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"Harmony is the greatest of virtues." [Masaru Emoto]

"Harmony is the simultaneous vibration of two or more bodies whose harmonics do not produce discords, and whose fundamental pitches are harmonies of the lowest pitch, or are a unison with the resultant notes or overtones, or undertones, of any two or more of them." [Keely]

All abnormal discordant aggregations in these resonating convolutions produce differentiation to concordant transmission; and according as these differentiations exist in volume, so the transmissions are discordantly transferred, producing antagonism to pure physical action. Thus, in motor ataxy, a differentiation of the minor thirds of the posterior parietal lobule produces the same condition between the retractors and extendors of the leg and foot, and thus the control of the proper movements is lost through this differentiation. The same truth can be universally applied to any of the cerebral convolutions that are in a state of differential harmony to the mass of immediate cerebral surroundings. Taking the cerebral condition of the whole mass as one, it is subservient to one general head centre; although as many neutrals are represented as there are convolutions. The introductory minors are controlled by the molecular; the next progressive third by the atomic; and the high third by the etheric. All these progressive links have their positive, negative, and neutral position. When we take into consideration the structural condition of the human brain, we ought not to be bewildered by the infinite variety of its sympathetic impulses, inasmuch as it unerringly proves the true philosophy that the mass-chords of such structures are governed by vibratory etheric flows. There is no structure whatever - animal, vegetable, or mineral - that is not built up from the cosmic ether. Certain orders of attractive vibration produce certain orders of structure; thus the infinite variety of effects; more especially in the cerebral organs. Discordance cannot exist in the molecule proper. Discordance in any mass is the result of differentiated groups induced by antagonistic chords, and any differentiated mass can be brought to a condition of harmony or equation by proper chord media, and an equated sympathy produced whether the mass be metal or brain. [Vibratory Physics - The Connecting Link between Mind and Matter]

"Harmony is health. Discord is disease." [Keely]


The action of Nature's sympathetic flows regulates the differential oscillatory range of motion of the planetary masses as regards their approach toward and recession from each other. These flows may also be compared to the flow of the magnet which permeates the field, existing between the molecules themselves, sensitising the combined neutral centres of the molecules without disturbing, in the least, the visible molecular mass itself. In the planetary masses - balanced as it were in the scales of universal space, floating like soap-bubbles in a field of atmospheric air, the concentration of these sympathetic streams evolves the universal power which moves them in their oscillating range of motion to and from each other. This sympathetic triple stream focalises and defocalises on the neutrals of all such masses polarising and depolarising, positive and negative action, planetary rotation, etc., etc.. It is thus that all the conditions governing light, heat, life, vegetation, motion, are all derived from the velocity of the positive and negative interchange of celestial sympathy with the terrestrial.

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]

"In setting the conditions of molecular sympathetic transmission by wire," writes Keely, "the same law calls for the harmonious adjustment of the thirds, to produce a non-intermittent flow of sympathy. Intermission means failure here. That differential molecular volume is required of sympathetic flow, seems at first sight to controvert the very law established by the great Creator, which constitutes harmony, a paradoxical position which has heretofore misled physicists who have propounded and set forth most erroneous doctrines, because they have accepted the introductory conditions, discarding their sympathetic surroundings. The volume of the neutral center of the earth is of no more magnitude than the one of a molecule, the sympathetic condition of one can be reached in the same time as the other by its coincident chord." Keely has ... attained the transmission of the etheric current in the same manner as the electric current with this one notable difference, that, in order to show insulation to the skeptical, he passes the etheric current, through blocks of glass in running his vibratory devices. [Snell Manuscript - The Book, page 2]

In all molecular dissociation or disintegration of both simple and compound elements, whether gaseous or solid, a stream of vibratory antagonistic thirds, sixths, or ninths, on their chord mass will compel progressive subdivisions. In the disintegration of water the instrument is set on thirds, sixths, and ninths, to get the best effects. These triple conditions are focalized on the neutral center of said instrument so as to induce perfect harmony or concordance to the chord note of the mass chord of the instruments full combination, after which the diatonic and the enharmonic scale located at the top of the instrument, or ring, is thoroughly harmonized with the scale of ninths which is placed at the base of the vibratory transmitter with the telephone head. The next step is to disturb the harmony on the concentrative thirds, between the transmitter and the disintegrator. This is done by rotating the siren so as to induce a sympathetic communication along the nodal transmitter, or wire, that associates the two instruments. When the note of the siren becomes concordant to the neutral center of the disintegrator, the highest order of sympathetic communication is established. It is now necessary to operate the transferable vibratory negatizer or negative accelerator, which is seated in the center of the diatonic and enharmonic ring, at the top of the disintegrator, and complete disintegration will follow (from the antagonisms induced on the concordants by said adjunct) in triple progression, thus: First thirds: Molecular dissociation resolving the water into a gaseous compound of hydrogen and oxygen. Second: sixths, resolving the hydrogen and oxygen into a new element by second order of dissociation, producing what I call low atomic ether. Third: ninths, the low atomic ether resolved into a new element, which I denominate high or second atomic harmonic. All these transmissions being simultaneous on the disturbance of sympathetic equilibrium by said negative accelerator. [Snell Manuscript - The Book, page 4]

"I find in my researches, as to the condition of molecules under vibration, that discordance cannot exist in the molecule proper; and that it is the highest and most perfect structural condition that exists; providing that all the progressive orders are the same. Discordance in any mass is the result of differentiated groups, induced by antagonistic chords, and the flight or motions of such, when intensified by sound, are very tortuous and zigzag; but when free of this differentiation are in straight lines. Tortuous lines denote discord, or pain; straight lines denote harmony, or pleasure. Any differentiated mass can be brought to a condition of harmony, or equation, by proper media, and an equated sympathy produced." [Keely and His Discoveries, Chapter VII]


"Discord is disease; harmony is health and every person starts from one or the other of these two bases. The word truth is applied to both, but if there was not any discord, there would be no need of harmony, for before there was discord all was quiet. So that it is a truth that there is such a state as discord in the mind, but the discord is in us and not in the thing spoken of. The discord is not in the tune but in those that hear it, for if there were no one to hear it, there would be no discord." [Quimby]

"For the joy of living, in an material experience, is dependent upon the peace of mind - not indolence but activative peace, activative harmony. Though the entity has seen and has known and touched much dis-harmony; the desire for harmony reaches almost to that which is sought by the musician, in bringing about the arousal of the emotions ... which answer to the chords within the body; whether in movements of the dance, or arousal of emotions for the celestial or terrestrial activity in the emotions." [Cayce (880-1)]

"Contentment, peace, harmony, glory, love, beauty, is from WITHIN; and is as a growth that makes for that activity, that expression, that which will bring the growth, the understanding, the environments, the necessary influences." [Cayce 165-21]

"Know that all comes to him who puts his trust in the all-powerful influence of love and harmony, the real poem of life, and then works like thunder for same!" [Cayce (2337-1)]

"Do you know that our soul is composed of harmony?" [Leonardo da Vinci]

Christ Returns - Speaks His Truth
"I was brought to a realization of the INFINITE POWER of the 'Intelligent Creativity' ever active within creation, maintaining order, co-operation, harmony, daily productivity, unequalled by man anywhere, at any time." [Christ Returns - Speaks His Truth, Letter 1, page 15]

"Creation is the product of PRIMARY IMPULSES working individually and together - making impressions upon the other, fulfilling inbuilt needs imprinted within consciousness - these needs being, at the outset to increase and experience self-expression leading to further separation then - to restore a sense of inner security and comfort - to be re-united within the harmony of UNIVERSAL CONSCIOUSNESS. Out of this driving force for a re-united harmony of being, came the male-female drive for re-union to recapture the bliss which is buried in the soul consciousness." [Christ Returns - Speaks His Truth, Letter 5, page 23]

The face of BONDING drags, draws, attracts, demands, pulls, buys, grabs, clutches, clings to the people and possessions it craves. This IMPULSE creates an illusion of security in togetherness and possessions. It is the 'tool' of 'MOTHER CONSCIOUSNESS' inspiring the building of families, communities and nations. It can be productive of beauty, joy, harmony and love. It can also wreck lives and destroy communities when it is 'Ego' driven. The face of REJECTION repels, thrusts aside, pushes away, evades, everything - people, animals, possessions it does not want. Thus the IMPULSE of REJECTION creates an illusion of privacy and security. [Christ Returns - Speaks His Truth, Letter 5, page 25]

Mary Baker Eddy
"Harmony is produced by its Principle, is controlled by it and abides with it. Divine Principle is the Life of man. Man's happiness is not, therefore, at the disposal of physical sense. Truth is not contaminated by error. Harmony in man is as beautiful as in music, and discord is unnatural, unreal.

"The science of music governs tones. If mortals caught harmony through material sense, they would lose harmony, if time or accident robbed them of material sense. To be master of chords and discords, the science of music must be understood. Left to the decisions of material sense, music is liable to be misapprehended and lost in confusion. So man, not understanding the Science of being, - thrusting aside his divine Principle as incomprehensible, - is abandoned to conjectures, left in the hands of ignorance, placed at the disposal of illusions, subjected to material sense which is discord. A discontented, discordant mortal is no more a man than discord is music." [Mary Baker Eddy; Science and Health with Key to the Scriptures. 1971]

R. A. Schwaller de Lubicz
"Proportion belongs to geometry and harmony, measurement to the object and to arithmetic; and one necessitates the other. Proportion is the comparison of sizes; harmony is the relationship to measures; geometry is the function of numbers." [R. A. Schwaller de Lubicz, The Temple in Man, page 61]

"In fact, each of these individual members of the vegetable kingdom belongs to a genus, and this genus to a family; and these families belong to an original "lineage." At the head of this lineage is a Neter, a "Principle" synthesizing all the characteristics of this lineage; its number, its rhythm, its classification in the general harmony." [R. A. Schwaller de Lubicz, The Temple in Man, page 63]

Lydian Chromatic Concept
"The notion of chord/scale unity as the logical approach to the vertical manifestation of harmony was simply overlooked by classical Western theorists. The understanding that the term HARMONY means UNITY, and already complete VERTICAL ONENESS of elements existing in the momentary NOW above time was either missed or dismissed by the founding fathers of Western classical music theory." [Lydian Chromatic Concept, p. 222]

"Harmony is the law of life, discord its shadow; whence springs suffering, the teacher, the awakener of consciousness." [Blavatsky's Gem of the Day]

"Since Savart and Chladni and Helmholtz and Tyndal, and others, have studied the notes of our diatonic scale by the aid of such instruments as mechanical art has put into the hands of science in these last days, we have come to have a much more perfect understanding of music in its acoustical domain, and have been given to behold the beautiful mathematical measurements which Nature has applied in the marshalling of this host of the lower heavens; and which may suggest similar, though grander, and probably more complicated rhythms and harmonies in the astral heavens far off." [Scientific Basis and Build of Music, page 21]

"centrifugal force. A third note produced by the prime 5 is derived from the note produced by the first power of 3, and this note by the first power of 5 having being slightly acted on by the force of gravity, and the first power of 5 having only a little centrifugal force, the result is that this note E in the scale of C, derived from the first power of 3 by the prime 5, is balanced between the two forces. It is the only note in the system which in the octave scale has not a large interval on the one side of it nor on the other, and consequently it is the only note which attracts and is attracted by two notes from proximity. Thus it is that the musical system is composed of three notes having specific gravity and three having specific levity or bouyancy, and one note, E, the center of the tonic chord, balanced between these two forces. As the attractions of notes from proximity take place when the notes with downward tendency meet the note with upward tendency, had the notes been animated by only one of these forces there could have been no system of resolutions of the notes either in melody or harmony; they would all have been by gravity weighing it downwards, or by levity soaring upwards." [Scientific Basis and Build of Music, page 28]

The law of gravitation is the law of Music as well as of Astronomy. The cycles of the distances, that is the intervals, in Music correspond to the cycles of the periods in Astronomy. In Astronomy the distances and quantities of matter are primary, and determine the periods; in Music the periods and quantities are primary, and determine the distances or intervals. In Astronomy the distances are commensurable; in Music the periods are commensurable. In Astronomy the periods are incommensurable; in Music the distances or intervals are incommensurable. In Astronomy, because the simplicity is not in the periods, the conjunctions are very few at one time; in Music, because the simplicity is in the periods, the conjunctions are very many at one time. And herein lies in the one case the harmony and permanence of the solar system, and in the other case the harmony and beauty of the musical system. The periods and distances in Astronomy and Music are inversely related. [Scientific Basis and Build of Music, page 30]

When the major scale has been generated, with its three chords, the subdominant, tonic, and dominant, by the primary mathematical ratios, it consists of forms and orders which in themselves are adapted to give outgrowth to other forms and orders by the law of duality and other laws. All the elements, orders, combinations, and progressions in music are the products of natural laws. The law of Ratio gives quantities, form, and organic structure. The law of Duality gives symmetry, producing the minor mode in response to the major in all that belongs to it. The laws of Permutations and Combinations give orders and rhythms to the elements. The law of Affinity gives continuity; continuity gives unity; and unity gives the sweetness of harmony. The law of Position gives the notes and chords their specific levities and gravities; and these two tendencies, the one upward and the other downward, constitute the vital principle of music. This is the spiritual constitution of music which the Peter Bell mathematicians have failed to discern: [Scientific Basis and Build of Music, page 37]

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]

Moreover, it is only from one to five, that is from C to G in ascending, which is its proper direction in the genesis, that the major in being harmonized does not admit of minor chords, but if we descend this same natural major scale of the fifth from five to one, that is from G to C, the first chord is C E G; the next chord is F A C; if this is succeeded by the minor chord A C E, there are two notes in common and one semitonic progression, as very facile step in harmony; and the following two notes are most naturally harmonized as minor chords. So modulation into the minor, even in this major scale, is very easy in descending, which is the proper direction of the minor genesis.2 In a similar way, it is only from five to one, that is from E to A in descending, which is its proper genetic direction, that the minor in being harmonized does not admit of major chords; but if we ascend this same minor scale of the fifth from one to five, the first chord is A C E, the next is E G B, and if this chord be followed by the major C E G, there are here again two notes in common and one semitonic progression; and the two notes following are then most naturally harmonized as major chords. So modulation into the major, even in this minor scale, is very natural and easy in ascending, which is the proper direction of the major genesis.3 The dominant minor and the tonic major are, like the subdominant major and the tonic minor, very intimately related in having two notes in common and one semitonic progression. [Scientific Basis and Build of Music, page 65]

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]

Chords in a harmony are not at liberty to succeed each other in the way that single notes in a melody may. The notes in a melody may succeed in seconds, or they may succeed in larger intervals, any interval in the octave, even sometimes very effectively there may be a leap or fall of a whole octave. Chords cannot follow each other in this free way; they are under law, and must succeed accordingly. Their law is that they must be linked together either by having something in common in their elements, or have small intervals, semitonic progressions, between them. The former way, by notes in common, is the most usual way in diatonic succession of chords, the latter way, by semitonic progression, is a chief feature and charm in chromatic succession; but both in diatonic and chromatic progression of chords in harmony, notes in common and semitonic progression are usually found together. [Scientific Basis and Build of Music, page 68]

the excess of the vibrations of the one note over the other makes one or more sounds which are called "grave harmonics;" e.g., in the interval of the fifth, in the ratio of 2:3, the excess of 3 over 2 is 1, so the grave harmonic is an octave below the lowest of the two notes, that is, the ratio of 1:2. This reinforces the lowest note, 2, and gives it a solid effect. In this way the octave is incorporated into the fifth, and unity with variety is combined with the law of continuity at the very threshold of harmony. In 32 of the 42 intervals the grave harmonics are notes which belong to the natural scale. In the 10 remaining intervals which have not the exact number of vibrations found anywhere in the natural scale, 6 of them are from the number 7, thus - 7, 7, 7, 21, 21, 35; the remaining 4 are from 11, 13, 13, and 19. [Scientific Basis and Build of Music, page 77]

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]

circumstances. And if we may add D to the subdominant chord of d F A C, so we may also, in other circumstances, add the subdominant chord as harmony to D, thus - D f a c, and no discord occur. There is only the interval of a second between F and G in this dominant 9th, and only an interval of a second between C and D in this subdominant 6th; a second standing alone is a discordant interval, as a poison by itself may kill; but as a poison by the processes of nature in chemistry compounded with something else may be an excellent medicine, so may a second when mixed and compounded with something else in music become an excellent harmony. Music is a great apothecary, skillful in compounds. [Scientific Basis and Build of Music, page 81]

The effects of different positions of chords. The first position is clear and solid; the second is light and pretty. The notes which have the most varied effect in a stream of harmony are the upper and under notes, the edges of the stream; the two outlines determine the effect:-


[Scientific Basis and Build of Music, page 84]

In respect of harmony, the natural scale of five notes is like the scale of man's five senses; as the other notes can be compounded so as to form the octave of harmony, so sensation is joined by reflection, and new elements of knowledge come into existence in the process of reasoning. But the knowledge we have in our logical deductions is knowledge on different terms from sensation, which is intuitive; though if the logical process be rightly done, it is knowledge as certainly as the compound chords of the octave scale are harmony, quite as much, and a little more, perhaps, though on more complex terms, as that of the five notes of the natural scale. [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]

When the chords follow each other placed in such a way as to bring the upper note of the one as near the upper note of the next as it can be, the upper surface of this stream of harmony is the melodic scale and the harmony is the bottom and the body of the stream.

Ramsay image page 88

[Scientific Basis and Build of Music, page 88]

In a musical air or harmony, i.e., when once a key has been instituted in the ear, all the various notes and chords seem animated and imbued with tendency and motion; and the center of attraction and repose is the tonic, i.e., the key-note or key-chord. The moving notes have certain leanings or attractions to other notes. These leanings are from two causes, local proximity and native affinity. The attraction of native affinity arises from the birth and kindred of the notes as seen in the six-octave genesis, and pertains to their harmonic combinations. The attraction of local proximity arises from the way the notes are marshalled compactly in the octave scale which appears at the head of the genesis, and pertains to their melodic succession. In this last scale the proximites are diverse; the 53 commas of the octave being so divided as to give larger and lesser distances between the notes; and of course the attraction of proximity is strongest between the nearest; a note will prefer to move 5 commas rather than 8 or 9 commas to find rest. Thus far PROXIMITY. [Scientific Basis and Build of Music, page 91]

By affinity the notes group in chords. The tonic is the center chord, the key of the harmony; the dominant is the fifth above it and the subdominant the fifth below it, and these two are balanced on the center chord as the scales on a balance beam. The dominant chord is vigorous and active, tending to soar; the subdominant is solemn, soft, and grave, tending to sink; the tonic is melodious and restful, and in it the harmony finds equilibrium. This far AFFINITY. [Scientific Basis and Build of Music, page 91]


In passing from one key to another in the fellowship of keys in a composition, the new key grows out of the top of the dominant and converts the old dominant into a tonic. The dominant and subdominant being at the opposite extremes of the key, with the tonic between them, are not related by affinity. This want of affinity makes an opening in the system for the new chord to come in by, and it, being related by affinity to the chord of the old dominant, which is now the new Tonic, comes in and establishes itself and the new key for the time. It is this gap between subdominant and dominant, along with the affinity existing between the new key and the old dominant, which makes this musical event to be so gracefully accomplished. This is what is called natural modulation, the passing for a time into another key in the course of a composition; and its abundant and habitual use in music, even in the simplest chorales, shows how natural and acceptable it is. The young student will find illustrations in the second lines of the Psalm tunes - Watchman, Sicily, Tranquility, Eaton, Birmingham, Jackson, Bethel, Bedford, and Sheffield. Take Watchman, for example, and let the young student follow carefully, noting each chord of the little passage, which we shall analyse for his help. It is by such practice that he will become by-and-by familiar with the kinship of keys and the legitimate resources of harmony. [Scientific Basis and Build of Music, page 93]

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]

Here on the keyboard we see, nearest to the front, the great 3-times-3 chord of the full genesis of the scale from F1 to F64. When this chord is struck by the notched lath represented in front of the keyboard, the whole harmony of the key is heard at once. Behind this great chord are placed, to the left the subdominant, tonic, and dominant chords of the minor. D F A, A E C, E G B; and to the right the subdominant, tonic, and dominant chords of the major, F A C, C E G, G B D. When the notched lath is shifted from F to D, the minor third below F, and the 3-times-3 minor is struck down in the same way as the major, the whole harmony is heard; and the complete contrast of effect between major and minor harmony can be fully pronounced to the ear by this means. Behind these six diatonic chords, major and minor, on the part of the keyboard nearest to the black keys, are the three chromatic chords in their four-foldness, in both major and minor form. The center one shows the diatonic germ of the chromatic chord, with its supplement of G# on the one hand completing its minor form, and its supplement of A♭ on the other hand completing its major form. A great deal of teaching may be illustrated by this plate.

ERRATUM. - B♭, first chromatic chord, misplaced.
[Scientific Basis and Build of Music, page 104]

The Plate shows the Twelve Major and Minor Scales, with the three chords of their harmony - subdominant, tonic, and dominant; the tonic chord being always the center one. The straight lines of the three squares inside the stave embrace the chords of the major scales, which are read toward the right; e.g., F, C, G - these are the roots of the three chords F A C, C E G, G B D. The tonic chord of the scale of C becomes the subdominant chord of the scale of G, etc., all round. The curved lines of the ellipse embrace the three chords of the successive scales; e.g., D, A, E - these are the roots of the three chords D F A, A C E, E G B. The tonic chord of the scale of A becomes the subdominant of the scale of E, etc., all round. The sixth scale of the Majors may be written B with 5 sharps, and then is followed by F with 6 sharps, and this by C with 7 sharps, and so on all in sharps; and in this case the twelfth key would be E with 11 sharps; but, to simplify the signature, at B we can change the writing into C, this would be followed by G with 6 flats, and then the signature dropping one flat at every new key becomes a simpler expression; and at the twelfth key, instead of E with 11 sharps we have F with only one flat. Similarly, the Minors make a change from sharps to flats; and at the twelfth key, instead of C with 11 sharps we have D with one flat. The young student, for whose help these pictorial illustrations are chiefly prepared, must observe, however, that this is only a matter of musical orthography, and does not practically affect the music itself. When he comes to the study of the mathematical scales, he will be brought in sight of the exact very small difference between this B and C♭, or this F# and G♭; but meanwhile there is no difference for him. [Scientific Basis and Build of Music, page 108]

It is very interesting to observe how the number seven, which is excluded from the genesis of the system of vibration, comes into view after the genesis is completed, not only in the seven seconds of the melodic scale, but also in the seven of each of the intervals. As there are seven days in the week, though the seventh was only after the genesis of creation was finished, so there are six intervals, but seven of each, as we have seen; and in each 7-fold group three magnitudes determined by the three genetic magnitudes of the seconds. There is much symbolic meaning in all this. Any of the intervals may be used in melody; in harmony also, either in simple or compound chords, they all have the honor of fulfilling a part; and even those, such as seconds and sevenths, which are less honorable in themselves, have great honor in compound chords, such as dominant sevenths and compound tonics, which fulfill exceedingly interesting functions in the society of chords. [Scientific Basis and Build of Music, page 110]

The scheme endeavours to prove that the development of harmonies 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 Lubbock's quoted
—The development of Numbers, the stream of Time, the Sevens of Creation, &c., may eventually be proved to proceed by the same laws, . . . . . . . 9 [Harmonies of Tones and Colours, Table of Contents1 - Harmonies]

General remarks on harmonies of tones and colours —The scheme gained without technical knowledge —Brief explanation of how the laws were gained —The development of numbers showed the "to and fro" in the development of soundsMultequivalency of harmonies veering round, or advancing and retiring in musical clef —Before judging, close examination requested, . 12 [Harmonies of Tones and Colours, Table of Contents1 - Harmonies]

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 cathedral attuning the Amen
—Why music as an art precedes painting
—Philosophers and mathematicians have only studied music to a certain point
—Every key-note a nucleus, including the past, the present, and the future; no finality in any ultimate
—The late Sir John Herschel's views on the musical gamut alluded to
—The imperfection of keyed instruments adapts 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 [as] keyed instrument should be circular, the seven octaves interlacing in tones a lower and a higher series, . 15 [Harmonies of Tones and Colours, Table of Contents1 - Harmonies]

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 them
—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, . . . . . . . 22 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]

The key-note C sounding from within itself its six tones to and fro 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 chasms 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, . 23 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]

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
—Retrace from Chapter V. the tones in musical clef as notes, each note still sounding its tones, leading the ear to its harmony, . . 25 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]

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, . . . . 36 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]


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, . . 50 [Harmonies of Tones and Colours, Table of Contents4 - Harmonies]

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# must 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. [Harmonies of Tones and Colours, Dr. Gauntletts Remarks1, page 13]

In a few remarks on "Tones and Colours," inserted in the Athenæum 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 points which I had gained. I remarked to him one day, "I find that, of the double tones, F# is a 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 without limit. On this point I have always felt the failure of the laws followed by the musician." [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]

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 mystery of music lies in its infinite resources; 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 arises 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 [Harmonies of Tones and Colours, The Method of Development or Creation of Harmonies1, page 15]

study of the natural sciences, as we progress, we find that "hills peep o'er hills, and alps o'er alps 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 is sounded, after traveling along the aisles, the chords always return 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.* [Harmonies of Tones and Colours, The Method of Development or Creation of Harmonies2, page 16]

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 developes 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, [Harmonies of Tones and Colours, The Method of Development or Creation of Harmonies2, page 16]

In the diagrams the circles 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 the higher series of sevens. [Harmonies of Tones and Colours, The Method of Development or Creation of Harmonies3, page 17]

Throughout the scheme seven tones and seven colours develope in every harmony. In the relationship between tones and colours the seven may be con- [Harmonies of Tones and Colours, On Colours as Developed by the same Laws as Musical Harmonies2, page 19]

The tones between the seven white notes of keyed instruments, and the tints and shades between the seven colours, cause the multequivalency of colours and of tones; consequently every colour, as every musical harmony, has the capability of ascending or descending, to and fro in circles, or advancing and retiring in musical clef. It is a curious coincidence that Wünsch, nearly one hundred years ago, believed in his discovery of the primary colours to be red, green, and violet; and in this scheme, red, answering to the note C, must necessarily be the first visible colour, followed by green and violet, but these not as primary colours, all colours in turn becoming primaries and secondaries in the development of the various harmonies. To gain facts by experiment, the colours must be exactly according to natural proportions—certain proportions producing white, and others black. In this scheme, green and red are shown to be a complementary pair, and therefore (as Clerk Maxwell has proved) red and green in right proportions would produce yellow. The same fact has been proved in Lord Rayleigh's experiments with the spectroscope. Yellow and ultra-violet, [Harmonies of Tones and Colours, On Colours as Developed by the same Laws as Musical Harmonies3, page 20]

The development into triplets or trinities has been especially remarked in the harmony caused by the falls of Niagara.* "A remarkable peculiarity in the Arabian system of music is the division of tones into thirds. I have heard Egyptian musicians urge against the European systems of music that they are deficient in the number of sounds. These small and delicate gradations of sound give a peculiar softness to the performances of the Arab musicians." [Harmonies of Tones and Colours, The Arabian System of Music, page 21]

The inequality of the equinoctial points is a well-known fact. It will be seen how apparent this is in the developments of harmonies. From the moment that trinities depart from unity, the balance is unequal, and the repeated endeavours after closer union cause a perpetual restlessness. May not this want of equilibrium be the life or motive power of the entire universe, with its continuous struggle after concord, even to oneness? "Closer and closer union is the soul of perfect harmony." In tracing harmonies of tones and colours, the double tones of keyed instruments will be seen to correspond with the intermediate tints and shades of colours. The twelve notes, scales, and chords in the major and minor series, the meetings by fifths, &c., all agree so exactly in their mode of development, that if a piece of music is written correctly in colours with the intermediate tints and shades, the experienced musician can, as a rule, detect errors more quickly and surely with the eye than the ear, and the correct eye, even of a non-musical person, may detect technical errors. Although the arithmetical relation has been most useful in gaining the laws, it is not here entered upon; but numbers equally meet all the intricacies both of tones and colours. The bass notes have been omitted, in order to simplify the scheme. [Harmonies of Tones and Colours, The Arabian System of Music, page 21]

THE five circles represent a musical clef on which the twelve notes of a keyed instrument are written. Six of the notes are shown to be double, i.e., sounding two tones, eighteen in all, including E#, which is only employed in the harmony of F#, all others being only higher or lower repetitions. [Harmonies of Tones and Colours, Diagram I - The Eighteen Tones of Keyed Instruments, page 22a]

The diagram begins with C, the third space of the treble clef, as being more convenient to write than C, the lowest note in the bass clef. The life of musical sounds rising from a hidden fountain of life is shown by the chasms of keyed instruments between B and C, and E and F; their great use will be strikingly manifest as the developments proceed. The fundamental key-note C and its root F rise from the chasms. B, the twelfth key-note, and E, its root, sound the octave higher of the fountain B. The generation of harmonies is by one law a simple mode of difference. Each major major key-note and its tones embrace the eighteen tones of keyed instruments which all lie in order for use. The power and extent of each are complete in itself, rising and developing, not from any inherent property in matter, but from the life communicated to matter. In the whole process of harmony there are limits, and yet it is illimitable. Its laws compel each key-note to follow certain rules within certain bounds; each separate key-note, being the fountain of its own system, has its own point of rest, and series after series rise and enlarge, or fall and diminish infinitely. [Harmonies of Tones and Colours, Diagram I - The Eighteen Tones of Keyed Instruments, page 22a]

IN tracing the origin of a harmony, or family of sounds, all divisions must come out of the one, or unit. Two powers are at work—cohesion and separation; a truth continually dwelt upon by the Greek philosophers. In the diagram, the note C may be considered as central, or as placed with four tones below and two above itself. [Harmonies of Tones and Colours, Diagram II - The Twelve Keynotes1, page 23]

A key-note developing its harmony may be compared to a seed striking its root downwards, and rising upwards. On striking a note, it sounds from within itself, in a rapid and subdued manner, the six kindred tones necessary to its harmony, and all which do not belong to that individual harmony are kept under; thus all harmonies are in sevens. Each seven forms an ascending and descending series; the ear is aware of the tones, but not of the order in which they rise. [Harmonies of Tones and Colours, Diagram II - The Twelve Keynotes1, page 23]

The arrangement of a key-note and the six tones which it sounds may be simply explained by writing tones in a musical clef as notes. In this diagram we have the harmony of C and its root F. Both of these rise from the chasms, and hence this harmony is not so closely linked to that of B, and its root E, as to the other eleven harmonies. [Harmonies of Tones and Colours, Diagram II - The Twelve Keynotes1, page 23]

The three lowest of the six tones are complementary pairs with the key-note and its two highest tones. Observe the curious order in which the tones sound, avoiding consecutive fifths. First, we have the key-note and its root, or fellow; next A; then D and its root; and then E, whose root, A, has already sounded between the first and the second pair. B, the fourth and central tone in depth, sounds seventh, and, finding no fellow within the compass of the harmony developing it, is isolated. Observe also how closely a key-note and its kindred tones are linked into each other. The Primaries spring from the key-notes, the Secondaries from the Primaries; the first pair comprises a key-note and a tone of the Primaries, the other two pairs have each a tone of the Primaries and a tone of the Secondaries. The key-note, after giving out its tones in trinities, or [Harmonies of Tones and Colours, Diagram II - The Twelve Keynotes1, page 23]

combinations of dissonance, rests, sounding neither scale nor chords. Dissonance does not express opposition or separation, for there is no principle in musical tones which is productive of contraries; the dissonances follow the attraction of the tonic, or key-note, and the neutralization of the musical disturbance is implied in the disagreement in their motion with the repose of the unit, or key-note. So far is this from producing separation, that the apparent discord is simply a preparation for growth, the life of harmony causing an inherent tendency towards closer union. [Harmonies of Tones and Colours, Combinations of dissonance, rests, page 24]

We here trace the twelve harmonies developing in succession. Notice how exactly they all agree in their mode of development; also the use of the chasms between E and F, B and C. Remark also the beautiful results from the working of the double tones, especially C#-D♭, and E#-F♭, causing the seven tones of each harmony, when ascending, to rise one tone, and, descending, to reverse this movement. F#-G♭ is the only double tone which acts as F# when a key-tone, and G♭ when the root of D♭. The root of each harmony is the sixth and highest tone in each succeeding harmony, rising one octave; when it is a double tone, it sounds according to the necessity of the harmony. The intermediate tones are here coloured, showing gradual modulation. The isolated fourths (sounding sevenths) were the previously developed key-tones; these also alter when they are double tones, according to the necessity of the harmony. Beginning with B, the isolated fourth in the harmony of C, the tones sound the twelve notes of a keyed instrument, E# being F♮, and the double tones, some flats, some sharps. [Harmonies of Tones and Colours, Combinations of dissonance, rests, page 24]

The only exception is the double tone F#-G♭, which is a curious study. F# as a harmony takes the double tones as sharps, and F♮ is E#. G♭ is also a harmony sounding the same tones, by taking the double tones as flats, and B♮ as C♭. F# therefore takes the imperfect tone of E#, and G♭ the imperfect tone of C♭. (See here the harmony of G♭ in musical clef.) [Harmonies of Tones and Colours, Combinations of dissonance, rests, page 24]

We find that on a keyed instrument each primary sounds the same tones as the secondaries of each third harmony below, but in a different order, and the double tones are altered sharp or flat as the harmony requires. For example, the secondaries of B are sharps; when primaries of D♭, they are flats. In order to trace this quickly, the sharps and flats are written to each note. [Harmonies of Tones and Colours, Combinations of dissonance, rests, page 24]

The Major Key-note of C is here shewn developing its trinities from within itself, veering round; C and the other 11 developing their trinities in musical clef. Below each is the order in which the pairs meet, avoiding consecutive fifths. Lastly, C# is seen to be an imperfect major harmony; and G♭, with B as C♭, make the same harmony as F#. The intermediate tones of sharps and flats of the 7 white notes are here coloured in order to shew each harmony, but it must be remembered that they should, strictly, have intermediate tints. [Harmonies of Tones and Colours, The Major Keynote of C, page 24c]

In the progression of harmonies these are always closely linked into each other. If any key-note is taken as central, its root will be the fifth note of its harmony below, and it becomes in its turn the root of the fifth note above. If we add the silent notes, the root of the central note is the eighth below, and becomes the root of the eighth above. To explain the lower series of the notes sounding the six tones from within themselves, the only plan appeared to be to write the tones as notes in musical clef. By reference to Chapter V., we see that the lowest series still sound their tones, and lead the ear to the higher series of a key-note, and the six notes of its harmony, as they follow each other in trinities. [Harmonies of Tones and Colours, Diagram III - The Major Keynotes Developing by Sevens, page 25a]

See Also

Bells Inequality
Bjerknes Effect
enharmonic third
Figure 9.18 - Harmonized Motions
Figure 9.19 - Enharmonized Motions
Full Harmonic Chord
harmonic attractive chord
harmonic circles
harmonic current
harmonic scale
Harmonic Series
Harmonies of Tones and Colours
harmony of the spheres
Helmholtz Subharmonic Series
key of harmony
Kepler Theory of Harmony
Law of Attraction
Law of Harmonic Attraction and Repulsion
Law of Harmonic Pitch
Law of Harmonic Relationship
Law of Harmonic Vibrations
Law of Harmony
organic harmony
polar harmonic current
Poles in Harmonies
Power of Beat Harmonics
Quantum Entanglement
rules of harmony
stream of harmony
Sympathetic Oscillation
Sympathetic Vibration
Table of Plate Harmonics and Intervals
Tertian harmony
Vibrating Rod Harmonics
8.17 - Law of Harmonic Vibrations
8.22 - Law of Harmonic Pitch

Created by Dale Pond. Last Modification: Saturday February 27, 2021 03:43:49 MST by Dale Pond.