmonics relative to the dominant harmonic, produce changes in the sentimental shadings of that einotion, and its blending with allied, but not similar, emotional states.
As structure in a vocal organ is the result of transmitted hereditary qualifications, it is evident the emotional state must precede the structure capable of giving it vocal expression.
Increased intensity of emotional experience enables the animal to more fully utter its feelings by means of the vocal sounds which it is capable of producing. Use and repetition strengthen and develop these vocal structures, and enable them more fully to represent by tone the dominant feeling at the time said feelings are expressed. This increased capacity is transmitted to the next generation, by heredity, as a more perfect struc: