Sympathetic Vibratory Physics | Mode (original) (raw)

MUSIC (1) A scale. (2) A species of scale, as, mode, mode, Greek modes, etc. [Dictionary of Music]

A system of scales in ancient Greek and early church music made up of octaves and using only the notes represented by the white keys of the piano.

SOUND & VIBRATION Frequency or resonance pattern in a media such as Chladni Plate Vibrations or .

Longitudinal Wave Compression/Sound
Rayleigh Wave Vortex, Surface, Love or Lamb Wave
Transverse Wave

's Modes of Vibration

There are properties or modes of vibration which can direct the component vibrations of a to the neutral center of that . These modes of vibration are called "neutral attraction", "neutral affinity", "negative attraction" or "polar negative attraction." [MASS VIBRATIONS]

" and dispersion are kept up on the atmospheric envelope of the by the and interatomic conflict as "between the dominant and the enharmonic". This is brought about by the reception and dispersion of sympathetic streams, the ruling mode of whose vibration is the dominant, and the of the coarser grades of matter, whose ruling vibratory mode is the enharmonic.

As every consists of vibrations in , balanced in harmonic equilibrium without cancellation or diminution of energy, it stands therefore in harmonic relation to every other . All forms of matter and of are thus interrelated and . Through resonance, increasing this sympathy, we can control the states of matter." [Mass action, Snell Manuscript - the book]

When Keely's discovery has been made known to scientists, a new field of research will be opened up in the realm of Philosophy, where all , , and truths are correlated; for Philosophy has been well defined by as the of that human thought which contains all human knowledges. He who possesses the structure of philosophic wisdom built up of all knowledges - grand and sublime - has a mental abode wherein to dwell which other men have not. Dr. says:- "The nearer we to the of being and of , the more magical must everything inevitably become, for that is pure volition. And pure volition, as a cause, is precisely what is meant by ; for by is merely meant a mode of producing a without appliances - that is, without that seeming continuity of resisting parts and that which satisfy our muscular and our , and bring the into the of what we call 'the natural' - that is, the of the , the gravitating, the into which the vis inertiae is alone admitted." In 's , as in Dr. 's "Sketch of a Philosophy," the of creation is not regarded as a of all in one , which is the popular , but as a in which, after and as its fruit, the last gives again the first. Herein is found the by which the law of continuity is maintained throughout, and the of things is made to be complete: - the which is missing in the popular of the day, with this very serious , that, to keep the break out of sight, the entire of spirit and the world is ignored or denied altogether." [The Fountain Head of Force]

Normal Mode
A normal mode of an oscillating system is a pattern of in which all parts of the system move sinusoidally with the same and with a fixed relation. The described by the normal modes is called resonance. The frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge or molecule, has a set of normal modes that depend on its structure, materials and boundary conditions.

When relating to music, normal modes of vibrating instruments (strings, air pipes, drums, etc.) are called "" or "overtones".

The most general of a system is a of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an of one mode will never cause of a different mode.

The concept of normal modes also finds application in wave theory, , quantum mechanics, and dynamics." Wikipedia, Normal Mode

In the , of , which operates along the transverse axis (centrifugally), i.e. in an axial->radial mode, the magnetism (= ) here acts as the resistance. Compared to the , it appears to be in a certain of , the of its resistance or commensurately with the of the downwardly (= ). This is the of the tragic that in all the resistance increases by the square of the . However, in this only happens when any given (matter) is made to move technically, hydraulically or dynamically[2], i.e. axially->radally (centrifugally), therefore unnaturally. For if any given (matter) is made to move radially->axially (centripetally), then the upwardly flowing magnetism () increases at the expense of the () () and thus the naturally ordained formative and levitative forces in proportion to the (radial->axial) rotational velocity. With this of , which is of course only possible with very special shapes (profiles), the effective amounts to about 96%. In this case only about 4% of the formative energies are lost in producing the resistance to required by . In , and precisely the is the case and this is how the enormous of came about, which is exclusively expended in a manner of . [The Energy Evolution - Harnessing Free Energy from Nature, Magnetism is the Function of Levitism and Electricism is the Function of Gravitism]

Ramsay

BY THE EDITOR

The Greeks most probably constructed their musical tetrachords in a symmetrical order in analogy with their sculpture, and showed the identical with the in its love of . With them, therefore, the Dorian mode would have a certain pre-eminence. Beginning this mode on D, without knowing the musical mystery that resides in D, they had two tetrachords with the semitones symmetrically in the in one mode; it was next possible for them to arrange in pairs, symmetrically, the other tetrachords.

D8 E5 F9 G8 A9 B5 C9 D

E5 F9 G8 A9 B5 C9 D8 E — C9 D8 E5 F9 G8 A9 B5 C

F9 G8 A9 B5 C9 D8 F5 F — B5 C9 D8 E5 F9 G8 A9 B

C9 D8 E5 F9 G8 A9 B5 C — E5 F9 G8 A9 B5 C9 D8 E

B5 C9 D8 E5 F9 G8 A9 B — F9 G8 A9 B5 C9 D8 E5 F

A9 B5 C9 D8 E5 F9 G8 A — G8 A9 B5 C9 D8 E5 F9 G

G8 A9 B5 C9 D8 E5 F9 G — A9 B5 C8 D9 E5 F9 G8 A

[Scientific Basis and Build of Music, page 45]

Here, then, we have an order of modes entirely symmetical in pairs placed thus; the only mode that can stand alone being the Dorian, built on D, whose duality has been discovered to reside in itself. All this build of , which was the watchword of Greek art, as it is also one of the watchwords of , presupposes that the tones of the scale, with lesser and larger intervals lying between them, were resting in their ears exactly as they are in ours,1 and as they are in all humanity, save where it has sunk down into the savage condition, benighted in the that is in the world. It is not to be concluded that the Dorian mode is Nature's primitive scale, although it might have a certain pre-eminence [Scientific Basis and Build of Music, page 45]

among the Greeks on account of having 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 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 modes above. Without seeing the genetic origin of music's duality they were led to arrange the modes by , which is one of the phases of duality. Symmetry is duality in practice. It may not always be apparent how originates in ; but in music, the art of the , duality emerges in the of the minor scale; in the true mathematical build of the on the root of the major subdominant F, and the true relation of the to it in the inverse genesis descending from the top of the minor dominant B. [Scientific Basis and Build of Music, page 46]

There was, then, something of truth and in the Greek modes as seen in the light now thrown upon them by the Law of Duality, at last discerned, and as now set forth in the and wedlock of the major and minor scales. The probably symmetrical arrangement of the modes, all unwitting to them, is an interesting exhibition of the true duality of the notes, which may be thus set in view by duality lines of indication. We now know that B is the dual of F, G the dual of A, C the dual of E, and D minor the dual of D major. Now look at the Greek modes symmetrically arranged:

D EF G A BC D

C D EF G A BC EF G A BC D E

A BC D EF G A G A BC D EF G

F G A BC D EF BC D EF G A B

Thus seen they are perfectly illustrative of the duality of music as it springs up in the genetic scales. The lines reach from note to note of the duals. [Scientific Basis and Build of Music, page 46]

The triplet B, D, F, has been called the imperfect triad, because in it the two diatonic semitones, B-C and E-F, and the two minor thirds which they constitute, come together in this so-called imperfect fifth. But instead of deserving any name indicating imperfection, this most interesting triad is the of the chromatic chord, and of the chromatic system of chords. Place this triad to precede the tonic chord of the key of C major, and there are two semitonic progressions. Place it to precede the tonic chord of the key of F# major, and there are three semitonic progressions. Again, if we place it to precede the tonic chord of the key of A minor, there are two semitonic progressions; but make it precede the tonic chord of E? minor, and there are three semitonic progressions. This shows that the chromatic chord has its in, and its outgrowth from the so-called "natural notes," that is notes without flats or sharps, notes with white keys; and that these natural notes furnish, with only the addition of either A? from the major scale or G# from the minor, a full chromatic chord for one major and one minor chord, and a secondary chromatic chord for one more in each mode. [Scientific Basis and Build of Music, page 52]

not mathematically identical, the genetic number of the last D, the top of the dominant major, being 27, and that of the first D, the root of the subdominant minor, being 26 2/3. Well, in the triplets of the we have minor thirds below their middles, D-F, A-C, E-G. In the triplets of the we have minor thirds above their middles, A-C, E-G, B-D. But here between the triplets of the two modes we have a triplet which has minor third both below and above its middle note, two minor thirds and nothing else, B-D-F. Here, then, the Diatonic progression chords presents us with a 3-note Chromatic chord, and marchals us the way that we must go to find [Scientific Basis and Build of Music, page 54]

This great genetic scale, the all-producer, the all-container, extends over six octaves on each side; for it is not till high in the sixth octave we get B in the , and it is not till low in the sixth octave that we get F in the . It is in the fifth octave, however, that the note which is the distinctive mark of the and modes is generated. D27 in the , and D26 2/3 in the , distinguishes the sex of the modes, and shows which is the head and which the helpmeet in this happy family.2 On the side F, the root of the subdominant chord, that is the chord which is a below the key-note C, is the of all. This is the beginning of this creation. If we call the of F one, for simplicity's sake, then F1 is multiplied by 3 and by 5, which natural process begets its , C, and its , A; this is the , , and of the first chord. From this , C3, grows the next chord by the same natural process, multiplying by 3 and by 5; thus are produced the and of the second chord, G and E. From the top of this second chord grows the third and last chord, by the repetition of the same natural process; multiplying G9 by 3 and by 5 we [Scientific Basis and Build of Music, page 66]

At the extremes of these two operations we find D the top of the major dominant, and D the root of the minor subdominant; and while all the other notes, whether produced by of the roots or division of the tops, are the same in their ratio-numbers, the two D's, by no speciality of production, are nevertheless specifically diverse by one comma in their , and make a corresponding diversity in the intervals of the two modes. These, the Ray and Rah of the Sol Fa expression, originate a very interesting and somewhat mysterious feature in this great twofold genetic scale. [Scientific Basis and Build of Music, page 67]

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 development of ." It is true, indeed, that the is the last judge; but the is to judge something which it does not create, but simply judges. is the maker of music in its scales and modes. The styles of 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 of the beautiful, rather than the 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 of a musical tone, that is, its quality or , depends on the number and comparative strength of the partial tones or 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 of times and individuals, for these partials are under 's mathematical usages, and quite beyond any for man's to change. It is these very partials or 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 every musical sound, which constitute the musical system of sounds. [Scientific Basis and Build of Music, page 78]

This plate is a representation of the area of a scale; the major scale, when viewed with the large , lowest; the when viewed the reverse way. It is here pictorially shown that and does not mean larger and smaller, for both modes occupy the same , and have in their structure the same intervals, though standing in a different . It is this in structural arrangement of the intervals which characterizes the one as and the other as , which are much preferable to the and as distinctive names for the two modes. Each scale, in both its modes, has three Fifths - subdominant, , and dominant. The middle fifth is the , and its lowest note the key-note of the scale, or of any written in this scale. The 53 commas of the are variously allotted in its 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 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 , is here illustrated, and the dual notes are indicated by oblique lines across the pairs. [Scientific Basis and Build of Music, page 106]

mathematical genesis, as seen in its D being a comma higher than that of the . This gravity and of the modes is a striking feature of them. In the Thirds it is different from the ; the larger of each seems gravitating toward the center of the tonic chord. The area of the scale has then the aspect of a with its north and south poles, and pervaded by a towards the center; the center itself being as to . [Scientific Basis and Build of Music, page 107]

The being divided into 53 commas, the intervals are measured, as usual, by these, the large second having 9-commas, the medium second having 8, and the small second 5. These measures are then made each the by which to draw hemispheres showing the various and comparative areas of the seconds. The comparative areas of the are shown by the hemispheres of the seconds which them facing each other in pairs. The comma-measures of the various thus determined are then made the radii by which to draw the two hemispheres of the fifths. The areas of the three fifths are identical, as also the attitudes of their unequal hemispheres. The of the six , on the other hand, in their two kinds, being reversed in the upper and under halves of the scale, their gives them the appearance of being attracted towards the center of the ; while the of the three fifths is all upward in the , and all downward in the ; their attraction being towards the common center of the twelve scales which has placed between the of the and the fourth of the , as seen in the two D's of the dual genetic scale, - the two modes being thus seen, as it were, revolving [Scientific Basis and Build of Music, page 113]

round a common center which is lying between them, as the double stars do in the astral heavens. When this plate is reversed we have before us exactly the minor scale, and all the parts and attitudes related in exactly the way, each to each, so perfect is the duality in unity of the two modes. [Scientific Basis and Build of Music, page 114]

The scales in this plate advance by semitones, not in their normal way by fifths; but their normal progress by fifths is shown by the line winding round under the and touching the ellipses containing the scales by semitonic advance; the scales being read to the right for the majors inside, and to the right for the minors outside. In each of the modes the scales are written in ?s and #s, as is usual in signatures; and since the scales [Scientific Basis and Build of Music, page 116]

advance by semitones, the keys with ?s and #s alternate in both modes. The between G# and A? in the , and between D# and E? in the , is in each mode, and the scale made one. The dotted lines across the plate lead from to relative minor; and the solid spiral line starting from C, and winding left and right, touches the consecutive keys as they advance normally, because genetically, by fifths. The relative major and are in one at C and A; and in the right opposite this the relative to F# is D#, and that of G? and E?, all in the same , and by one set of notes, but read, of course, both ways. [Scientific Basis and Build of Music, page 117]

This is a twofold mathematical table of the and modes of the twelve scales, the so-called and relative minor. The is set a minor third below the in every pair, so that the figures in which they are the same may be beside each other; and in this , in the fourth column in which the figures of the major second stand over the minor fourth, is shown in each pair the sexual note, the being always a comma lower than the . An index finger points to this distinctive note. The note, however, which is here seen as the distinction of the feminine mode, is found in the of the preceding masculine scale in every case, except in the first, where the note is D26 2/3. D is the of the octave scale of A minor, and the Second of the octave scale of C major. It is only on this note that the two modes differ; the major Second and the minor Fourth are the sexual notes in which each is itself, and not the other. Down this column of seconds and fourths will be seen this sexual distinction through all the twelve scales, they being in this table wholly developed upward by sharps. The is always left this comma behind by the of the . The major A in the key of C is 40, but in the key of G it has been advanced to 40 1/2; while in the key of E, this relative minor to G, the A is still 40, a comma lower, and thus it is all the way through the relative scales. This note is found by her own downward from B, the top of the feminine dominant. But it will be remembered that this same B is the middle of the dominant of the masculine, and so the whole feminine mode is seen to be not a terminal, but a lateral outgrowth from the . Compare Plate II., where the whole twofold yet continuous is seen. The mathematical numbers in which the vibration-ratios are expressed are not those of concert pitch, but those in which they appear in the genesis of the scale which begins from F1, for the sake of having the simplest expression of numbers; and it is this series of numbers which is used, for the most part, in this work. It must not be supposed, however, by the young student that there is any necessity for this . The from which to begin may be any ; it may, if he chooses, be the of F. But let him take good heed that when he has decided what his will be there is no more coming and going, no more by him; comes in [Scientific Basis and Build of Music, page 117]

This plate sets forth the essential duality of the musical system of vibrations. It is a remarkable fact that the numbers of the vibrations of the major mode are the numbers for the string proportions of the minor mode; and vice versa, the string proportions in the are the numbers of the vibrations in the . We have, however, to see that we use the proper notes and numbers; we must know the of . This rests in the duality of the notes, and begins from the two D's. The center of gravity of the musical system of vibrations is found in the comma space between the two D's as they are found in the of the two modes. In these two D's the vibration number and string proportions are nearly identical. Starting from this point as the center of gravity in the [Scientific Basis and Build of Music, page 118]

Another remarkable thing is that these dual numbers, when multiplied into each other, always come to 720. Now this , as we see in the great , corresponds to 1 in the , being the point of departure for the development of the feminine mode, as 1 is the point of departure in the masculine mode. This 720 is the octave of 360, which is the of the degrees of the circle, so divided in the hidden depths of human antiquity; and when F1 becomes F2, then B360 is the answering note and in the dual system. All the notes in the development are above F2; and all the notes in the development are below B360. The unoccupied octave between F1 and F2 and that between B720 and B360 may be counted as the octave heads or roots of the two modes, and then F2 and B360 as the points from which the development of music's diversity begins; and it is noteworthy that the of the degrees of the circle should be found in this connection. When was the circle so divided? Who divided it so? And why did he, the unknown, so divide it? Was 's known in that far-off day before the confusion of man's sinking history had blotted out so much of the pure knowledge of pristine days? [Scientific Basis and Build of Music, page 119]

Fig. 2. - In this figure the two modes are placed in their relation, in order to show the notes standing opposite each other in their duality. Here the two D's come also opposite each other, inasmuch as in the two modes the C-D-E interval is inverted, becoming C D E in the one and E D C in the other. And so the 9-comma second between C and D in the comes opposite the 9-comma second between D and E in the , and the two 8-comma seconds, of course, come opposite each other also. [Scientific Basis and Build of Music, page 120]

Fig. 4 is a setting of the minor and the major chord-scales, showing how they stand linked by notes in common in their direct sequence from dominant minor to dominant major. To each of the six chords is placed the first chromatic chord, showing how it resolves in its three-fold manner by 1, 2, and 3 semitonic progressions in each mode, and by 1 and 2 notes in common variously in each mode; and here again the law of duality is seen in its always symmetrical adjustments. , when once clearly and familiarly come into possession of musicians, will be sure to become an operative and in . [Scientific Basis and Build of Music, page 121]

The of the equinoctial points is a well-known fact. It will be seen how apparent this is in the developments of . From the moment that trinities depart from , the balance is unequal, and the repeated endeavours after closer cause a perpetual restlessness. May not this want of be the life or motive power of the entire , with its continuous struggle after , even to oneness? "Closer and closer 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 and , 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 than the , and the correct , 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 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 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 F rise from the chasms. B, the key-note, and E, its , sound the octave higher of the B. The generation of is by one law a simple mode of . Each major key-note and its tones embrace the eighteen tones of keyed instruments which all lie in 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 of its own system, has its own point of rest, and after rise and enlarge, or fall and diminish infinitely. [Harmonies of Tones and Colours, Diagram I - The Eighteen Tones of Keyed Instruments, page 22a]