Sympathetic Vibratory Physics

noun: three constituent or aliquot parts comprising a single whole or unit.
noun: a group of three people or things.
noun: the union of the Father and Son and Holy Ghost in one Godhead.

Keely
"The great and universal Trinity of cause, motion and matter__ - or of will, thought and manifestation - was known to the Rosicrucians as prima materia. Paracelsus states that each of these three is also the other two; for, as nothing can possibly exist without cause, matter and energy - that is, spirit, matter and soul (the ultimate cause of existence being that it exists), we may therefore look upon all forms of activity as being the action of the universal or Divine will operating upon and through the ether, as the skilled artificer uses his tools to accomplish his designs; making the comparison in all reverence." [More Science]

Bloomfield-Moore
"Science admits that nature works with dual force, though at rest she is a unit. "Nature is one eternal cycle." Keely's discoveries prove that the doctrine of the Trinity should be set down as an established canon of science - the Trinity of force. All nature's sympathetic streams - cerebellic, gravital, electric and magnetic - are made up of triple currents. The ancients understood this dogma in a far deeper sense than modern theology has construed it. The great and universal Trinity of cause, motion and matter - or of will, thought and manifestation - was known to the Rosicrucians as prima materia. Paracelsus states that each of these three is also the other two; for, as nothing can possibly exist without cause, matter and energy - that is, spirit, matter and soul (the ultimate cause of existence being that it exists), we may therefore look upon all forms of activity as being the action of the universal or Divine will operating upon and through the ether, as the skilled artificer uses his tools to accomplish his designs; making the comparison in all reverence." [Bloomfield-Moore, More Science] [True Science]

Keely
"Life begets life; the celestial life begets the terrestrial life; the God life begets the man life. Celestial Radiation is the pure soul of all matter, both earthy and gaseous. Thus we are linked in all our environments to the divine, our cerebral aggregations being the highest medium whereby celestial sympathetic reflection associates with our organisms, and is our only source of knowledge of ourselves. We have, with our mental and physical forces, a duality of action which, when combined with the celestial, makes up the triplet or trinity. With the mental, the superficial visible, or outward sight; with the inward, or spiritual invisible, we have the spiritual link connecting mind and matter, the order of transfer being:

"First. Celestial Radiation, or etheric.
"Second. Mental impregnation, or interatomic.
"Third. Physical movements, or intermolecular.

Or again:

"Ninths. Sympathetic transfer from the celestial luminous.
"Sixths. Sympathetic impregnation of matter.
"Thirds. Physical movements." [Newton of the Mind]

"The sympathetic acoustic impulses are:  
"the DOMINANT - a diatonic third -  
"the HARMONIC - the connective "sixth" - and  
"the ENHARMONIC - or diminished seventh - which Keely calls a ninth -  
"inducing "infinite trajective velocity" or "neutral radiation" from neutral centers. [Snell Manuscript]

Reference Links:
ninths
Trinity of Matter and Force
Three Laws of Being

Russell
"Thus the One Light of God's knowing extended to the two of His thinking, pulsed as the three of all creating things, the One centering the two, the two extended from the One; the Spirit; the Father-Mother polarity of Light; the Trinity centering the shaft of Creations' seeming, fulcrum of its heartbeat, all ONE." [Walter Russell, The Secret of Light, page 99]

"God, the One Knower, becomes three by His imagining. The still Light of the Knower, and the moving lights of His thinking, are the Trinity which God is in all things in this universe.

God, the One Father-Mother divides His sexlessness to extend

p. 108

(courtesy University of Science and Philosophy)
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Fig. 19 illustrates the entire process of creating – and recreating matter. The Father-Mother electrically divides His ONENESS into pairs of father and mother bodies. The electrical strain of seperation is equalled by an opposite strain, or tension, of desire for ONENESS. Unity thus attained is repeated in similar electrically dividing and uniting pulsations, forever.

ANOTHER WAY OF STATING THE SAME THING

God, the Creator, divides His one white Light by extending its ONENESS into electrical tensions of vibrating red and blue pairs. The tensions of this electrical division are equalled by a desire for unity, which is attained at the point of white incandescense in matter. Unity thus attained is repeated forever by the same dividing, uniting process of electrical action-reaction pulsations. Reproduction cannot take place until the red and the blue lights of sex-divided motion are voided in the still White Light of the Creator. Man alone, of all Creation, ever knows of his Omniscience.

p. 109

father and mother bodies from His Oneness. The one desire of these separated male and female particles, or masses, is to unite to void their separateness. Upon this formula God's electric universe of motion is founded.

The sexless Father-Mother Creator is One. His extended sex-conditioned, male and female bodies are the completion of His Trinity.

Rest and action are three. Space and matter are three. Equilibrium and motion are three. Dimensions and pressures are three. The heartbeat of the universe, and yours, are three. Likewise, its breathings and yours, its temperatures and yours, and all things else of the universe, and you, are three.

The swinging of the pendulum is three, as the spectrum and the fulcrum and lever, also, are three.

The cathode is one - but its extended pairs of anodes in the electric current of man, and of space, adds up to three.

Silence is one - but sound springs from silence when its divided moving pair collide - so sound is three, and its vibrations in sequences of rest and action, are also three.

God is ONE in all CAUSE - but in all EFFECT He is three. And all that are three are nine - for all that are three are multiplied by three in this visible cube dominated universe of three dimensions." [Atomic Suicide, page 107-109]

Ramsay
8, and one 5, making 31 commas, while this supposed fourth-fifth major would only have 30. The fifths of the musical system are thus strictly kept as a symbol of the Trinity of the Creator, Three in One. [Scientific Basis and Build of Music, page 78]

Hughes
Helmholtz's experiments on developing colours shown to agree 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 meetings 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, 18 [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]

The twelve major scales
—The term key-note employed in the ordinary sense of the musician
—The twelve 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 series
—Keys mingled
—The modulating of scales, the eleventh notes rising to higher keys, . . . . . . 26 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]

The twelve keys, their trinities, scales, and 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, . . . 28 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]

The modulating gamut
—One series of the twelve keys meeting by fifths through seven octaves
—Keys not mingled
—A table of the key-notes and their trinities thus meeting
—The fourths not isolated
—The table of the twelve scales meeting by fifths
—The twelve keys, trinities, scales, and chords thus meeting are written in musical clef
—The twelve meeting through seven circles, each circle representing the eighteen tones
—The keys of C and G meeting, coloured
—Retrospection of the various major developments, . . . . 29 [Harmonies of Tones and Colours, Table of Contents3 - 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]

The twelve keys, trinities, scales, and chords are written in musical clef,..38 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]

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 fifths, keys not mingled
—Third, the twelve minor keys mingled
—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, 42 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]

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

I add quotations 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." [Harmonies of Tones and Colours, Dr. Gauntletts Remarks1, page 13]

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]

"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]

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 first trinity of sounds (hereafter called the Primaries) rise veering from left to right; the second trinity (hereafter called the Secondaries) follow, veering from right to left. The life of sound always causes a variety of movement to and fro. [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]

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]

The twelve key-notes, with the six notes of each as they veer round in trinities, are again written in musical clef, and the scales added. The key-note leads the scale, and, after striking the two next highest notes of the seven of the harmony, goes forward, with its four lowest, an octave higher. The seven of each harmony have been traced as the three lowest, thus meeting the three highest in three pairs, the fourth note being isolated. Notwithstanding the curious reversal of the three and four of the scale, the three lowest pair with the three highest, and the fourth with its octave. The four pairs are written at the end of each line, and it will be seen how exactly they all agree in their mode of development. Keys with sharps and keys with flats are all mingled in twelve successive notes. If we strike the twelve scales ascending as they follow each other, each thirteenth note being octave of the first note of the twelve that have developed, and first of the rising series, the seventh time the scales gradually rise into the higher series of seven octaves beyond the power of the instrument. Descending is ascending reversed. After the seven and octave of a scale have been sounded ascending, the ear seems to lead to the descending; but ten notes of any scale may be struck without the necessity of modulation; at the seventh note we find that the eleventh note in the progression of harmonics rises to meet the seventh. For instance, B, the seventh note in the scale of C, must have F#. This point will be fully entered into when examining the meeting of fifths. To trace the scale of C veering round as an example for all, we may begin with C in Diagram II., and go forward with F, G, A, and B an octave higher. If the twelve scales were traced veering round, they would be found to correspond with the twelve as written in musical clef. [Harmonies of Tones and Colours, Diagram IV - The Development of the Twelve Major Scales, page 26a]

The roots of the chords are first written. The Key-note C and its trinities are shewn to have 2 chords. The chords of the 12 Major Keys, as they follow in order. [Harmonies of Tones and Colours, The Roots of the Chords, page 26c]

IF we strike the twelve keys of harmonies in trinities, scales, and chords, as written in musical clef, beginning with the lowest C in the bass clef, this first development is linked into the lower series of seven octaves by the four lower tones sounded by C. If we follow with the twelve keys six times, at the seventh time they will gradually rise into the higher series. We obtain a glimpse of the beauty arising from musical notes in the Pendulograph. How exquisite would they be if they could be represented in their natural coloured tones! — as, for instance, the chord of the scale of C in red, yellow, and blue, with the six coloured tones rising from each, and harmoniously blended into each other. [Harmonies of Tones and Colours, The Twelve Keys Rising Seven Times, page 28a]

The 12 Key-notes and their trinities and scales written in musical clef, with their chords added, all rising in the two octaves, as before. [Harmonies of Tones and Colours, The 12 Keynotes and Their Trinities and Scales, page 28c]

In the retrogression of harmonies, a key-note and its trinities, by sounding the same tones as when ascending, leads the ear to the same notes, and the root of each key-note becomes the fifth lower key-note. F, the root of C, becomes key-note; B?, the root of F, the next key-note, and so on. [Harmonies of Tones and Colours, Diagram VII - The Modulating Gamut of the Twelve Keys1, page 29]

The following table shows the regularity of each seven of the twelve key-notes ascending by fifths, and the use of the two poles is again seen. The key-notes and their trinities are closely linked into each other, the three highest notes of the lower fifth key becoming the three lowest of the higher fifth key, and the four lowest becoming the four highest in an octave higher. The twelve keys, rising in each note a tone higher and descending a tone lower, cause the meetings by fifths. Having examined the table, we may strike the keys by fifths as written in the musical clef, beginning with the lowest C in [Harmonies of Tones and Colours, Diagram VII - The Modulating Gamut of the Twelve Keys1, page 29]

In the development of the key-notes, the sharp or flat is written to each note, but not to the keys. The reversal of the three and four notes of each seven of the twelve key-notes and their trinities meeting by fifths having been traced, we will now examine the twelve scales meeting by fifths, and the results arising from the reversal of the three and four notes of each fifth lower scale in the fifth higher. Take as an example the scale of C: C D E F G A B, and that of G: G A B C D E F#. The four lowest notes of the seven of C are the four highest, an octave higher, in G; F, the central and isolated note of the seven of C, having risen a tone higher than the octave in the scale of G. The twelve scales thus modulate into each other by fifths, which sound the same harmonies as the key-notes and their trinities. Refer to the twelve scales written in musical clef ascending by fifths, and strike them, beginning at the lowest C in the bass clef; this scale sounds no intermediate tones, but these must be struck as required for all the scales to run on in fifths. After striking the seven notes of C, if we fall back three, and repeat them with the next four notes of the seven; or strike the seven and octave of C, and fall back four, repeating them and striking the next four, the four last notes of each scale will be found to be always in the harmony of the four first of the fifth higher scale. When the twelve scales ascending have been thus gained, as we trace them also on the table, they may be struck descending by following them as written in musical clef upwards, and [Harmonies of Tones and Colours, Diagram VII - The Modulating Gamut of the Twelve Keys2, page 30]

The keys of C and G meeting are coloured, and show the beautiful results of colours arising from gradual progression when meeting by fifths. Each key-note and its trinities have been traced as complete in itself, and all knit into each other, the seven of each rising a tone and developing seven times through seven octaves, the keys mingled. The twelve scales have been traced, developing seven times through seven octaves, all knit into each other and into the key-notes and their trinities. The chords have also been traced, each complete in itself, and all knit into each other and into the key-notes, trinities, and scales. And lastly, one series of the twelve keys, no longer mingled, but modulating into each other, have been traced, closely linked into each other by fifths through seven octaves, three keys always meeting. Mark the number of notes thus linked together, and endeavour to imagine this number of tones meeting from the various notes. [Harmonies of Tones and Colours, The Twelve Scales Meeting by Fifths, page 31a]

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We pass on to the developing of the minor keys. [Harmonies of Tones and Colours, The Twelve Scales Meeting by Fifths, page 31a]

DIAGRAM IX.—THE MINOR KEY-NOTE "A" AND ITS SIX NOTES VEERING ROUND IN TRINITIES—THE TWELVE KEY-NOTES THUS DEVELOPING WRITTEN IN MUSICAL CLEF BELOW.

"Lord, on Thee Eternity had its foundations—all

Spring forth from Thee; of light, joy, harmony

Sole origin:—all life, all beauty Thine!"—Sir J. Bowring.

[Harmonies of Tones and Colours, Diagram IX - The Minor Keynote A and Its Six Notes, page 34a]

AS an example of the twenty-four, compare A major, developing, in Diagram II., with A minor, Diagram IX., taking the notes in the order which they sound in trinities. The three notes of the primaries sounded by A minor are, first, the same root as the major; the two next are the fourth and seventh higher notes (in the major, the fifth and sixth); the secondaries only vary by the sixth and seventh notes being a tone lower than in their relative major. Observe the order in which the pairs unite; the fourth in depth, sounded seventh, isolated. A and its root do not rise from the chasms. The fundamental key-note C was seen not to be interfered with, neither is the fundamental minor key-note A; G# on the one side, and B? on the other, being the key-notes. The seven of each minor harmony embrace only seventeen tones. C major and A minor are the only two keys which sound the seven white notes of keyed instruments. The minor scale and chords of A are not included in this remark. [Harmonies of Tones and Colours, Diagram IX - The Minor Keynote A and Its Six Notes, page 34a]

The diagram represents the Minor Key-note A and its 6 notes veering round in trinities; A and the other 11 developing their trinities in musical clef. Below each is the order in which the pairs unite, avoiding consecutive fifths, Lastly, D? is shewn to be an imperfect minor harmony, and by employing B as C?, E? is seen to be the same harmony as D#. As before, it should be remembered that the sharp and flat notes should, strictly, have intermediate tints. [Harmonies of Tones and Colours, The Diagram Represents the Minor Keynote, page 34c]

CHAPTER XIV .

DIAGRAM XI.—THE TWELVE MINOR KEY-NOTES, WITH THE SIX NOTES OF EACH, ARE AGAIN WRITTEN AS THEY VEER ROUND IN TRINITIES, AND THE SCALES ADDED.

"Unfaith in aught is want of faith in all.

It is the little rift within the lute

That by-and-by will make the music mute,

And, ever widening, slowly silence all."—Tennyson.

[Harmonies of Tones and Colours, Diagram XI - The Twelve Minor Keynotes with the Six Note of Each, page 36a]

CHAPTER XVI.

DIAGRAM XIII.—THE TWELVE KEY-NOTES, WITH THEIR TRINITIES, SCALES, AND CHORDS, THE THIRTEENTH BEING OCTAVE, ARE REPEATED IN MUSICAL CLEF, RISING SEVEN TIMES THROUGH SEVEN OCTAVES, AND FALLING AGAIN.

[Harmonies of Tones and Colours, Diagram XIII - The Twelve Keynotes with Their Trinities, page 38a]

IF we strike the twelve as written in musical clef, beginning with the lowest A in the bass clef, each key-note, with its trinities, scale, and chords, sounds three harmonics. We may follow with the twelve keys as they rise, and descend by following the keys upwards as written in musical clef, each key falling lower. [Harmonies of Tones and Colours, Diagram XIII - The Twelve Keynotes with Their Trinities, page 38a]

The twelve key-notes with their Trinities and Scales repeated, with the addition of the chords. [Harmonies of Tones and Colours, The Twelve Keynotes with Their Trinities and Scales Repeated, page 38c]

BEGINNING with the lowest A in the bass clef, let us strike the trinities, scale, and chords, carrying each key-note a fifth higher, counting the seven belonging to its harmony. If the silent notes are included, each fifth is the eighth meeting. [Harmonies of Tones and Colours, Diagram XIV - The Modulating Gamut of the Twelve Minor Keys by Fifths1, page 39]

If we strike the ascending scales as written in musical clef again, beginning with the lowest A in the bass clef, we see that the second and sixth notes of each scale meet in higher harmony; the sharp or flat of the scale which varies from the seven notes of its harmony is written to each note. We descend as written in musical clef upwards; each third and seventh note meet in lower harmony, and thus all exactly agree in their mode of development. Having examined the scales as written in the table below, where the sharp or flat as before is marked to each note, but not to the keys, let us strike the key-notes, trinities, scales, and chords. The three harmonies of each key are written at the end of each line of musical clef. To descend, we follow the musical clef upwards, as before. [Harmonies of Tones and Colours, Diagram XIV - The Modulating Gamut of the Twelve Minor Keys by Fifths2, page 40]

TO recapitulate from the beginning, observe, firstly, the twelve major key-notes as they have developed from within themselves in succession, six tones in trinities seven times through seven octaves, each thirteenth note being the octave of the first note of the twelve that have developed, and being also the first of the higher series. We may retrace all as still sounding their tones, the key-notes leading the ear to the six notes of each harmony, the keys with sharps and those with flats being mingled. The ascending and descending scales always agree in their harmonies with the key-notes and their trinities. [Harmonies of Tones and Colours, Diagram XV - The Twelve Major and the Twelve Minor Keys, page 42a]

Secondly, we have the one series of the twelve keys as they meet by fifths through the seven octaves. The keys are no longer mingled; the scales meet by fifths in the same keys and their trinities. [Harmonies of Tones and Colours, Diagram XV - The Twelve Major and the Twelve Minor Keys, page 42a]

Thirdly, the twelve minor keys as they develope in succession seven times through seven octaves, always sounding their major harmony in trinities, and, as with the majors, each thirteenth note being the octave of the first note of the twelve, and first of the following series, the keys all mingled. [Harmonies of Tones and Colours, Diagram XV - The Twelve Major and the Twelve Minor Keys, page 42a]

Fourthly, we have one series of the seven of each of the twelve minor keys meeting by fifths through seven octaves. The keys of the twelve ascending scales are written in musical clef above the former, and the keys of the descending scales below. The ascending scales sound the fifth higher harmonies than the key-notes and their trinities, and the lower scales the fifth harmony lower than the key-notes and their trinities. The three series follow out their keys in three successive series, and all meet by fifths. [Harmonies of Tones and Colours, Diagram XV - The Twelve Major and the Twelve Minor Keys, page 42a]

THE above quotation from that beautiful work, The Pendulograph, shows how firmly its author believes that the Almighty Himself will be proved to be the key to His works; a belief frequently expressed also in a striking work, Nature and the Supernatural, by the Rev. J. W. Reynolds, M.A. For many years I have been endeavouring to resolve some of the intricacies of natural harmony with the same views. In the pursuit of knowledge it is eminently important to "avoid profane and vain babblings, and oppositions of science falsely so called" (I Tim. vi. 20), and to remember that facts gained from the study of God's marvellous works, that "ought to be had in remembrance" (Psa. cxi. 4, Prayer Book Version), and the truths of Holy Scripture, can never really oppose each other. Research shows us countless varieties developed by trinities springing from unities, and we find true scientific depth in the Scriptural phrases, where the whole earth is continually mentioned as worshipping the Almighty. This truth is beautifully expressed in the Te Deum Laudamus—"Holy, holy, holy, Lord God Almighty; heaven and earth are full of Thy glory." [Harmonies of Tones and Colours, Reflections on the Scheme1, page 43]

"I esteem myself fortunate in being introduced to you, and becoming acquainted with your beautiful work on 'Tones and Colours.' I have, to the best of my ability, worked out your idea, by writing down in music the various discords in use amongst musicians, and resolving them according to the laws of Harmony, and I find in all cases the perfect triad agrees with what you term the trinities in colours. The way in which you find the whole circle of Major and Minor keys by pairs in colours is deeply interesting, and must be true. The only point of divergence between your system and that recognised by all musicians is the ascending Minor Scale. No musically trained ear can tolerate the seventh note being a whole tone from the eighth. The Minor second in the lower octave descending is very beautiful, and it is strange how all composers feel a desire to use it. To mention one case out of hundreds, I may cite Rossini's well-known air, 'La Danza.'
"Yours faithfully,
"W. CHALMERS MASTERS." [Harmonies of Tones and Colours, Supplementary Remarks and Diagrams, page 53]

If, as I believe, the Natural Sciences throughout Creation develope by Trinities, how silently, yet how strikingly, may we trace the wonders of Redeeming Love. "Wisdom hath builded her house; she hath hewn out her seven pillars."— Prov. ix. I. We strikingly see in the development of harmonies the type of 2 Cor. iii. 18, as each key rises from darkness to light, or, descending, falls from light to darkness.
F. J. Hughes
BEDWYN LODGE,
SANDOWN, ISLE OF WIGHT,
February, 1885 [Harmonies of Tones and Colours, Supplementary Remarks, page 54]

DIAGRAM XVI.—The seven of each harmony, with its scale—The pairs of the trinities and scales. [Harmonies of Tones and Colours, Additional Diagrams, page 57]

DIAGRAM XVIII.—The 12 key-notes with their trinities and scales repeated, with the addition of the chords. [Harmonies of Tones and Colours, Additional Diagrams, page 57]

The seven of each Harmony, with its Scale. The pairs of the Trinities and Scales. [Harmonies of Tones and Colours, The Seven of each Harmony with its Scale, page 59]

In the Minor Scale, the Trinities and Scale develope five pairs; the last pair become the fifth higher key-note and its root, consequently the sixth pair would develope the higher key.[Harmonies of Tones and Colours, The Seven of each Harmony with its Scale, page 59]

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