Same as vibration, frequency.
MUSIC: One whole step. Same as a single pitch, sound or note but may also be a complex sound; i.e., composed of more than one single-frequency (multiple aliquot parts).

"In the image of man" Keely constructed his liberator. Not literally, but, as his vibrophone (for collecting the waves of sound and making each wave distinct from the other in tone when the "wave plate" is struck after the sound has died away) is constructed after the human ear so his liberator corresponds in its parts to the human head. [Snell Manuscript - The Book, page 2]

"All motion of thinking Mind is born in the maximum high speed of the universal constant of energy. It runs the gamut of periodic and opposing deceleration and acceleration in six full tones, one double tone, and a master tone, to each of ten lowering octaves, and a variable number of mid-tones in each of the last four octaves." [Russell, The Universal One; Book 01 - Chapter 02 - The Life Principle]

"Tone means sound. Mass accumulates all down the entire ten octaves; tone lowers from the highest note down the cosmic keyboard to the lowest." [Russell, The Universal One; Book 01 - Chapter 15 - The Formula of the Locked Potentials.]

0 - 1 - 2 - 3 - 4 * 4 - 3 - 2 - 1 - 0
Eight tones of amplified gravity
which accumulate in each octave wave
[Geometry and Mathematics of Octave Waves]

It is in their inverse relations that the major and the minor are equal. Every note, chord, and progression in the one has its reciprocal or corresponding note, chord, and progression in the other. This is the Law of Duality. And this general law of Nature is so deeply rooted in music, that is the numbers which represent the vibrations in the major system be made to represent quantities of string, these quantities will produce the minor system (beginning, of course, with the proper notes and numbers); so that when the quantities are minor the tones are major, and when the quantities are major the tones are minor.1[Scientific Basis and Build of Music, page 44]

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

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

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]

A very important thing in the making of a violin, after a good form, a right balancing of part against part, and all of wood in skillful condition, is the violin varnish. Composition:-

Linseed oil boiled,... ... ... 1 part.
Isinglass, ... ... ... ... 1/2 part.
Turpentine, ... ... ... ... Quantum suf.

Give two coats with this, then rub down with fine sandpaper. Then, best copal varnish, one coat. Finish then with boiled linseed oil, thickened with sifted 'rotten stone.' This gives a fine, smooth, and dull surface. Ramsay's violins are of surpassing tone; and he considered the varnish an important element in violin-making. [Scientific Basis and Build of Music, page 85]

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

Nine-tenths of a string, if stopped and acted on, gives a tone the ratio of 9:10, but if touched and acted on as a harmonic it gives a note which is three octaves and a major third above the whole string. If the remaining tenth of the string be acted on either as a stopped note or a harmonic it will give the same note which is three octaves and a major third above the whole string the ratio of 1:10, so that the stopped note of one-tenth and the harmonic of nine-tenths are the same. Indeed the bow acting on stopped note of one-tenth, on harmonic of nine-tenths, or on harmonic of one-tenth, produces the same note, as the note is the production of one-tenth in each case; for in the harmonic, whether you bow on the nine-tenths or the one-tenth, while it is true that the whole string is brought into play, yet by the law of sympathy which permeates the entire string, it vibrates in ten sections of one-tenth each, all vibrating in unison. This is what gives the harmonic note its peculiar brilliancy. [Scientific Basis and Build of Music, page 92]

"There are three chromatic chords, and each of these three is related to eight particular tonic chords. When one the these chromatic chords goes to any one of its eight tonic chords, three of its notes move in semitonic progression, and the other note moves by the small tone, the ratio of 9:10. There is exception to this rule, whether the key be major or minor. But when the chromatic chord which should resolve to the tonic of C is followed by the subdominant, or the tonic of F (the example in Mr. Green's book), only two of its notes move in semitonic progress. Your friend describes the chord as if it had gone to the tonic of B; and what he said about it, and about D going to C, is what is supposed to be [Scientific Basis and Build of Music, page 94]

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

Whatever interval is sharpened above the tone of the open string, divide the string into the number of parts expressed by the larger number of the ratio of the interval, and operate in that part of the string expressed by the smaller number of it. For example, if we want to get the major third, which is in the ratio of 4:5, divide the string into five parts and operate on four. The lengths are inversely proportional to the vibrations. [Scientific Basis and Build of Music, page 100]

When Leonhard Euler, the distinguished mathematician of the eighteenth century, wrote his essay on a New Theory of Music, Fuss remarks - "It has no great success, as it contained too much geometry for musicians, and too much music for geometers." There was a reason which Fuss was not seemingly able to observe, namely, that while it had hold of some very precious musical truth it also put forth some error, and error is always a hindrance to true progress. Euler did good service, however. In his letters to a German Princess on his theory of music he showed the true use of the mathematical primes 2, 3, and 5, but debarred the use of 7, saying, "Were we to introduce the number 7, the tones of an octave would be increased." It was wise in the great mathematician to hold his hand from adding other notes. It is always dangerous to offer strange fire on the altar. He very clearly set forth that while 2 has an unlimited use in producing Octaves, 3 must be limited to its use 3 times in producing Fifths. This was right, for in producing a fourth Fifth it is not a Fifth for the scale. But Euler erred in attempting to generate the semitonic scale of 12 notes by the use of the power of 5 a second time on the original materials. It produces F# right enough; for D27 by 5 gives 135, which is the number for F#. D27 is the note by which F# is produced, because D is right for this process in its unaltered condition. But when Euler proceeds further to use the prime 5 on the middles, A, E, and B, and F#, in their original and unaltered state, he quite errs, and produces all the sharpened notes too low. C# for the key of D is not got by applying 5 to A40, as it is in its birthplace; A40 has already been altered for the key of G by a comma, and is A40 1/2 before it is used for producing its third; it is A40 1/2 that, multiplied by 5, gives C#202 1/2, not C200, as Euler makes C#. Things are in the same condition with E before G# is wanted for the key of A. G# is found by 5 applied to E; not E in its original and unaltered state, E30; but as already raised a comma for the key of D, E30 3/8; so G# is not 300, as Euler has it, but 303 3/4. Euler next, by the same erroneous methods, proceeds to generate D# from B45, its birthplace number; but before D# is wanted for the key of E, B has been raised a comma, and is no longer B45, but B45 9/16, and this multiplied by 5 gives D#227 13/16, not D225, as Euler gives it. The last semitone which he generates to complete his 12 semitones is B♭; that is A#, properly speaking, for this series, and he generates it from F#135; but this already altered note, before A# is wanted for the key of B, has been again raised a comma [Scientific Basis and Build of Music, page 107]

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 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 difference in the development of a major and a minor harmony
—The twelve developing keys mingled
D♭ shown to be an imperfect minor harmony
E♭ taking B♮ as C♭ to be the same as D#
—The intermediate tones of the seven white notes are coloured, showing gradual modulation
—As in the diagram of the majors, the secondaries are written in musical clef below the primaries, each minor primary sounding the secondaries of the third harmony below, but in a different order, and one tone rising higher, . . . . . 34 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]

I had for a long time studied the development of the harmonics of colour, and believed that I had gained them correctly; but I saw no way of proving this. The thought occurred—Why not test the laws in musical harmonies? I wrote down the development of the seven major keys of the white notes in keyed instruments. I was perplexed by the movement as of "to and fro," but the development of numbers explained this point, and I found that the method of development in colours, tones, and numbers agreed. I remembered the keys with sharps, but had forgotten that B♭ belonged to the key of F, and here I thought that the laws failed. But I found by reference that all were correct, the eighth being the first of a higher series, the laws having enabled me to distinguish between flats and sharps, [Harmonies of Tones and Colours, General Remarks on Harmonies of Tones and Colours, page 12]

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

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

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

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]

C rises from the fountain, and contains all tones within itself. Red also rises from the fountain, and contains all colours, with white and black.
D=the notes C and E mingled. Orange, red and yellow mingled.
E=the root of the fountain. Yellow, containing all colours, is white in its extreme.
F=the notes E and G mingled. Green=yellow and blue mingled.
G contains all tones. Blue, with more or less of black and white.
A=G and B mingled. Violet=blue, and all colours, inclining to black.
B, the key-note of the fountain. Ultra-violet=violet mingled with more black: a deeper shade of all colours—in its extreme, black. Orange, red and yellow mingled.
[Harmonies of Tones and Colours, On Colours as Developed by the same Laws as Musical Harmonies3, page 20]

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]

"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 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 twelve which develope twelve major harmonies are written thus

Half Note

the other six which are incapabable of developing major harmonies thus

Whole Note

without regard to musical time. The seven colours are shown to answer to the seven white notes, the other five being intermediate tones and colours. A flat marked to a note indicates that it is nearer to the tone or colour below; a sharp means that it is nearer to the tone or colour above. The notes and chasms are not written according to accurately measured degrees. [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]

The 18 tones of keyed instruments are represented round this circle, and again below in musical clef. As all, with the exception of G♭ and A#, become in turn either Major or Minor Key-notes, or both, no distinction is made between tones and semitones throughout the scheme. In this diagram the 12 Major Key-notes are written thus

Half Note
[Harmonies of Tones and Colours, Diagram I - Eighteen Tones of Keyed Instruments, page 22c]

the 7 white notes of a keyed instrument are here coloured; the intermediate tones, shown by a flat or a sharp marked to a note, are left uncoloured, being intermediate tints. [Harmonies of Tones and Colours, Diagram I - Eighteen Tones of Keyed Instruments, page 22c]

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]

This diagram represents the two last major primaries of a series of 12; 12 of a higher series follow, and the two first of a still higher series: the secondaries are written below the primaries, the sharps or flats belonging to the different harmonies are written to each note. 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 harmonies require.
By reference to previous coloured notes it will be seen that all these agree. [Harmonies of Tones and Colours, The Two Last Major Primaries, page 24e]

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]

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]

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]

Below the circular diagram are seen in musical clef the twelve minor key-notes, as gained from the majors. There is only one meeting of the same note in the seven of every major harmony. All the twelve follow the same plan; the lowest note of the seven of C is F, the highest note of the seven is E. The lowest tone sounded by E and the highest tone sounded by F is the same, A—leading the ear from C to its relative minor A. [Harmonies of Tones and Colours, The Minor Harmonies, page 33a]

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]

If we examine the line last quoted by the laws of life which regulate the foregoing scheme, we may compare it with the fundamental threefold chord of the scale of C and its relative colours,

C red rises

from the fountain key-note which contains in itself all tones. "Him first," the Son of God proceeding from the Almighty, and yet in Himself the Trinity in Unity. E, yellow or light. E is the root of B, ultra indigo, or black. "Him midst," the Almighty Father, the Fountain of life, light gradually rising and dispelling darkness. G, blue, "Him last," the Holy Spirit, proceeding from the Father and the Son, Trinity in Unity. The Son of God and the Holy Spirit are the complemental working pair throughout the universe; each containing "the seven spirits of life." Red and blue contain all colours in each. C and G are a complemental pair, C rising from the fountain key-note which contains in itself all tones, and C and G combine all tones in each. In Chapter III. it is explained that all varieties of tones and colours may be condensed into this pair, rising from and falling again into the fountain. [Harmonies of Tones and Colours, Reflections on the Scheme2, page 44]

1871.—"There has been much written lately respecting colour and tone, but nothing bearing on your own view." "The new theories in music seem inclined to go back to the ancient faith of Pythagoras, everything being used up with the modern notions of tonality. Perhaps we may find a great change at hand; the present system, limiting, as it does, that which is illimitable, cannot be right." [Harmonies of Tones and Colours, Extracts from Dr. Gauntlett's Letters1, page 48]

1873.—"It seems to me, from so many curious coincidences, that truth lies within, the system." "I by no means resign the possibility of being able to satisfy myself." "There is no insuperable objection that I can see." "Your theory of the illimitable nature of tones, the limits of six as a one complete and perfect view, and the simplicity of the three pairs, dwell much on my mind. I believe it to be quite new, and in one way or the other quite true." [Harmonies of Tones and Colours, Extracts from Dr. Gauntlett's Letters1, page 48]

Rudolf Steiner
Tone, however, is a direct expression of the will itself, without interpolation of the mental image. When man is artistically engaged with tone, he puts his ear to the very heart of nature itself.” [Rudolf Steiner]

Hans Jenny
“The more one studies these things, the more one realizes that sound is the creative principle. It must be regarded as primordial. No single phenomenal category can be claimed as the aboriginal principle. We cannot say, in the beginning was number, or in the beginning was symmetry, etc. These are categorical properties which are implicit in what brings forth and what is brought forth. By using them in description we approach the heart of the matter. They are not themselves the creative power. This power is inherent in tone, in sound.” [Hans Jenny]

See Also

double tone
double tones
Eighteen Attributes or Dimensions
Imperfect tone
Laws of Being
music note or sound colors
Part 08 - What Vibration Is. - Part 1
Part 09 - What Vibration Is. - Part 2
Part 11 - SVP Music Model
Progressive Evolution
six tones
Square Law
whole tone
12.40 - Color
12.42 - Tone

Created by Dale Pond. Last Modification: Friday April 9, 2021 04:59:03 MDT by Dale Pond.