Usually refers to difference tones
"The maximum test was made to placing an iron weight of 580 lbs. on the extreme end of the long arm of the lever. To lift this weight required a pressure of 18,900 lbs. to the square inch counting the difference in the length of the two arms and the area of the piston. When Keely turned the valve-wheel leading from the receiver to the flexible tube and through it into the steel cylinder beneath the piston, simultaneously with the motion of his hand the weighted lever shot up against its stop a distance of several inches, as if the iron were cork. [Snell Manuscript - The Book, page 3]
The following definitions of weight are in keeping with Natural Law.
Weight is the sum of the differences between the two pressures which act upon every mass.
Weight is the measure of the differences in electric potential between any mass and the volume it occupies.
Weight is the measure of unbalance between any mass and its displaced environment.
Weight is the measure of the force which a body exerts in seeking its true potential.
Weight is the sum of the difference between the inward pull of gravitation and the outward thrust of radiation.
Weight is the measure of intensity of the desire within all matter to express motion or seek rest from motion. [Walter Russell, The Secret of Light, pages 184-185]
Blood formation or blood decomposition - synthesising or analysing current - vitalisation or devitalisation - health in mind and body or disease, death and economic disaster, all these are decreed by what in the opening paragraph science calls molecular motion whilst having no knowledge of the differences in the forms of motion, which not only determine existence or non-existence, but also all economic progress or decline. [The Energy Evolution - Harnessing Free Energy from Nature, The Life-Current in Air and Water]
Eight hundred million people, i.e. about one third of those alive today , will be mercilessly condemned to starve, if at the final hour it is not possible to produce the practical examples necessary to open the eyes of those who do not perceive the differences between different current-sources, from which, depending on the choice of trifling starting impulse - life or death originate. [The Energy Evolution - Harnessing Free Energy from Nature, The Life-Current in Air and Water]
palatable in order to act as levitational fuel for the others (viz. the branches swaying in the wind, whose source of motion - the wind - also arises through reactive differences in temperature). The vertically disposed forces of cyclones, typhoons, hurricanes, etc. are also founded on this developmental process and owe their kinetic energy to cold processes of oxidation. [The Energy Evolution - Harnessing Free Energy from Nature, New Forms of Motion and Energy]
When the fruit juices that have flourished in the Sun begin to ferment, it is a sign that reactive temperature differences have triggered the fermenting movement, which in the initial stages has to separate the inferior from the superior. The former will be separated and centrifugated out through cycloid-space-curve-motion. The latter interconnects with itself, as it were, and the product of this remarkable marriage process is that something, which also brings us out of the delicately balanced equilibrium that the Earth ceaselessly enjoys. Not being in a state of stable equilibrium, she has constantly to rotate about her own axis in a form of movement that declinates and oscillates in two directions. This is how she generates the inversely symmetrically- and inversely proportionally-acting force, which enables everything that crawls and flies on this dung-heap Earth to move 'originally' (autonomously) in order to seek out its food, which also contains allotropic energy-producing substances. These are then broken down through the vibration of the organs, leading to the familiar development of physical strength and mental vigour, whose ur-causes have not been perceived by physico-technical scientists, who calculate with common calories and measure them with decimal scales and rulers. Moreover, they also believe they have captured everything with their tweezers that is proper to Nature. Unfortunately, however, this cannot be accomplished with such an instrument, because the producer of 'measure' and 'weight' is an imperceptible extraordinary energy-form, which as the 'essential' is the 'reactivated' itself, which actively moves the ordinary. [The Energy Evolution - Harnessing Free Energy from Nature, New Forms of Motion and Energy]
This two-fold interplay of perpetual motion can be directly observed and studied in deep, cool cellars, for through differences in temperature, what has grown large in the Sun and then reduced in size by squashing, will be moved 'cycloidally' in the cellar. First refined, then made 'cloudy', it slowly becomes clear after termination of this adolescent period. This is how wise Nature operates, who is known to have unlimited developmental periods at her disposition for all things. We, poor souls, to whom only a single, unique life is available in which we will also be forced to make use of cycloid-space-curve-motion in order to alleviate almost intolerable reactive energies through their abreaction, will have to behave more sensibly in order to become somewhat more blissful while still on this Earth than has been the case due to the efforts of 'active' technicians. In other words, we must reverse the way things are done. Cycloid-space-curve-motion must therefore be given pride of place, which logically leads to the almost cost-free mechanical generation of reactive differences in potential, which in turn give rise to increased and intensified active differences in motion. Harnessed once more, these trigger further high-grade differences in potential of a reactive nature, and so on and so forth until temperatures and reactive forces of such a kind are triggered that it is a veritable art to devise an operating load heavy enough to brake and control these elemental suctional and pressural forces. At the right time, therefore, we must keep our eyes open for the specialists and experts, who function as super-brakes on development!! Most certainly, however, we must replace those, who today brake the normal course of development with the reversed interplay of forces, which they do in such a way as to increase and intensify precisely those kinds of energy that promote decomposition and the expulsion of what is unsuitable for further development. In so doing they trigger a form of perpetual motion, because here too the self-intensifying decomposive and repulsive forces also increase by the square owing to the cycloid-space-curve-motion of the Earth. Sadly they do not see what they have themselves created, namely boundless decline and disintegration instead of an equally [The Energy Evolution - Harnessing Free Energy from Nature, New Forms of Motion and Energy]
In the same way that it would be impossible, for example, for human beings and animals to reproduce and further develop (increase and qualitatively improve), were Nature not to enforce an interaction between their primary sexual substances through intolerable urge-driven differences in tension, which function reactively, there would likewise be no possibility for the reproduction and further development of plants, minerals and metals, and the physical (active) forms of heat and cold. Today's science is not only founded on a false developmental basis, but also on too low a level of knowledge. It ignores the formative reaction and using combustion processes gives pride of [The Energy Evolution - Harnessing Free Energy from Nature, The Practical Application of Cycloid-Space-Curve-Motion arising from Processes of Cold Oxidation]
What triggers this reaction is the well-known dynamics of the sexual urge, which re-establishes equilibrium between intolerable differences in tension and potential. Because these differences are always present, this original form of movement will constantly be provoked by a motivating force that never wanes. As a form of motion, we are here primarily concerned with the motion that the Earth has demonstrated to us since the beginning of time. Referred to as 'cycloid-space-curve-motion', it is synonymous with what the naturalistic doctor calls the 'life-creating life-spiral', and the biotechnologistcalls 'double screw-form wave motion'. [The Energy Evolution - Harnessing Free Energy from Nature, The Economy Founded on Reactively Produced Energy]
These concentrations of subtle matter are bacteriophagous threshold conformations (being neither corpuscular, nor metaphysical embryos) in which the opposing energy-forms mentioned at the beginning are suspended, which oscillate gently in liquid or gaseous media in a wavering state of equilibrium. That is to say, they possess too much levitational force to gravitate and too much lower-grade mass to levitate autonomously. Their inner processes of motion are sustained by the ambient differences in temperature. These, however, are insufficient to determine the fate of these threshold substances as they vacillate at this cross-roads. [The Energy Evolution - Harnessing Free Energy from Nature, Magnetism - Electricism]
"In the outbirth of water we have to differentiate between two different kinds. Namely water as a carrier-substance that contains predominantly negative potentialities (substances attuned to earth frequencies) or predominantly positive potentialities (substances attuned to air frequencies). The former are to be viewed as upwardly-impelling geospheric instrumentalities and the latter as downwardly-impelling atmospheric instrumentalities. The former refine and exalt the higher-grade constituents, i.e. they serve the build-up of levitative potencies. The latter serve to cleanse the atmosphere of suspended matter, which as threshold substances still possess too little self-weight and too high a quota of levitative essences and can neither rise nor fall. It is these threshold substances that can be transformed and exalted through cycloid-space-curve motion. From a practical point of view, this is only possible through their co-oscillation with their respective carrier-substances, be it air or water. This leads to a build-up of those substances incapable of further development, resulting in a renewed intensification of the differences in potential through the spacial separation of the difference-substances. The end result is an increased motive force. This explains the concept of perpetual motion in its most natural sense." [Viktor Schauberger, Implosion Magazine, No. 118, p. 8.] [The Energy Evolution - Harnessing Free Energy from Nature, THE NATURE OF WATER - ITS CONDUCTION AND USE FOR TRANSPORT]
The origins of all motion are differences in potential. If these differences cannot be maintained during flow, the water's kinetic energy wanes and the sediment is deposited in the wrong place. New bends are formed in this way, which have a greater significance than has hitherto been assumed. [The Energy Evolution - Harnessing Free Energy from Nature, The Transport of Ore in Double-Spiral-Flow Pipes]
A second cause of difference in degree of contrast between two notes and other two notes in which the ratios are the same lies in this - whether the two notes belong to one chord or to different chords. Two notes in the subdominant chord have a different contrast from two in the dominant chord which have the same ratio. [Scientific Basis and Build of Music, page 61]
A third cause of difference of contrast in notes is the individual character which belongs to them according to their place in the genetic scale - that is, their birthplace character - the amount, namely, of centrifugal force which they have inherited. [Scientific Basis and Build of Music, page 61]
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]
And it is another very interesting fact that those numbers multiplied into each other always make 720, the number in the minor genesis which corresponds to 1 in the major; F1 being the generative root of the major, and B720 the generative top of the minor; so adjusted they place the two D's beside each other - D26 2/3 and D27 - and we see the comma of difference between these two numbers which are distinctive of the major and the minor; 26 2/3 x 3 = 80, and 27 x 3 = 81, and 80:81 is the ratio of the comma. This is the Ray and the Rah in which there lurks one of music's mysteries. Let him that is wise unravel it. It is symbolic of something in the spiritual realm of things; its full meaning is only found there. [Scientific Basis and Build of Music, page 88]
When 25 pendulums are arranged and oscillated to represent the different musical ratios in their natural marshalling, they will all meet at 1 when 64 of the highest is counted. This plate is intended to show that there are two kinds of meeting and passing of the pendulums in swinging out these various ratios. In the ratio of 8:9 the divergence goes on increasing from the beginning to the middle of the period, and then the motion is reversed, and the difference decreases until they meet to begin a new period. This may be called the differential way. In the ratio of 45:64 there is an example of what may be called the proximate way. In this kind of oscillations meet and pass very near to each other at certain points during the period. In 45:64 there are 18 proximate meetings; and then they exactly meet at one for the new start. This last of the ratios, the one which finished the system, is just as if we had gone back to the beginning and taken two of the simplest ratios, [Scientific Basis and Build of Music, page 105]
save the octave, and made them into one, so that in its proximate meetings during its period it seems composed of the ratio 2:3 twelve times, and 3:4 seven times; twelve times 2 and seven times 3 are 45; twelve times 3 and seven times 4 are 64. This long period of 45 to 64 by its proximate meetings divided itself into 19 short periods, and oscillates between the ratios of 2:3 and 3:4 without ever being exactly the one or the other; the difference being always a very small ratio, and the excess of the one being always the deficiency of the other. This fifth, B to F, has been misnamed an "imperfect fifth." When these two notes in the ratio of 45:64 are heard together, the oscillating proximately within it of the two simple ratios gives this fifth a trembling mysterious sound. [Scientific Basis and Build of Music,page 106]
This plate is a representation of the area of a scale; the major scale, when viewed with the large hemisphere, lowest; the minor when viewed the reverse way. It is here pictorially shown that major and minor does not mean larger and smaller, for both modes occupy the same area, and have in their structure the same intervals, though standing in a different order. It is this difference in structural arrangement of the intervals which characterizes the one as masculine and the other as feminine, which are much preferable to the major and minor as distinctive names for the two modes. Each scale, in both its modes, has three Fifths - subdominant, tonic, and dominant. The middle fifth is the tonic, and its lowest note the key-note of the scale, or of any composition written in this scale. The 53 commas of the Octave are variously allotted in its seven notes - 3 of them have 9 commas, 2 have 8, and 2 have 5. The area of the scale, however, has much more than the octave; it is two octaves, all save the minor third D-F, and has 93 commas. This is the area alike of masculine and feminine modes. The two modes are here shown as directly related, as we might figuratively say, in their marriage relation. The law of Duality, which always emerges when the two modes are seen in their relationship, is here illustrated, and the dual notes are indicated by oblique lines across the pairs. [Scientific Basis and Build of Music, page 106]
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]
In the center column are the notes, named; with the lesser and larger steps of their mathematical evolution marked with commas, sharps, and flats; the comma and flat of the descending evolution placed to the left; the comma and sharp of the ascending evolution to the right; and in both cases as they arise. If a note is first altered by a comma, this mark is placed next to the letter; if first altered by a sharp or flat, these marks are placed next the letter. It will be observed that the sharpened note is always higher a little than the note above it when flattened; A# is higher than ♭B; and B is higher than ♭C, etc.; thus it is all through the scales; and probably it is also so with a fine voice guided by a true ear; for the natural tendency of sharpened notes is upward, and that of flattened notes downward; the degree of such difference is so small, however, that there has been difference of opinion as to whether the sharp and ♭ have a space between them, or whether they overlap, as we have shown they do. In tempered instruments with fixed keys the small disparity is ignored, and one key serves for both. In the double columns right and left of the notes are their mathematical numbers as they arise in the Genesis of the scales. In the seven columns right of the one number-column, and in the six on the left of the other, are the 12 major and their 12 relative minor scales, so arranged that the mathematical number of their notes is always standing in file with their notes. D in A minor is seen as 53 1/3, while the D of C major is 54; this is the comma of difference in the primitive Genesis, and establishes the sexual distinction of major and minor all through. The fourth of the minor is always a comma lower than the second of the major, though having the same name; this note in the development of the scales by flats drops in the minor a comma below the major, and in the development of the scales by sharps ascends in the major a comma above the minor. In the head of the plate the key-notes of the 12 majors, and under them those of their relative minors, are placed over the respective scales extended below. This plate will afford a good deal of teaching to a careful student; and none will readily fail to see beautiful indications of the deep-seated Duality of Major and Minor. [Scientific Basis and Build of Music, page 109]
with her irrevocable proportions to measure his scales for him. The stars at the C of the first scale and at the B# of the last show the coincidence of 12 fifths and 7 octaves. The number of B# is 3113 467/512; C24 multiplied 7 times by 2 brings us to the number 3072; these two notes in the tempered system are made one, and the unbroken horizon of the musical world of twelve twofold keys is created. The very small difference between these two pitches is so distributed in the 12 tempered scales that no single key of the 12 has much to bear in the loss of perfect intonation. [Scientific Basis and Build of Music, page 118]
Fig. 1. - This figure shows the major and minor measured in commas and placed directly as they stand related, major and relative minor, the minor being set a minor third lower than the major. The interval between C and E in the minor is an 8-and-9-comma interval; between C and E in the major it is a 9-and-8-comma one. This difference arises from the minor D being a comma lower than the major D. In all the other intervals minor and major are the same. [Scientific Basis and Build of Music, page 120]
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]
The roots of the minor chords
—The difference between a major and a minor chord
—The chords of the twelve keys in musical clef, those of A coloured, . . .37 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]
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]
Figure 8.6 - Difference Tones
electric potential difference
electrostatic potential difference
Figure 8.6 - Difference Tones
Ramsay - The Nature and Origin of Difference Sounds