Sympathetic Vibratory Physics -It's a Musical Universe!
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Topic: Keely Information
Section: Harmonies of Tones part 1
Table of Contents to this Topic
Harmonies of Tones and Colours Through Evolution


The scheme endeavours to prove that the development of harmonics of sound and of colours is regulated by the law of Evolution as gained from the Scriptures-Youthful impressions regarding my great-uncle Dr. Darwin's views-My. cousin Charles Darwin's views touched upon-The scheme involves the belief that life developing from the Almighty is the general key to disentangle the intricacies of the Natural Sciences-A remark of Sir John Lubbork's quoted-The development of Numbers the stream of Time, the Sevens of Creation, &c., may eventually be proved by the same laws,



General remarks on harmonies of tones and colours-The scheme gained without technical knowledge-Brief explanation of how the laws gained-The development of numbers showed the "to and fro" in the development of sounds-Multequivalency of harmonies veering round, or advancing and retiring in musical clef-Before judging, close examination requested,


General remarks on the method of harmonies developing on all kinds of instruments, including the human voice-Much paradox, but yet the scheme will admit of clear demonstration-A musical note compared to a machine the motive power not of our creation-The imperfection of keyed instruments, from some notes acting two parts, attuned to the ideal of harmony within us-Macfarren quoted on the echoing power of a catedral attuning the Amen-Why music as an art precedes painting-Philosopher and mathematicians have only studied music to a certain point-Every key-note a nucleus, including the past, the present, and the future; no finally in any ultimate-The late Sir John Herschel's views on the musical gamut alluded to-The imperfection of keyed Instruments adpts them to our present powers=The laws will be seen to develope the twelve major and the twelve minor keys in unbroken sequence and in harmonious ratio; to gain them in geometric order a keyed instrument should be circular, the seven octaves interlacing in tones a lower and a higher series,


On colour developing by the same laws as musical harmonies- The physical properties of light and darkness briefly considered-If the laws are correctly gained, harmonies of tones and of colours will agree-Quotation from a lecture by Professor W. F. Barrett on the order of sonorous and luminous wave-lengths-Fountain of musical harmonies, E root of B; in colours yellow and ultra-violet, being tints and shades of white and black-All harmonies of sound and colour condense into a primo springing from the fountain-Multequivalency of tones and colours-Wdnsch's views nearly one hundred years ago-Clerk Maxwell's, Lord Rayleigh's, and Helmholtz's experiments on developing colours shown to agreee with the scheme-The sounds of the Falls of Niagara are in triplets or trinities-The Arabian system divides tones into thirds-Two trinities springing from unity apparently the germ of never-ending developments in tones and colours-Inequality of the equinoctial points; is the want of equilibrium the motive power of the entire universe-The double tones of keyed instruments, the meeting by fifths, the major and minor keys, so agree with the development of colours, that a correct eye would detect errors in a piece of coloured music-Numbers not entered upon, but develope by the same laws-Bass notes omitted in order to simplify the scheme,



The eighteen tones of keyed instruments veering round and in musical clef below, the twelve seen that develope major keys-The seven colours answer to the seven white notes-The use of the two chasms, the key-note C and its root F rising from the-A major key-note complete in itself, embracing the eighteen tones-In the whole process of harmony there is limit, every key-note having its point of rest, and yet it is illimitable.


The key-note C sounding from within itself its six tones to and from in trinities, the tones written as notes in musical clef-The trinities hereafter termed primaries and secondaries-The seven of each of the twelve key-notes developing their tones-The order in which the tones meet, avoiding consecutive fifths-Dissonance is not opposition or separation-The use of the chasmes and double tones is seen-The isolated fourths sound the twelve notes-Each double tone developes only one perfect major harmony, with the exception of F#-G'; F# as the key-tone sounds F# as E# and G' as the key-tone sounds B# as C' - The primaries of the twelve key-notes are shown to sound the same tones as the secondaries of each third harmony below, but in a different order-All harmonies are linked into each other,


Major key-notes developing by sevens veering round and advancing and retiring in musical clef-The use of the two poles F#-G' in tones and colours-Retroce from Chapter V. the tones in musical clef as notes, each note still sounding its tones, leading the ear to its harmony,


The twelve major scales-The term key-note employed in the ordinary sense of the musician-Thetwelve key-notes, with the six notes of each as they veer round in trinities, are written in musical clef, and the scales added-The reversal of the four and three of the key-note and its trinities in the seven of its scale-The twelve keys follow each other seven times through seven octaves linked into the lower and higher serie-Keys mingled-The modulating of scales,the eleventh notes rising to higher keys,


The chords-The fourteen roots of the chords of the twelve major Keys-A threefold major chord examined, fourfold with its octave-The seven of each key seen to have two chords and its scale one chord, thirty-six in all, forty-eight with octaves-The chords of the twelve keys as they follow in order are witten in musical clef-Colours seen to agree,


The twelve keys, their trinities, scales, are chords, rising seven times through seven octaves, each thirteenth note octave of the previous twelve and first of the rising twelve-Descending, ascending reversed-Keys mingled-The pendulograph alluded to,


The modulating gamut-One series of the twelve keys meeting by 6 fths through seven octaves-Keys not mingled-A table of the key-notes and their trinities thus meeting-The fourth not isolated - The table of the twelve scales meeting by 6fths-The twelve keys, trinities, scales, and chords thus meeting are writting in musical claf-The twelve meeting through seven circles, each circles representing the eighteen tones-The keys of C and G meeting, coloured-Retrospection of the various major developments.



The minor harmonies-The eighteen tones repeated veering round, and in musical clef below, showing thetwelve that develope minor harmonies-The twelve minor key-notes as gained from the twelve major,


The difference in the development of a major and a minor harmony-The twelve developing keys mingled-D' shown to be an imperfect minor harmony-E' taking B# as C' to be the same as D#-The intermediate tones of the seven white notes are coloured, showing gradual modulation-As in the diagram of the major, the secondaries are written in musical clef below the primaries, each minor primary sounding the secondaries of the third harmony below, but in a different order, and one tone rising higher,


MInor key-notes developing by sevens, veering round and in musical clef below-The use of the two poles D#-E' is seen,


The same laws, developing the minor scales, show that the ascending and descending scales vary from the harmony of the key-note and its trinities-Each key developing three harmonies -The tenth note of a minor scale modulates into a higher key,


The roots of the chords-The difference between a major and a minor chord-The chords of the twelve keys in musical clef, those of A coloured,


The twelve keys, trinities, scales, and chords are written in musical clef,


The twelve keys meeting by fifths, one series modulating through seven octaves, keys not mingled-The twelve veering round, the intermediate notes not coloured-The keys of A and E meeting the intermediate notes coloured in musical clef,


The twelve major and the twelve minor keys written in musical clef-First, the twelve major keys rising mingled as they develope seven times through seven octaves-Second, one series of the twelve meeting by gigths, keys not mingled-Third, the twelve minor keys mingle-Fourth, the twelve minor key-notes and their trinities, the keys meeting by fifths in the line above the keys of the ascending scales, and in the line below the keys of the descending scales,


Reflections on the scheme-Our present powers are as darkness groping after light-A quotation from Milton compared with the scheme-Major and minor chords respond to our feeling-Milton had a glimpse of the laws of Evolution-Evade the belief of the development of trinities from unity and the scheme falls into ruin,



On harmonical parallel between tone and colour-On the term of "rest," fifths, and the sympathy of music with life-Relativities of sounds and vibrations of strings-The doctrines of three pairs, six tones, and the law of "two and from"-The germ of the system propably to be found in the adaptability of numbers-Sudden death of Dr. Gauntlett,


Harmony expressed by pulsations, ebb and flow, stress and accent-Necessity of combining religious feeling with natural science in true music-Remarks on the new College of Music,



"The words of the Lord are pure wo???????silver tried in a furnace of earth, purified seven ??????.-Psa xiii. 6.

"Life, presence everywhere sublimely vast.
And endless for the future as the past."

THE following scheme endeavours to show that the development of the musical gamut and the colours of the rainbow are regulated by the same laws. I wish it to be clearly understood that I have gained the evolutions from the mysterious type of Life-a golden thread running throughout the Scriptures, from the first chapter of Genesis to the last of Revelations;-life developing around us and within us from the Almighty, who is its Eternal Fountain. My youthful impressions included the belief that the views of Dr. Darwin, my great-uncle, contradicted the teaching of the Scriptures, and I therefore avoided them altogether. Having endeavoured for years to again correctly the laws which develope Evolution, I suddenly discovered that I was working from Scripture on the same foundation which he had found in Creation; and as Creation and Revelation proceed from the same Author, I knew that they could not contradict cach other. It is considered by many that my cousin, Charles Darwin, gained his first ideas of Evolution from his grandfather's works; but I know from himself that he was ignorant of them, and that his theory of Evolution was arrived at by his close experiments and observations of the laws of creation alone. Only a few months since, after reading his work on "the Movement of Plants," published in 1881, and wishing to be certain that I had not an incorrect belief, I asked the following question-"Did you gain your views on Evolution by your wonderfully acute observations, ignorant of your grandfather's ideas?" The reply was, that he had done so entirely from his own observations.

It is my firm belief that, if a poweful intellect takes up the radical idea contained in the following pages, it will be found to be the directing force or general key-note which will gradually disentangle intricacies in all the natural sciences, and link, by the same mode of physical evolution, the past, the present, and the future.

I enter upon the subject with the deepest sense of my own inability to do justice in any measure to the grandeur of the topic; but I trust that my remarks my prove suggestive to others of far higher truths. They are the result of the leisure hours of nearly fifty years, during which the conviction has ver deepened, that "philosophy of the natural kind does but push man's ignorance father back," and that, in the concluding words of Sir John Lubbock's inaugural address to the British Association at York in 1881, "the great lesson which Science teches is, how little we yet know, and how much we have still to learn."

If health is still granted to me, and if an interest is created on the subject of these pages, I shall endeavour to explain by what means I gained the laws here described, and to enter upon the development of numbers as showing the stream of time ever failling into infinity, and gliding onwards; also the sevens in creation, with several other branches of the subject which are here untouched, or but briefly alluded to. It is my earnest desire that all may be closely examined. Indifferencewill grieve me, but even severe criticism will afford me pleasure, as proving that the subject is considered worthy of investigation.

The publication of this work has been unavoidably delayed for a year, and I now quote briefly from an address of Dr. C. W. Siemens, during the late meeting of the British Association at Southampton, as reported in the Times. I have strictly endeavoured to make my investigations according to his views of combining scientific knowledge with practical utility.

"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 other, who, with only commercial aims in view, did not aspire to further the object 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 phisical 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 question, 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 in minor bodies for the better prosecution of special object, the points of contact between the different branches of knowledge are ever multiplying, all tending to form part of a mighty tree-the tree of modern science." "In this short word energy we find all the efforts in Nature-energy 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."

Bedwyn Lodge,
Sandown, Isle of Wight,
April, 1883




"On crazy fabrics III-timed cost bestowed
No purpose answers, when discretion bids
To pull them down, and wait a season fit
To build anew."

ALTHOUGH I am confident that the foundation on which I have been building is firm, and will never fail. I also feel that there are probably errors in raising the superstructure. "Thoughtful deduction must ultimately harmonise; like light, they will shine by their own effulgence." "If, however, we determine that we will not receive any truth against which objections can be raised, we shall remain in a state of universal scepticism, for against truths of every description objections have been and may be suggested." Appearances are often contrary to facts-"the straight stick looks crooked in the tide." And the question has always in favour of the truth of any assertion.

It seems desirable that I should briefly state my entire ignorance of natural science, and that what I do know has been gained without technical knowledge, with the determination that imagination should not interfere with strict investigation.

I had for a long time studied the development of the harmonics of colour, and believed that I had gained them dorrectly: but I saw no way of proving this. The thought occurred-Why not test the laws in musical harmonies? I wrote down the development of the seven major keys of the white notes in keyed instruments. I was perplexed by the movement as of "to and fro," but the development of numbers explained this point, and I found that the method of development in colours, tones, and numbers agreed. I remembered the keys with sharps, but had forgotten that B' belonged to the key of F, and here I thought that the laws failed. But I found by reference that all were correct, the eighth being the first of a higher series, the laws having enabled me to distinguish between flats and sharps, whether veering round, or advancing and retreating in musical clef. I next tried the major keys which develope flats, and I thought that G' would develope a perfect harmony, but found that it must be F=, and that in this one harmony E= most be used in place of F=, on reference, I found that thus the twelve keys developed correctly in succession, the thirteenth being the octave, or first of a higher series.

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=.

In a few remarks on "Tones and Colours," inserted in the Athenaum of February 24, 1877, I alluded to the great loss I had sustained by the sudden death of Dr. Gauntlett. I often retrace with grateful remembrance the kind manner in which he examined this scheme when it was but crude and imperfect; with a very capacious intellect, he had a warm and generous heart, causing him to think over with candour any new ideas placed before him. He was of the greatest use to me, by corroborating the point which I had gained. I remarked to him one day, "I find that, of the double tones, F= is key-note and G' a root." He replied, "You must have a right foundation to work upon, or you would never have ascertained the necessity of the two poles; you have gained the double tones correctly, and the development of harmonies withiut limit. On this point I have always felt the failure of the laws followed by the musician."

I add quotation from the first letter I received from him. "I have read the MS., and there are some very curious coincidences-exceedingly so-here and there. Whether it will clear out into a demonstrable system, I cannot say at present. If we can get our harmonical start, I think all will come out plainly, for there is so much that is consistent in sequence. There has been nothing at all like it at present, and some of it squares singularly with the old Greek notions." "I am more than half a disciple of your theory of the six tones, and am inclined to imagine that it would do away with much complication, and keep the mind bent on a smaller circle. We can only see things in patches, and hear in trinities, and every single sound is a trinity."

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 graduation, 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.

I also wish to explain that I have, in several instances, interwoven sentences from different authors, and other remarks of the late Dr. Gauntlett; but as they are not verbatim they are not always noticed as quotations.

I am aware that I have entered upon many points well known to musicians; as I had to learn, so I wished to explain to those who have not studied the science. There are many interesting points on which I have not entered. I ask any who look into the subject to suspend their judgment until they have closely examined it from beginning to end.



"In every art or science, we expect accuracy according to the nature of the subject-matter, and the end which it is proposed to atain."

This scheme is grounded upon the belief that a key has been gained which unites grandeur with simplicity, the laws of which are wonderfully simple, although most complex in their working, explaining all the intricacies which arise in the developments of harmonies.

There is much paradox, and the scheme differs so much from any hitherto published on the subject, that I am aware that, if any link can be found to be wanting in the chain, the defect will immediately be seized upon. I believe, however, that it will be found to admit of clear demonstration. Anyone who has studied the subject knows the difficulties that arise on all sides. In the problem before us, we have to reduce large fields of thought to certain elementary truths. In my endeavour to do this, I have been entirely dependent upon the discovery of the laws of Nature, as my ear is not musical enough to assist me in the matter. "All mysteries are either truths concealing deeper truths, or errors concealing deeper errors," and thus, as the mysteries unfold, truth or error will show itself in a gradually clearer light. The great mysteries of music lies in its infinite resource; it teems with subtle elements and strange analogies. A musical note may be compared to a machine, we touch the spring and set the machine in motion, but the complex machinery exists beforehand, quite independent of our will; the motive power is not of our creation, and the laws on which its operation depends are superior to our control. The complex work of harmony is governed by the laws which are originated by the Creator; every note performs what He has willed, and in tracing these laws let us not be indifferent about their Author, but ever bear in mind that the source or fountain of the life and activity of harmonies aries from the Power who created the machine, and who knows how it will act. Let us also remember that we understand this machine but partially, and govern it but imperfectly, as indeed the finite can only, in a small measure, grasp the Infinite; and in any study of the natural sciences, as we progress, we find that "hills peep o'er hills, and alps o'er alpes arise." As regards keyed instruments. it appears that the effect of those notes which act two parts, such as C# and D', is rectified in some way so as to be perfectly attuned to the ideal of harmony within us. Again, the "Amen" sung by the choir in a Cathedral may not be in accurate tune, but if nearly the correct intonation in sounded, after travelling along the aisles, the chords always rethrn to the ear in perfect harmony, because the natural laws of music, assisted by the echoing power of the building, have attuned them to the perfect harmonical triad. If the "Amen" be too much out of tune, these laws decline to interfere, and there is no such helpful resonance.* Here we see why music, as a science takes the priority of painting; for if music is good, it is perfect 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 resource. 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 parts, have only studied the subject of musical sounds up to a certain point, and have then left. it. The musician
*See remarks on the womderful power of the ear in adjusting defect of intonation in Macfarren's Lectures Harmony, No. II. - must take the chromatic scale-not as it exists in Nature, for that offered by the mathematician, without the ordinary compensation of conventional theory, is of no use to the parctical musician. 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 consists 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 tones 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 Herchel studied this subject; and it was his opinion that there was some principle in the science of music which had yet to be discovered.

I think it will be seen that most of the difficulties in the rules of harmony arise from not taking the key-note, with the six tones which it develope from itself, as guiding the ear, first to the six notes of its harmony, and then to the key-note which becomes the leader of the scale. In the study of the natural gamut, the artificial system must not be mixed up. The wonders of Nature's laws in the developments of harmonies, consists in the beautiful adaption of keyes 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 large 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 instruments, including that most perfect of all-the human voice.

If the laws which I shall endeavour to esplain develope the twelve major harmonies, with each note in succession expanding its six tones from within itself; and if each of these is found to be a lower development, which leads the ear to a corresponding higher expansion of the twelve major key-notes, and the six tones of each ascending and descending in an unbroken sequence from any twelve consecutively, the thirteenth being the octave of the first, which commences a higher or a lower series; and if the twelve minor harmonies are also gained by the same laws from their twelve relative key-notes (the thirteenth again being octave): if, again, all other notes are shown to be but higher or lower repetitions of these twenty-four harmonies-may we not consider the probles as in some measure solved? especially as the harmonies proceed in geometric as well as harmonical ratio, and an accurate parallel can be traced between the development of notes and colours, which latter correspond with all the intricacies of harmonic sounds.

In the diagrams the circle are not drawn as interlacing into each other, from the difficulty of representing them accurately as rising spirally in geometric progression. If we endeavour to realise the development of harmonies, both in geometric order, and at the same time advancing and retiring, as in musical clef, we must imagine a musician having the physical power of striking all the notes on a circular keyed instrument of seven octaves, linked to a lower series of seven octaves, and a corresponding series of seven higher. But in fact the depth of the lower series, and the height of the higher, are alike unfathomable to our present powers. C, the first note of the seven octaves, sounds the four lowest tones, F, G, A, B of the lower series; and B, the last and highest note of the seven octaves, sounds in its harmony C# and D# of thehigher series of sevens.
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