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Nature

noun: the natural physical world including plants and animals and landscapes etc.
noun: a causal agent creating and controlling things in the universe.

Keely
Every harmonious condition of Nature's evolutions is governed by one incontrovertible law; that of concordant assimilative harmony. This concordant key is the ruling one over all the antagonistic, negative, discordant ones; the one that diverts the disturbance of sympathetic equilibrium to one general concentrative centre for redistribution. Harmony concentrates, Harmony distributes. The focalising point of concordant sympathetic concentration is the percussive electric field, where the velocity of its sympathetic streams rebounds with a power that throws them far out into universal space; and so far beyond their equative centre of equilibrium, as to bring them in sympathy with the universal attraction of the combined neutral centres of all planetary masses. KEELY. [True Science]

The vapor from the liberator, registered at 20,000 lbs. per square inch has a range of atomic motion of 1333 1/3 the diameter of the atmospheric molecule with constant rotary vibratory action. At 10,000 lbs., 666 2/3, at 5,000, 333 1/3, at 2500, 166 2/3, at 1250, 83 1/3, at 625, 41 2/3. The higher the range of atomic motion the greater its tenuity and pressure. The very evolution on the negative shows a vacuum of a much higher order than was ever produced before confounding all theory to analyze. The highest vacuum known is 17.999999, or not quite 30 inches, but Keely produced etheric vacuums repeatedly of 50 to 57 inches ranging down to 30 inches or 57 lbs. All operations of nature have for their sensitizing centers of introductory action, triple vacuum evolutions. These evolutions are centered in atomic triple revolutions, highly radiophonic in their character and thoroughly independent of all outside forces in their spheres of action. No conceivable power, however great, can break up their independent centers. These triple centers are the foundation of the universe, and mathematically considered, the respective and relative motion of these atomic triplets, gravitating to and revolving around each other, is about one and one-third of their circumference. The problem of this action, when analyzed mathematically, (taking it as the quadrature of the circle) would baffle mathematical science to bring it to a numerical equation. Every revolving body is impressed by nature with certain laws making it susceptible of the operation of force, which being applied, impels motion. These bodies never can approach nearer than a certain limit, nor farther than a certain point. They are, at some mean point, made perfectly equal, and may therefore be considered as one force and as one element. It matters not that other and disturbing forces exist outside or inside the space these bodies revolve in, because if this force must be considered as acting uniformly, applying itself to each of these bodies in a way to produce a perfect equation on all, it is as if this outside force were nonexisting. [Snell Manuscript - The Book, page 2]

The structure of the air molecule according to Keely is as follows: Broken up, by vibratory action, he finds it to contain the "atomic triplet." This exists in a triangular position within the molecule, at its center, unless acted upon by electricity, when the molecule becomes oblate and the three atoms are ranged in a line within unless broken up by vibration. Nature never gives a vacuum, consequently the space within the molecule not occupied by the atomic triplet must be filled with something. This is where the "all-pervading ether" has made its secret abode through untold aeons. [Laurence Oliphant] [Snell Manuscript - The Book, page 3]

"Science will in time classify the important modifications of the one force in nature as sympathetic streams, each stream composed of triple flows. Keely maintains that the static condition which the magnetic needle assumes when undisturbed by any extraneous force outside of its own sympathetic one, proves conclusively that the power of the dominant third, of the triple combination of the magnetic terrestrial envelope, is the controlling one of this sympathetic triplet, and the one towards which all the others coordinate. All the dominant conditions of nature represent the focal centers towards which like surrounding ones become sympathetically subservient. The rapid rotation of the magnetic needle of a compass shown in his experiments rests entirely on the alternating of the dominant alone, effected by a triple condition of vibration that is antagonistic to its harmonious flow as associated with its other attendants. A rapid change of polarity is induced and rapid rotation necessarily follows. [Snell Manuscript - The Book, DISTURBANCE OF MAGNETIC NEEDLE, page 8]

"The human ear cannot detect the triple chord of any vibration, or sounding note but every sound that is induced of any range, high or low, is governed by the same laws, as regards triple action of such that govern every sympathetic flow in Nature. Were it not for these triple vibratory conditions, change of polarity could never be effected, and consequently there could be no rotation. Thus the compounding of the triple triple, to produce the effect would give a vibration in multiplication reaching the ninth, in order to induce subservience, the enumeration which it would be folly to undertake, as the result would be a string of figures a mile in length to denote it. [Snell Manuscript - The Book, DISTURBANCE OF MAGNETIC NEEDLE, page 8]


Hughes
"The time was when Science was cultivated only by the few, who looked upon its application to the arts and manufactures as almost beneath their consideration: this they were content to leave in the hands of others, who, with only commercial aims in view, did not aspire to further the objects of Science for its own sake, but thought only of benefiting by its teachings. Progress could not be rapid under this condition of things, because the man of pure science rarely pursued his inquiry beyond the mere enunciation of a physical or chemical principle, while the simple practitioner was at a loss how to harmonise the new knowledge with the stock of information which formed his mental capital in trade. The advancement of the last fifty years has, I venture to submit, rendered theory and practice so interdependent, that an intimate union between them is a matter of absolute necessity for our future progress." "It is to the man of science, who also gives attention to practical questions, and to the practitioner, who devotes part of his time to the prosecution of strictly scientific investigation, that we owe the rapid progress of the present day, both merging more and more into one class, that of pioneers in the domain of Nature." "These considerations may serve to show that, although we see the men of both abstract and applied science group themselves [Harmonies of Tones and Colours, Introduction2 - Harmonies, page 10]

in minor bodies for the better prosecution of special objects, the points of contact between the different branches of knowledge are ever multiplying, all tending to form pail of a mighty tree—the tree of modern science." "In this short work energy we find all the efforts in Natureenergy is life in action." "We shall thus find that in the great workshop of Nature there are no lines of demarcation to be drawn between the most exalted speculation and commonplace practice, and that all knowledge must lead up to one great result, that of an intelligent recognition of the Creator through His works."
F.J. Hughes [Harmonies of Tones and Colours, Introduction3 - Harmonies, page 11]

I had forgotten all the minor keys, except that A is the relative minor of C major; but although I had only faint hopes of success, I determined to try, and I gained the twelve keys correctly, with the thirteenth octave. I found also that E♭ was usually printed as a minor key-note, Nature's laws having shown that it must be D#. [Harmonies of Tones and Colours, Dr. Gauntletts Remarks1, page 13]

There is amazing grandeur, united with simplicity, in the working of Nature's laws in the development of harmonies of sound, so that the smallest conceivable point has its complementary and corresponding gradation, which renders it capable of development into its peculiar harmony, causing the "multequivalency of harmonies" in endless variety, whether veering round, to and fro, ascending or descending, or advancing and retiring in musical clef. [Harmonies of Tones and Colours, Dr. Gauntletts Remarks1, page 13]

"In every art or science, we expect accuracy according to the nature of the subject-matter, and the end which it is proposed to attain."
[Harmonies of Tones and Colours, The Method of Development or Creation of Harmonies1, page 15]


Here we see why music, as a science, takes the priority of painting; for if music is good, it is perfected by natural laws which cause its tones to melt into each other in the most delicate gradations, while the painter who endeavours to represent the exquisite variations of tints and lights in the living landscape is dependent entirely upon his own resources. The early writers on music were philosophers and mathematicians on the broad basis of general science, not on that of music only. Mathematicians, for the most part, have only studied the subject of musical sounds up to a certain point, and have then left it. The musician must take the chromatic scale—not as it exists in Nature, for that offered by the mathematician, without the ordinary compensations of conventional theory, is of no use to the practical musician. [Harmonies of Tones and Colours, The Method of Development or Creation of Harmonies2, page 16]

Of course, true Art cannot be opposed to Nature, although all the rules of the musician are not the facts of Nature. Music, pure, natural, and harmonical, in the true and evident sense of the term, is the division of any key-note, or starting-point, into its integral and ultimate parts, and the descending divisions will always answer to the ascending, having reference to a general whole. The essence and mystery in the development of harmonies consist in the fact that every key-note, or unit, is a nucleus including the past, the present, and the future, having in itself an inherent power, with a tendency to expand and contract. In the natural system, as each series rises, its contents expand and fall back to the original limit from any point ascending or descending; we cannot perceive finality in any ultimate; every tone is related to higher and lower tones, and must be a part of an organised whole. It is well known how deeply the late Sir John Herschel studied this subject; and it was his opinion that there was some principle in the science of music which had yet to be discovered.[Harmonies of Tones and Colours, The Method of Development or Creation of Harmonies2, page 16]

the artificial system must not be mixed up. The wonders of Nature's laws in the developments of harmonies, consist in the beautiful adaption of keyed and all other musical instruments to a range commensurate with human powers. The chromatic scale of twelve notes (the thirteenth being the octave) is not the scale of Nature. To construct a musical instrument upon real divisions of musical tones, each of them being in correct ratio with the others, it would be necessary to have a larger number of tones to the octave. In the development of harmonies on the natural system, we trace the perfect adaptation of means to ends, meeting the intricacies of every musical instrument, including that most perfect of all— the human voice. [Harmonies of Tones and Colours, The Method of Development or Creation of Harmonies3, page 17]

Notes and colours are thus condensed into a pair springing from the fountain, and mingling with each other in an endless variety. Although yellow as a colour is explained away as white, it is, nevertheless, the colour yellow in endless tints and shades throughout nature, and proves to us that the three great apparent primaries correspond to the tonic chord of the scale of Ci.e., C, E, G = red, yellow, blue; or more correctly, C and G correspond to red and blue with the central fountain of E, white and black mingled, from which all tones and colours arise. [Harmonies of Tones and Colours, On Colours as Developed by the same Laws as Musical Harmonies3, page 20]

"Their music is of a style very difficult for foreigners to acquire or imitate, but the children very easily and early attain it. I low much the Arabs profited by the works of ancient Greek writers is well known."† As knowledge increases, may not the beginning of every physical science be traced first as a trinity springing from a trinity in unity, followed by a second partaking of the nature of the first, so as to unite with it in complementary pairs as here described in tones and colours, trinity in unity being the germ of never-ending developments? [Harmonies of Tones and Colours, The Arabian System of Music, page 21]

CHAPTER V.
DIAGRAM II.—THE TWELVE KEY-NOTES, EACH DEVELOPING ITS SIX TONES IN THE ORDER IN WHICH THEY SOUND.

"Nature's universal law is progress with self-adaptation."
[Harmonies of Tones and Colours, Diagram II - The Twelve Keynotes1, page 23]


DIAGRAM III.—MAJOR KEY-NOTES DEVELOPING BY SEVENS. "Creation is the realization of Divine Thought."::

"The divine and spiritual are not unnatural, but the very soul of nature." F. W. Reynolds, M.A.
[Harmonies of Tones and Colours, Diagram III - The Major Keynotes Developing by Sevens, page 25a]

CHAPTER XIII.
DIAGRAM X.—MINOR KEY-NOTES DEVELOPING BY SEVENS, VEERING ROUND AND IN MUSICAL CLEF.

"Life implies this interdependence and harmonious interaction of parts, and the subordination of all to some universal plan." "Life and intelligence are powers, and rule; but Nature cannot create power, therefore life and intelligence are from a higher source."—J. W. Reynolds, M.A.
[Harmonies of Tones and Colours, Diagram X - Minor Keynotes Developing by Sevens, page 35a]

CHAPTER XV.
DIAGRAM XII.—THE CHORDS OF THE TWELVE MINOR KEYS.

"No development can help anything which does not have corrective causes working with it; some power must shape the growth, and work correctively by laws impressed and authority maintained. The law of progress must be operated upon and moulded by guiding forces. That which acts, lives; and the universe lives as much by its soul as we do by ours."

"And what if all of animated nature
Be but organic harps diversely formed,
That tremble into thought as o'er them sweeps,
Plastic and vast, one intellectual breeze,
At once the soul of each and God of all?"—Coleridge.

"In all things, in all natures, in the stars
Of azure heaven, the unenduring clouds,
In flower and tree, in every pebbly stone
That paves the brooks, the stationary rocks,
The moving waters, and the invisible air,
. . . . From link to link
It circulates, the soul of all the worlds."—Coleridge.
[Harmonies of Tones and Colours, Diagram XII - The Chords of the Twelve Minor Keys, page 37a]

"Thou art Thyself the secret of Thy works;
Thou art the key: Thine image bear they all,
Or more or less. And heaven-born music, as
Thine ordinance in air and ear, and in
The balance of the force elastic, with
The gravitating force that holdeth all,—
Music the statute is, which more than most,
Of all that stands on Nature's statute-book,
Image and superscription—Three in one
In interlacing monogram doth show of Thee!"
[Harmonies of Tones and Colours, Reflections on the Scheme1, page 43]


"Adore with steadfast unpresuming gaze,
Him, Nature's essence, mind, and energy." Coleridge. [Harmonies of Tones and Colours, Reflections on the Scheme2, page 44]

All the energies of nature are the results of Divine operations flowing from the fountain of life, and all the forces of nature are the forces of life. [Harmonies of Tones and Colours, Reflections on the Scheme3, page 45]

Hughes
Among the many subjects which excite interest at the present time is the question whether the doctrine of Evolution is true or false. Milton had evidently some glimpse of its truth, as we see in the following lines:—

"Air and ye elements! the eldest birth
Of Nature's womb, that in quaternion run
Perpetual circle, multiform, and mix
And nourish all things; let your ceaseless change
Vary to our great Maker still new praise!" [Paradise Lost, Book V.] [Harmonies of Tones and Colours, Reflections on the Scheme4, page 46]


Viktor Schauberger
"Our work is the embodiment of our will. The spiritual manifestation of this work is its effect. When such work is properly done it brings happiness, and when carried out incorrectly it assuredly brings misery. Humanity! Your will is paramount! You can command Nature if you but obey her!" [Viktor Schauberger]


Cayce
"And know that nature is that from which man may take his lesson to learn of the Creative Forces..." [Cayce (5214-1)]

"Keep close to all of those things that have to do with outdoor activities, for it is the best way to keep yourself young - to stay close to nature." [Cayce (3374-1)]

Johann Wolfgang von Goethe
"The time will inevitably come when mechanistic and atomic thinking will be put out of the minds of all people of wisdom, and instead dynamics and chemistry will come to be seen in all phenomena. When that happens, the divinity of living Nature will unfold before our eyes all the more clearly." [Johann von Goethe, 1812]


Novalis
"Nature is an Aeolian harp, a musical instrument the sounds of which are keys of higher strings within us. All method is rhythm; if one has grasped the rhythm of the world, one has comprehended the world. Every human being has his own individual rhythm... Every sickness is a musical problem, and the cure is the musical solution. The briefer and more perfect the solution, the greater the musical gift of the physician..." Wikipedia, Novalis


Russell
"Our very name for God's Creation is NATURE, for that is what Nature is. I shall define Nature for you in simple words. Nature is an electric wave thought image of God's nature, electrically projected from His formless and unconditioned ONE LIGHT into countless many forms of conditioned light which we call matter." [Walter Russell, Home Study Course, 04 - Unit One - Lesson 2.1]

"Also the statement that uncharged particles are ejected from one end is not true to Nature. There are no uncharged particles in Nature. Wherever there is matter there is motion. Motion is an electric effect, which charges all matter." [Atomic Suicide, page 274]

"Nature is continually moving to the senses but within Mind-knowing it stands perfectly still as but a thought-picture of Idea. See Fig. 76." [Atomic Suicide, page 287]

"Every effect in Nature is divided into pairs of opposition. Each one of each pair is the reverse of the other. Each one is like a mirror reflecting the other. Nature is like unto a clock with two hands which bend away from each other in opposite directions but equal potentials. If one hand multiplies potential the other simultaneously multiplies it equally. Nature will not allow her balance to be disturbed. Each polarized hand moves away from the other from zero to four. Each then reverses its polarity from a charging body to a discharging one. Generation also reverses and becomes radiation. Heating bodies cool. Living bodies die. Solids become gases and dissolve. Fast motion slows until it ceases." [Atomic Suicide, page 288]

"The science I read was so utterly complex that it was beyond the comprehension of average people without special training, whereas the science of God's plan in Nature, which I wished to give, was so simple that anyone of average intelligence could master it without difficulty." [Walter Russell, Prelude to the Home Study Course, 1950, p. iii.]


Christ Returns - Speaks His Truth
"After the Big Bang, the Father-Mother Creative Process was divided into two different energies, continually working apart and together, independent yet mutually constrained to work together having individual characteristics or 'natures' - and different functions. Therefore, their work load was/is different yet indivisible." [Christ Returns - Speaks His Truth, Letter 5, page 23]


Blavatsky
“Help Nature and work on with her; and Nature will regard thee as one of her creators and make obeisance. And she will open wide before thee the portals of her secret chambers.” [H. P. Blavatsky, The Voice of the Silence, I.66-67]


Nikola Tesla
"Inside the Earth, there are energies of joy, peace, and love that are expressed for example through a flower that grows from the Earth, food that comes out of it and everything that makes it our home. I’ve spent years looking for ways that this energy could influence people. The beauty and aroma of roses can be used as a medicine and the sun’s rays as food. Life has an infinite number of forms, and the duty of scientists is to find them. All I do is look for them. I will not give up.
The Universe is alive in all its manifestations. The stone is a sensitive being, such as plants, animals, and people. A star that shines asks to be seen, and if we were not self-absorbed, we would understand its language and its message. The breath, the eyes and the ears of a human being have to fulfill the breath, the eyes and the ears of the Universe." [Nikola Tesla]


Ramsay
"Of these three chords, which constitute a scale or key, Nature next proceeds to generate, in a similar way, a family of scales or keys, and these in two lines, the Major and the Minor. The twice twelve-fold family of keys is brought forth in much the same way as were the chords which constitute them, and as were the notes which constitute the chords. There is a beautiful growth-like continuity in the production of all." [Scientific Basis and Build of Music, page 20]

"The science of music is the knowledge of how Nature proceeds in this beautiful region of creation in which so much of pleasure for mankind is found, and meet expression for the praise of God. "Music hath charms to soothe the savage beast;" how much more to gratify the civilized and educated ear; to stir with inspiration the prophetic gift; to comfort the troubled heart; and to draw forth the best feelings of our nature." [Scientific Basis and Build of Music, page 20]

Well, how are we to get the true minor scale? There is a remarkable fact, and a beautiful one, which suggests the method. Such is the economy of Nature, that from one system of proportion employed in two different ways, in the one case as periods of vibrations and in the other as quantities of strings, everything in Music's foundation is produced. It is a remarkable fact that the numbers for the lengths of the strings producing the major scale are the numbers of the vibrations producing the minor scale; and the numbers for the lengths of the strings for the minor scale are the numbers of the vibrations of the notes of the major scale. Here Nature reveals to us an inverse process for the discovery of the minor scale of notes. [Scientific Basis and Build of Music, page 31]

The Art of Music, which is music on its spiritual and inspirational side, has been carried to a wonderful perfection of development; while the Science of Music, which is music on its intellectual and logical side, has been left far behind. Works on the Science of Music have been a failure, not because music has not a scientific basis, but, and for the most part, because Mathematicians have dealt only with the law of Ratios, ignorant of other laws which play an important part in music's scientific basis and build. They have carried the law of ratios beyond its legitimate sphere, and so their conclusions do not represent the method of Nature truthfully. [Scientific Basis and Build of Music, page 33]

Either the one or the other must be at fault. Had the dictates of the mathematicians and the scale of mathematical intonation wholly ruled, the advent of the great masters would have been impossible. It was well said by one writing in The Choir - "Theory should be made from music, and not music from theory . . . the final judge of music is the Ear." The Great Masters are the exponent artists of what is true in the Science of Music, though it may differ from what has been taught by the merely mathematical-intonation advocates of music science. It should not be forgotten that the science of the mathematical theorists is one thing, and that of the composers is another. Schubert, Beethoven, Mozart, Haydin, Mendelssohn, and such inspired musicians, who walked in the liberty wherewith Nature made them free, are sufficient authority against the bondage of the one-law theorists who would tie us down to the mathematical command which comes from without, but who know nothing of the life within music which is the law unto itself.1
With twelve divisions in the Octave, each note is adapted to serve in any capacity, and does serve in every capacity by turns. It is quite clear that this cannot be said of the mathematically perfect notes. And this is where it is seen that what is perfect in mathematical ratios becomes imperfect in the Musical System. Indeed, the mathematical intonation does not give a boundary within which to constitute a System at all, but goes off into never-ending cycles.
In music, Nature begins by producing the Diatonic Octave of seven notes, derived by the mathematical ratios2; [Scientific Basis and Build of Music, page 34]

character of its own. And as Nature has constituted them, these various forces all converge to the Center of the Tonic Chord, and, with the exception of the interval of the octave itself, the notes of the tempered scale being a little nearer each other than the mathematically perfect notes, these converging forces and this tempering mutually assist each other, and give a greater decision to the resolution of chords. [Scientific Basis and Build of Music, page 36]

B, namely G#, they come in touch of each other like the two D's. When this three fifths below F major and three fifths above B minor have been developed, the extremes A♭ and G#, though standing like the two D's in duality, are so near that here again one note can be made to serve both. The major series of scales and the minor series at these limits are thus by two notes which have duality in themselves hermetically sealed; but not till Nature has measured off for any one of these scales a sphere of twelve keys in which to move in perfect freedom of kinship by softly going modulations. [Scientific Basis and Build of Music, page 39]

It runs in all the polarities of Nature. Music, as belonging to Nature - as one of the things which the Great Numberer hath created - is under this Law of Duality as well as that of mathematical ratios and other laws. The Law of Duality in music gives the major and minor systems. As the major is derived from certain primes in ratios ascending, and the minor from the same primes in the same ratios descending, they are inversely related; and these diatonic scales have in the responding parts exactly the same quantities. But as multiplying by 3 three times gives the framework of the major system in the ascending genesis, and dividing by 3 three times gives the framework of the minor system in the descending genesis. They are in this view also directly related. The Law of Duality in music emerges into view from the genesis [Scientific Basis and Build of Music, page 42]

The specific levity of notes increases in proportion to the number of times the ratios are multiplied in order to produce them, going upward by sharps; and their specific gravity increase in proportion to the number of times the ratios are divided in order to produce them, going downward by flats. The knowledge of this is attained when everything is in its perfect order. It is the discovery of the Law of Duality in music which shows the method of applying the ascending and the descending ratios so as to exhibit that perfect order of Nature. [Scientific Basis and Build of Music, page 43]

Here, then, we have an order of modes entirely symmetical in pairs placed thus; the only mode that can stand alone being the Dorian, built on D, whose duality has been discovered to reside in itself. All this build of symmetry, which was the watchword of Greek art, as it is also one of the watchwords of Nature, presupposes that the tones of the scale, with lesser and larger intervals lying between them, were resting in their ears exactly as they are in ours,1 and as they are in all humanity, save where it has sunk down into the savage condition, benighted in the evil that is in the world. It is not to be concluded that the Dorian mode is Nature's primitive scale, although it might have a certain pre-eminence [Scientific Basis and Build of Music, page 45]

among the Greeks on account of having symmetry in itself. The primitive scale was doubtless that which is the model of all major music; and our minor model is its dual, as Ramsay has shown, which in its genesis indicates the duality of all the rest of the notes, although it is not probable that the Greeks saw the musical elements in this light. It is remarkable and significant that in their modes the Greeks did not lift up the scale of Nature into different pitches, preserving its model form as we do in our twelve major scales, but keeping the model form at one pitch they built up their symmetrical tetrachords, allowing the larger and lesser tones of the primitive scale to arrange themselves in every variety of place, as we have shown in the table of tetrachord modes above. Without seeing the genetic origin of music's duality they were led to arrange the modes by symmetry, which is one of the phases of duality. Symmetry is duality in practice. It may not always be apparent how symmetry originates in Nature; but in music, the art of the ear, duality emerges in the genesis of the minor scale; in the true mathematical build of the major on the root of the major subdominant F, and the true relation of the minor to it in the inverse genesis descending from the top of the minor dominant B. [Scientific Basis and Build of Music, page 46]

Nature has not finished when she has given us the Diatonic Scale of notes as first generated. In the diatonic scale, in ascending from C, the root of the tonic, the first step is an interval of 9 commas, supposing that we adopt the common division of the octave into 53 commas, which is the nearest practical measuring rule; the second step has 8 commas; the third has 5; the fourth has 9; the fifth has 8; the sixth has 9; and the seventh and last has 5 commas. So we have three steps of 9 commas, two steps of 8, and two of 5. The order of the steps in the major is 9, 8, 5, 9, 8, 9, 5. In the minor the magnitudes are the same, but the order is 9, 5, 8, 9, 5, 9, 8. So there are three magnitudes.1 But Nature has an equalizing process in the course of her musical marshallings, in which these greater ones get cut down, and have to change places with the lesser, when her purpose requires them so to do. [Scientific Basis and Build of Music, page 47]

It should not be supposed that this division of the notes into semitones, as we call them, is something invented by man; it is only something observed by him. The cutting of the notes into twelve semitones is Nature's own doing. She guides us to it in passing from one scale to another as she builds them up. When we pass, for example, from the key of C to the key of G, Nature divides one of the intervals into two nearly equal parts. This operation we mark by putting a # to F. We do not put the # to F to make it sharp, but to show [Scientific Basis and Build of Music, page 47]

that Naturehas done so.1 And in every new key into which we modulate Nature performs the same operation, till in the course of the twelve scales she has cut every greater note into two, and made the notes of the scale into twelve instead of seven. These we, as a matter of convenience, call semitones; though they are really as much tones as are the small intervals which Nature gave us in the genesis of the first scale between B-C and E-F. She only repeats the operation for every new key which she had performed at the very first. It is a new key, indeed, but exactly like the first. The 5 and 9 commas interval between E and G becomes a 9 and 5 comma interval; and this Nature does by the rule which rests in the ear, and is uttered in the obedient voice, and not by any mathematical authority from without. She cuts the 9-comma step F to G into two, and leaving 5 commas as the last interval of the new key of G, precisely as she had made 5 commas between B and C as the last interval of the key of C, she adds the other 4 commas to the 5-comma step E to F, which makes this second-last step a 9-comma step, precisely as she had made it in the key of C.2 [Scientific Basis and Build of Music, page 48]

This subtracting and adding process of Nature by which she so freely handles the notes is the way she gives us the materials of the Chromatic Scale, in which an entirely new series of chords with strikingly different effects, and with exceedingly interesting, subtle, and at the same time easy progressions, is put in possession of the practical musician. This new series of chords forms, in fact, materials for the Chromatic System, which D. C. Ramsay has discovered, and which he has elaborated, as his custom was, exhaustively - his last labor in the interests of music science and art. [Scientific Basis and Build of Music, page 48]

The common chord is a group of notes which come together by generic affinity, much like the chemical combinations of our system of atoms. The common chord is a triplet, and in the progression from one chord to another these triplets have always something in common; by the law of continuity one of the notes of the chord first is also found in chord second; and chord second also finds one of its notes in chord third. This is the way Nature gives them to us [Scientific Basis and Build of Music, page 48]

In the progression - that is, the going on from one to another - of these triplets in harmonizing the octave scale ascending, Nature goes on normally till we come to the passage from the sixth to the seventh note of the scale, whose two chords have no note in common, and a new step has to be taken to link them together. And here the true way is to follow the method of Nature in the birthplace of chords.1 The root of the subdominant chord, to which the sixth of the octave scale belongs, which then becomes a 4-note chord, and is called the dominant seventh; F, the root of the subdominant F, A, C, is added to G, B, D, the notes of the dominant, which then becomes G, B, D, F; the two chords have now a note in common, and can pass on to the end of the octave scale normally. In going down the octave scale with harmony, the passage from the seventh to the sixth, where this break exists, meets us at the very second step; but following Nature's method again, the top of the dominant goes over to the root of the subdominant, and F, A, C, which has no note in common with G, B, D, becomes D, F, A, C, and is called the subdominant sixth; and continuity being thus established, the harmony then passes on normally to the bottom of the scale, every successive chord being linked to the preceding note by a note in common. [Scientific Basis and Build of Music, page 49]

In the progression - that is, the going on from one to another - of these triplets in harmonizing the octave scale ascending, Nature goes on normally till we come to the passage from the sixth to the seventh note of the scale, whose two chords have no note in common, and a new step has to be taken to link them together. And here the true way is to follow the method of Nature in the birthplace of chords.1 The root of the subdominant chord, to which the sixth of the octave scale belongs, which then becomes a 4-note chord, and is called the dominant seventh; F, the root of the subdominant F, A, C, is added to G, B, D, the notes of the dominant, which then becomes G, B, D, F; the two chords have now a note in common, and can pass on to the end of the octave scale normally. In going down the octave scale with harmony, the passage from the seventh to the sixth, where this break exists, meets us at the very second step; but following Nature's method again, the top of the dominant goes over to the root of the subdominant, and F, A, C, which has no note in common with G, B, D, becomes D, F, A, C, and is called the subdominant sixth; and continuity being thus established, the harmony then passes on normally to the bottom of the scale, every successive chord being linked to the preceding note by a note in common. [Scientific Basis and Build of Music, page 49]

In the following treatise of our author Nature will be found beckoning us toward the Chromatic in an exceedingly interesting way; and the exhibition of the Chromatic as a system, and an exceedingly important system, of chords and progressions is a monument to the genius of D. C. Ramsay. [Scientific Basis and Build of Music, page 49]

But, as the subdominant sixth and dominant seventh suggest that the chromatic chord should be a 4-note chord, we must find out how Nature completes this diatonic chromatic triad and makes it a 4-note chord, and that according to its own intrinsic character as of minor thirds. Nature has always a rationale in her operations which it is ever delightful to discover. Wedged in between the minor dominant and the major subdominant, this triad, B D F, has already B, the top of the dominant minor, for its root; and F, the root of the subdominant major, for its top; and its middle is the mysterious D which, in its two positions as root of the minor subdominant and top of the major dominant, stands at the two extremes of the whole twofold diatonic key, bounding and embracing all; and which in its two degrees as D26 2/3 and D27 claims kindred with both minor and major modes of the twofold key system. Surely this Janus-faced D, looking this way toward the minor and that way to the major, seems to say, "the complement of this chord, of which I am the heart, is not far to seek nor hard to find on either side." It has already B in common with the minor dominant; the very next step is to the middle of this chord, G. Roots and tops of chords may not be altered, but middles may with impunity be flattened or sharpened as occasion may require. No two of them in succession in the chord-scale have the same structure; the chromatic triad, in claiming this middle, claims it sharpened, for it must have [Scientific Basis and Build of Music, page 54]

Image Page 56


In the above line it will be readily observed that these three chromatic chords, having each of their intervals a minor third, involve, as necessary elements of their build, every one of the twelve semitones at one point or another of the line. This is a second witness to the legitimacy of the chromatic scale of twelve semitones. We have our first witness to the same in the evolution of the semitones progressively in the course of the modulations by which, in growth-like continuity, Nature links the successive keys; whether developed upward, as is the natural way of the majors; or downward, as in the natural way of the minors; or half upward and half downward, which is an expedient in order to simplify the signatures. In whichever direction the modulation is effected, one note is always divided, and must, true to Nature, be signified by placing a sharp or a , as the case may be, to the 4-comma altered interval, and this always leaves a 5-comma interval to occupy the place to which Nature has assigned such interval in the original scale. When this operation has been twelve times performed, we have the chromatic scale of twelve semitones. Thus by two witnesses the thing is established. By further examination of these chromatic chords we find other interesting features beside their witness to the twelve semitones of the octave. [Scientific Basis and Build of Music, page 56]

dividing itself by 2 or 3 or 5, etc., up through the whole geometrical series of numbers, not keeping fixed at one thing; but while the whole length is vibrating the fundamental partial, it keeps shifting the still nodes along its length, and sometimes longer and sometimes shorter segments are sounding the other partials which clothe the chief sound. It has been commonly said that "a musical sound is composed of three sounds," for every ear is capable of hearing these three, and with a little attention a few more than these; but many will be startled when told that there are twenty-five sounds in that sound. Eighteen of them are simply the octaves of the other seven, all of these seven except one having one or more octaves in the sound. Four of the seven also are very feeble, the one which has no octave being the feeblest of all. Two of the other three are so distinctly audible along with the chief partial that they gave rise to the saying we have quoted about a musical sound being composed of three sounds.1 If the three most pronounced partials were equally developed in one sound, it could not be called one sound - it would decidedly be a chord; and when in the system they do become developed, they form a chord; but in the one sound they, the partials, having fewer and fewer octaves to strengthen them, fade away in the perspective of sound. The sharp seventh, which in the developed system has only one place, not coming into existence until the sixth octave of the genesis, is by far the feeblest of all the partials, and Nature did well to appoint it so. These harmonics are also sometimes called "overtones," because they are higher than the fundamental one, which is the sound among the sounds, as the Bible is the book among books. [Scientific Basis and Build of Music, page 59]

Now we come to a remarkable arrangement of Nature. The minor does not grow in the same way out of this third chord's top. Two features come before us: first the minor chord grows out of the major, but it is taken not from the top but from the middle, from a rib out of his side. B, the middle of the major dominant chord; B, the last-born of the major genesis; B is the point of departure in the outgrowth of the minor mode. The feminine is a lateral growth from the masculine. Another feature: it grows downward, like a drooping ash or willow. Its first generated chord is its dominant, and its last is its subdominant. Its middle chord, like the middle one of the major, is its tonic. Still further, it is generated by division, not multiplication; B45 is divided by 3 and by 5 for the root and middle of this highest chord, E and G. E15 is divided by 3 and 5 for the root and middle of the tonic chord, A and C. A5 is divided by 3 and 5 for the root and middle of the lowest chord, D and F. Thus we have the whole generation of the elements of music, six generations of harmony, like the six days of creation. Up to this point the whole process and aspect is inverse; growing from a middle; growing downward; growing by division;- while the major is growing from the top; growing upward; growing by multiplication. But here the inverse aspect ends. The generating primes of the major are 3 and 5; 3 and 5 are also the generating primes of the minor. In this essential phase of their creation their comparison is direct, not inverse. [Scientific Basis and Build of Music, page 67]

Why do we compound? Because it produces variety, and variety is one of the aspects of the beautiful; Nature loves and abounds in variety, without violation of her unity. And further, all creation throbs with sympathy, one thing feeling and tending toward another, nothing content in isolation; and compound chords are chords reaching out after assimilation to an affiliation with other adjacent chords, that they may be able, through something in [Scientific Basis and Build of Music, page 70]

Helmholtz falls into a mistake when he says- "The system of scales and modes, and all the network of harmony founded on them, do not seem to rest on any immutable laws of Nature, but are due to the aesthetical principle which is constantly subject to change, according to the progressive development of taste." It is true, indeed, that the ear is the last judge; but the ear is to judge something which it does not create, but simply judges. Nature is the maker of music in its scales and modes. The styles of composition may vary with successive generations, and in the different nations of men; but the scientific basis of music is another thing. It is a thing, belonging to the aesthetic element of our being and our environment; it is under the idea of the beautiful, rather than the idea of the useful or the just; but all these various aspects of our relation to creation have their laws which underlie whatever changes may be fashionable at any period in our practice. If the clang-farbe of a musical tone, that is, its quality or timbre, depends on the number and comparative strength of the partial tones or harmonics of which it is composed, and this is considered to be the great discovery of Helmholtz, it cannot be that the scales and modes are at the caprice of the fickle and varied taste of times and individuals, for these partials are under Nature's mathematical usages, and quite beyond any taste for man's to change. It is these very partials or harmonics brought fully into view as a system, and they lead us back and back till they have brought us to the great all-prevading law of gravitation; it is these very partials, which clothe as an audible halo every musical sound, which constitute the musical system of sounds. [Scientific Basis and Build of Music, page 78]

as the savage state. The savage is the sunken state of man, consequent on falling away from God by distrust and disobedience, and the loss of paradisial converse with Him. We may presume that music in the beginning, when the first human pair sang out with unbroken voices the joy of their hearts, was in the scale to which mankind, risen and restored by God's mercy, have returned. Our last days are thus become like the first again; and the lost dominion of Nature has returned, in the Incarnate One, into the hands of mankind. [Scientific Basis and Build of Music, page 79]

"To say that I was surprised at what Mr. Keely has discovered would be saying very little indeed ... It would appear that there are three different spheres in which the laws of motion operate.
1 - The first is the one in which Nature plays her grand fugue on the silent harp of Pendulums. In one period of Nature's grand fugue, as illustrated by pendulums, there are 19 ratios in 25 circles of oscillations ranging over 6 octaves; but all in silence. [Scientific Basis and Build of Music, page 86]

2 - In the second sphere the tension of strings and other elastic bodies imbues them with forces operating upon the elastic air, producing vibrations quick enough to awaken sounds for the human ear. Here Nature plays on her tuneful harp the same grand fugue; from which everything in music is derived. [Scientific Basis and Build of Music, page 86]

musical vibrations in both acute and grave harmonics, generate a concentration of mighty action, an ever-outgoing of Nature's own power, so that she, by her own laws of vibratory motion, can reproduce and perpetually maintain outgoing power of action; and, again, play in perfect harmony her grand fugue with these tremendous all-resolving forces in that high and hidden and silent region in which Mr. Keely is experimenting. [Scientific Basis and Build of Music, page 87]

The sympathy of one thing with another, and of one part of a thing with another part of it, arises from the principle of unity. For example, a string requires to be uniform and homogenous to have harmonics producing a fine quality of tone by the sweet blendings of sympathy; if it be not so, the tone may be miserable ... You say you wish I were in touch with Mr. Keely; so do I myself ... I look upon numbers very much as being the language which tells out the doings of Nature. Mr. Keely begins with sounds, whose vibrations can be known and registered. I presume that the laws of ratio, position, duality, and continuity, all the laws which go to mould the plastic air by elastic bodies into the sweetness of music, as we find them operative in the low silence of oscillating pendulums, will also be found ruling and determining all in the high silence of interior vibrations which hold together or shake asunder the combinations which we call atoms and ultimate elements, but which may really be buildings of wondrous complexity occupying different ranges of place and purpose between the visible cosmos and Him who built and evermore buildeth all things. The same laws, though operating in different spheres, make the likenesses of things in motion greater than the differences. [Scientific Basis and Build of Music, page 87]

The scales march on following each other methodically, whether they be written with sharps or flats, and

"Not a step is out of tune, as the tides obey the moon."

The most natural, because the genetic, way to write the scales is to make the major scales all in sharps, after C, because the major genesis is upward in ratios ascending; and to make the minor scales all in flats, after A, because the minor genesis is downward in ratios descending. Let the young student, however, always keep in mind that the sharps and flats are simply marks to show how Nature, at whatever pitch we are taking the scales, is securely keeping them in the same form as when they are first generated; and in their birthplace no sharps or flats are needed. [Scientific Basis and Build of Music, page 90]

In the opening of the third measure the tune returns to its own key by striking the tonic. This case is a very simple illustration of how a composition will move with perfect naturalness in more keys than one, the keys so grow out of each other, and may either merely snatch a passing chord from a new key, or pass quite into it for a phrase or two, or for a whole measure, then return as naturally, either by a smooth and quiet or by a strongly contrasted turn, according to the chords between which the turn takes place. In such modulation there may or there may not be marked a sharp, , or , in the air itself; the note which Nature raises in the new key may occur in one of the other parts of the harmony. In Watchman it is A, the fourth, which is altered; from being it is made . The change which takes place in the sixth of the scale, which is C in Watchman, is only one comma, the ratio of 80 to 81, and it slips into the new key as if nothing had happened. No mark is placed to it, as the comma difference is never taken notice of, although it is really and regularly taking place, with all the precision of Nature, in every new key. It is, however, only the note which is altered four commas, which is marked by a sharp, , or , as the case may be. [Scientific Basis and Build of Music, page 94]

Subdominant - F, A, C E G, B, D - dominant


- and it is balanced between the two forces. If the effects of notes or chords depended solely on their ratios, then the effect of the subdominant, tonic, and dominant would have been alike, for these chords have exactly the same ratios. The centrifugal force of the notes of the dominant chord would take if away from the tonic chord; but Nature, in her skill to build and mix, has in the octave scale placed the middle of the dominant B under the root of the tonic C, and the top of the dominant D under the middle of the tonic E; so that these two rising notes are inevitably resolved into the tonic chord. The gravitating tendencies of the notes of the subdominant would take it also away from the tonic; but in the octave scale Nature has placed the middle of the subdominant A above the top of the tonic G, and the root of the subdominant F above the middle of the tonic E; so that these two falling notes also are inevitably resolved into the tonic chord. In this way two notes resolve to the center of the tonic, D upwards and F downwards; one to the top, A to G, and one to the root, B to C. Nature has thus placed the notes which have upward tendencies under the notes having downward tendencies; she has also related them by proximity, the distance from the one to the other being always either a semitone or the small tone of the ratio 9:10. [Scientific Basis and Build of Music, page 95]

"The three notes of the dominant chord resolve by each note going to the next note upward - G soars to A, B to C, D to E. The three notes of the subdominant resolve by each note going to the next note downward - C sinks to B, A to G, F to E. The two upper notes of the dominant resolve into the tonic chord according to the Laws of Proximity and Specific Levity; and the two lower notes of the subdominant resolve into the tonic chord according to the Laws of Proximity and Specific Gravity. And in this way Nature, in chord-resolution, has two strings to her bow." [Scientific Basis and Build of Music, page 96]

"Dividing the octave into twelve semitones is a near approach to the mathematical quantities, and this saves the musical artist from errors in tone - at least to any extent; but it does not save from errors in judgment. In the case of G#, for example, not one of the reasons given for the use of the sharp seventh in the minor scale is a correct one. A touch of nature makes the world akin, and a touch of the Law of Duality balances everything in music." [Scientific Basis and Build of Music, page 99]

Six Octaves required for the Birth of the Scale

EXPLANATION OF PLATES.
[BY THE EDITOR.]
"NATURE'S GRAND FUGUE."


THIS plate is a Pendulum illustration of the System of musical vibrations. The circular lines represent Octaves in music. The thick are the octave lines of the fundamental note; and the thin lines between them are lines of the other six notes of the octave. The notes are all on lines only, not lines and spaces. The black dots arranged in these lines are not notes, but pendulum oscillations, which have the same ratios in their slow way as the vibrations of sounding instruments in the much quicker region where they exist. The center circle is the Root of the System; it represents F1, the root of the subdominant chord; the second thick line is F2, its octave; and all the thick lines are the rising octaves of F, namely 4, 8, 16, 32, and 64. In the second octave on the fifth line are dots for the three oscillations which represent the note C3, the Fifth to F2, standing in the ratio of 3 to 2; and the corresponding lines in the four succeeding Octaves are the Octaves of C3, namely 6, 12, 24, and 48. On the third line in the third Octave are 5 dots, which are the 5 oscillations of a pendulum tuned to swing 5 to 4 of the F close below; and it represents A5, which is the Third of F4 among musical vibrations. On the first line in the fourth Octave are 9 dots. These again represent G9, which stands related to C3 as C3 stands to F1. On the seventh line of the same octave are 15 dots; these represent the vibrations of E15, which stands related to C3 as A5 stands to F1. On the sixth line of the fifth Octave are 27 dots, representing D27, which stands related to G9 as G9 stands to C3, and C3 also to F1; it is the Fifth to G. And last of all, on the fourth line of the sixth Octave are 45 dots, representing B45, which, lastly, stands related to G9 as E15 stands to C3, and A5 to F1; it is the Third to this third chord - G, B, D. The notes which arise in each octave coming outward from the center are repeated in a double number of dots in the following Octaves; A5 appears as 10, 20, and 40; G9 appears as 18 and 36; E15 appears as 30 and 60; D27 appears as 54; and last of all B45 only appears this once. This we have represented by pendulum oscillations, which we can follow with the eye, the three chords of the musical system, F, A, C; C, E, G; and G, B, D. C3 is from F1 multiplied by 3; G9 is from C3 multiplied by 3; these are the three Roots of the three Chords. Their Middles, that is their Thirds, are similarly developed; A is from F1 multiplied by 5; E15 is from C3 multiplied by 5; B45 is from G9 multiplied by 5. The primes 3 and 5 beget all the new notes, the Fifths and the Thirds; and the prime 2 repeats them all in Octaves to any extent. [Scientific Basis and Build of Music, page 102]

Nature does give us the chromatic scale of 12 semitones, but she does so by a very different process.
We have, however, to thank Euler, perhaps, for starting the genesis of the scale from F instead of C, which he does without assigning any reason for it, and, it seems without seeing the deep significance of it; and since he does this as a mere matter of course, it would be interesting to know if he had not seen F thus used by some other, it may be some obscure genius who had insight to discern, more than push to put forth his finding - a case in which the world has doubtless sometimes been a loser. - Editor. [Scientific Basis and Build of Music, page 108]

ratio of 5:8; three, 3:5; and one, 16:27. There are seven fifths - one in the ratio of 45:64; one, 27:40; and five, 2:3; and seven corresponding fourths - five in the ratio 3:4; one, 40:54; and one 32:45. These are the ratios of the intervals in their simplest expressions as given in the second outer space above the staff in the plate. In the outer space the intervals are given less exactly, but more appreciable, in commas. The ratios of the vibration-numbers of each interval in particular, counting from C24, are given in the inner space above the staff. These vibration-numbers, however, are not given in concert pitch of the notes, but as they arise in the low audible region into which we first come in the genesis from F1, in the usual way of this work. The ratios would be the same at concert pitch; Nature gives the numbers true at whatever pitch in the audible range, or in the low and high silences which lies out of earshot in our present mortal condition. [Scientific Basis and Build of Music, page 110]

DIATONIC RESOLUTIONS, SIMPLE AND COMPOUND.


In the major system, when the tonic chord follows the subdominant one, there is one semitonic progression to the middle of the tonic, and one note in common with the root, so these two chords are linked together in different ways. When the tonic chord follows the dominant one, there is one semitonic progression to the root of the tonic, and one note in common with its top, so these two chords also are linked together in two different ways. When the tonic chord follows the compound dominant, i.e., the dominant seventh, there are two semitonic progressions, one to the middle and one to the root, and one note in common with its top, so these two are linked together in the same two ways; but the semitonic progression being double gives this resolution great urgency. And now we come to the two chords, the subdominant and dominant, which have no note in common, and must, when they succeed each other, be helped to come together. Nature teaches us how this is to be done by a process of borrowing and lending which will establish between them a similar relationship to that which keeps the continuity of the other chords in succession. We have seen that the top of the subdominant and the root of the tonic are a note in common to these chords, and so the top of the tonic and the root of the dominant also are a note possessed in common by these two chords. In like manner in this disjunct part, when the dominant follows the subdominant, the root of the subdominant is lent to the top of the dominant, and thus they come to have a note in common. The top of the [Scientific Basis and Build of Music, page 111]

With perfect duality of response does resolution of chords go on in the minors. When the tonic chord follows the subdominant one, they have for their note in common A, i.e., in the key of A; and the middle of the subdominant moves by semitonic progression to the top of the tonic. When the tonic chord follows the dominant one, the top of the tonic and the root of dominant E is a note in common, and the top of the dominant goes by semitonic progression to the middle of the tonic. These simple chords are thus linked together exactly with the same degree of continuity as the simple chords of the major. When the tonic chord follows the compound subdominant, this compound chord, like the compound dominant in the major, has two semitonic progressions - one to the top and one to the middle of the tonic - and they have one note in common. When the compound dominant follows the subdominant, the root of the subdominant is lent to the top of the dominant, and thus a note in common is created, and the middle of the subdominant moves by semitonic progression to the root of the dominant. When the compound subdominant follows the dominant, the top is lent to the root of the subdominant, creating a note in common between them, and the root of the dominant goes to the middle of the subdominant in semitonic progression. This is the way of Nature. The unbroken continuity of her ways is perfectly illustrated in the linked sweetness and kinship of chords in a key; or when one key passes by modulation to another key; and that through all the chords and all the keys. We shall see wondrously more of this when we come to the study and contemplation of the Chromatic System of Chords. [Scientific Basis and Build of Music, page 112]

given to this scale, as the D of A minor would be a comma too low; it would make a 9-comma interval between D and E, the seventh and eighth, where the minor mode has an 8-comma one. So its two new notes are thus found in the relative and sub-relative majors. This is the way of their mutual providing in the region of the #s; the # seventh of the major is given to be the # second of the minor, and the comma-higher second of the sub-relative becomes the seventh of the minor; and then we have a true written representation of what Nature has done. [Scientific Basis and Build of Music, page 113]


The Octave being divided into 53 commas, the intervals are measured, as usual, by these, the large second having 9-commas, the medium second having 8, and the small second 5. These measures are then made each the radius by which to draw hemispheres showing the various and comparative areas of the seconds. The comparative areas of the thirds are shown by the hemispheres of the seconds which compose them facing each other in pairs. The comma-measures of the various thirds thus determined are then made the radii by which to draw the two hemispheres of the fifths. The areas of the three fifths are identical, as also the attitudes of their unequal hemispheres. The attitude of the six thirds, on the other hand, in their two kinds, being reversed in the upper and under halves of the scale, their attitude gives them the appearance of being attracted towards the center of the tonic; while the attitude of the three fifths is all upward in the major, and all downward in the minor; their attraction being towards the common center of the twelve scales which Nature has placed between the second of the major and the fourth of the minor, as seen in the two D's of the dual genetic scale, - the two modes being thus seen, as it were, revolving [Scientific Basis and Build of Music, page 113]


When Plate XIII. is divided up the middle of the column, as in Plate XIV., so as that one side may be slipped up a fifth, representing a new key one-fifth higher, its subdominant made to face the old tonic, the two new notes are then pictorially shown, the second being altered one comma and the seventh four commas. The key at this new and higher pitch is by Nature's unfailing care kept precisely in the same form as the first; and wherever the major scale is pitched, higher or lower, the form remains unaltered, all the intervals arranging themselves in the same order. The ear, and the voice obedient to it, carry Nature's measuring-rule in them, and the writing must use such marks as may truly represent this; hence the use of sharps, flats, and naturals; these, however, be it observed, are only marks in the writing; all is natural at any pitch in the scale itself. All this is equally true of the minor mode at various pitches. These two plates are only another and more pictorial way of showing what the stave and the signature are usually made to express. [Scientific Basis and Build of Music, page 114]


This is a twofold mathematical table of the masculine and feminine modes of the twelve scales, the so-called major and relative minor. The minor is set a minor third below the major in every pair, so that the figures in which they are the same may be beside each other; and in this arrangement, in the fourth column in which the figures of the major second stand over the minor fourth, is shown in each pair the sexual note, the minor being always a comma lower than the major. An index finger points to this distinctive note. The note, however, which is here seen as the distinction of the feminine mode, is found in the sixth of the preceding masculine scale in every case, except in the first, where the note is D26 2/3. D is the Fourth of the octave scale of A minor, and the Second of the octave scale of C major. It is only on this note that the two modes differ; the major Second and the minor Fourth are the sexual notes in which each is itself, and not the other. Down this column of seconds and fourths will be seen this sexual distinction through all the twelve scales, they being in this table wholly developed upward by sharps. The minor is always left this comma behind by the comma-advance of the major. The major A in the key of C is 40, but in the key of G it has been advanced to 40 1/2; while in the key of E, this relative minor to G, the A is still 40, a comma lower, and thus it is all the way through the relative scales. This note is found by her own downward genesis from B, the top of the feminine dominant. But it will be remembered that this same B is the middle of the dominant of the masculine, and so the whole feminine mode is seen to be not a terminal, but a lateral outgrowth from the masculine. Compare Plate II., where the whole twofold yet continuous genesis is seen. The mathematical numbers in which the vibration-ratios are expressed are not those of concert pitch, but those in which they appear in the genesis of the scale which begins from F1, for the sake of having the simplest expression of numbers; and it is this series of numbers which is used, for the most part, in this work. It must not be supposed, however, by the young student that there is any necessity for this arrangement. The unit from which to begin may be any number; it may, if he chooses, be the concert-pitch-number of F. But let him take good heed that when he has decided what his unit will be there is no more coming and going, no more choosing by him; Nature comes in [Scientific Basis and Build of Music, page 117]


This diagram shows pictorially the open in the spiral of the mathematical scales, in which, if written in sharps only, B# is seen a little, that is, a comma and the apotome minor, in advance of C, and as the first scale of the new cycle; for it is a violation of Nature's beautiful steps to call it a thirteenth scale of this order, since every scale in the order is 31 commas in advance of the preceding, whereas B# is only one comma and a small fraction in advance of C. If the scales be written in ♭s and #s for convenience of signature, then G# is seen a comma and apotome in advance of A♭; while the whole circle of keys advancing by fifths are each 31 commas in advance of the preceding. We may therefore cast utterly from us the idea of there being more than twelve mathematical scales, and view the so-called thirteenth as simply the first of a new round of the endless spiral of scales. There is, however, in this note a banner with the strange device, "Excelsior," for it leads us onward into ever-advancing regions of vibrations, and would at last bring us to the ultimate and invisible dynamic structure of the visible world. The tempered system of 12 keys, as in Fig. 1, is by causing the G# and A♭ to coalesce and be one, as the two D's are already literally one by Nature's own doing. [Scientific Basis and Build of Music, page 118]


This plate sets forth the essential duality of the musical system of vibrations. It is a remarkable fact that the numbers of the vibrations of the major mode are the numbers for the string proportions of the minor mode; and vice versa, the string proportions in the major are the numbers of the vibrations in the minor. We have, however, to see that we use the proper notes and numbers; we must know the secret of Nature. This secret rests in the duality of the notes, and begins from the two D's. The center of gravity of the musical system of vibrations is found in the comma space between the two D's as they are found in the genesis of the two modes. In these two D's the vibration number and string proportions are nearly identical. Starting from this point as the center of gravity in the [Scientific Basis and Build of Music, page 118]

dual system, as the strings are shortened the vibrations of course are more, and as the strings are lengthened the vibrations are fewer. This is household lore now; but the new insight and the deeply interesting order of Nature is that the major and the minor contain each other and respond to each other in this striking way; and while manifesting such diversity of character are so essentially one. [Scientific Basis and Build of Music,page 119]

Fig. 3 illustrates the way Nature teaches us by example how to compound so as to enable chords that are separated by the intervention of others to pass to each other. In the middle of the chord scale Nature gives the root of the one chord to the top of the other, and the top of the one to the root of the other; in compounding we are taught by this example to do the same, and the top of the separated dominant is given to the root of the [Scientific Basis and Build of Music, page 120]


Jesus
Part of your growth is to understand that if the technology that man develops offends or contradicts the Laws of Nature or the Universe, the Universe herself will make it right. So, along with technology, a chain reaction of events is established. If the thinking of the head alone is used to develop methods to meet challenges, the Universe is not being duly consulted, thus the implications rest upon the individual. There is Nature to answer to. If one uses the more harmonious thinking of the Heart in conjunction with the mental faculties, one becomes sensitized to far-reaching effects more keenly, thus avoiding typically unseen pitfalls. Until you feel that you can offer assurance that your technologic advances will not be misused and create more pain, you need to consult your Heart as a guide. By using your head, you engage in a realm of exercise that is an invitation to be altered by another’s thinking and perception of “need”. Are you willing to take on this responsibility? You must be more clever than I, if you answered in the affirmative. [Jesus, Good Heart]

See Also


Base 12
Laws
Laws of Nature
Natural Forces
Wheelwork of Nature
4.4 - Idle Wheels on Natures Machinery
11.04 - Nature Dances to a Natural Music Scale
15.19 - All forces in nature are mind forces

Created by Dale Pond. Last Modification: Saturday April 3, 2021 05:07:08 MDT by Dale Pond.