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genesis

noun: the first book of the Old Testament: tells of creation; Adam and Eve; the Fall of Man; Cain and Abel; Noah and the flood; God's covenant with Abraham; Abraham and Isaac; Jacob and Esau; Joseph and his brothers
noun: a coming into being, birth

Music
Ramsay
"While Mr. Ramsay was meditating on these teachings of the great mathematician, Euler, and studying these notes and their vibrations, he was led to discover that the order of quantities above F, when taken below B, constitutes the Minor System. This was the discovery of the Law of Duality in Music. This Law of Duality in Mr. Ramsay's hands asserts an importance not second even to the Law of Mathematical Ratios which rules in the genesis of the notes." [Scientific Basis and Build of Music, page 8]

GENESIS. - The begetting and birth of notes by numbers. [Scientific Basis and Build of Music, page 25]

It runs in all the polarities of Nature. Music, as belonging to Nature - as one of the things which the Great Numberer hath created - is under this Law of Duality as well as that of mathematical ratios and other laws. The Law of Duality in music gives the major and minor systems. As the major is derived from certain primes in ratios ascending, and the minor from the same primes in the same ratios descending, they are inversely related; and these diatonic scales have in the responding parts exactly the same quantities. But as multiplying by 3 three times gives the framework of the major system in the ascending genesis, and dividing by 3 three times gives the framework of the minor system in the descending genesis. They are in this view also directly related. The Law of Duality in music emerges into view from the genesis [Scientific Basis and Build of Music, page 42]

of the major being upward, and the genesis of the minor being downward. The ascending genesis, beginning with the root of the subdominant major F, produces in the ascent a scale of notes at varying distances, and of increasing levities; the middle note, D27, being carried a little above the center of the system. The descending genesis, beginning with the top of the dominant minor B, produces in the descent a scale of notes with identical variety of distances, but with increasing gravities; the middle note, D26 2/3, being pressed a little below the center of the system, thus giving rise to these two D's - one whose genetic number is 27, the major D, and one whose genetic number is 27 2/3, the minor D - the duality of D is thus residing in itself.1 [Scientific Basis and Build of Music, page 43]

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]

There was, then, something of truth and beauty 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 genesis 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]

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]

The Dual Genesis of the Two Diatonic Semitones

CHAPTER VI
TREATISE ON THE CHROMATIC SYSTEM
[Scientific Basis and Build of Music, page 50]


dividing itself by 2 or 3 or 5, etc., up through the whole geometrical series of numbers, not keeping fixed at one thing; but while the whole length is vibrating the fundamental partial, it keeps shifting the still nodes along its length, and sometimes longer and sometimes shorter segments are sounding the other partials which clothe the chief sound. It has been commonly said that "a musical sound is composed of three sounds," for every ear is capable of hearing these three, and with a little attention a few more than these; but many will be startled when told that there are twenty-five sounds in that sound. Eighteen of them are simply the octaves of the other seven, all of these seven except one having one or more octaves in the sound. Four of the seven also are very feeble, the one which has no octave being the feeblest of all. Two of the other three are so distinctly audible along with the chief partial that they gave rise to the saying we have quoted about a musical sound being composed of three sounds.1 If the three most pronounced partials were equally developed in one sound, it could not be called one sound - it would decidedly be a chord; and when in the system they do become developed, they form a chord; but in the one sound they, the partials, having fewer and fewer octaves to strengthen them, fade away in the perspective of sound. The sharp seventh, which in the developed system has only one place, not coming into existence until the sixth octave of the genesis, is by far the feeblest of all the partials, and Nature did well to appoint it so. These harmonics are also sometimes called "overtones," because they are higher than the fundamental one, which is the sound among the sounds, as the Bible is the book among books. [Scientific Basis and Build of Music, page 59]

lastly it is altered again and becomes, by the power of 3 once more, F#,#, and serves in four keys. But this carries us beyond the horizon of our musical world of twelve keys; for in B#, the top of the tonic E, we have reached our twelfth fifth, and it here coalesces with C of the seventh octave, and closes the circle. This is the way that all notes become alternately altered, either by commas and sharps in the upward genesis of scales, or by commas and flats in the downward genesis, by the alternate powers of 3 and 5. In the upward genesis in this illustration, notes by the power of 5 serve in three keys, and those by the power of 3 serve in four keys. In the minors it is just the inverse on this by the Law of Duality. But no note serves for more than either three or four keys, as the case may be. [Scientific Basis and Build of Music, page 63]

If we view the Diatonic scale from the standpoint of their harmonizing, it is the first five notes of the octave which are the natural scale. The eight notes of the octave form a compound scale. So, in this view, in the octave of notes we have before us two scales; and this is true in both major and minor modes after their own dual fashion. In each of these two diatonic modes, the major and the minor, there are two semitones; but there are only two semitones altogether in the twofold system. When the major is generated by itself it has them both; and when the minor is generated by itself it also has both; but when the major and the minor are generated simultaneously, or as one great dual outgrowth, while the major in the ascending genesis is producing the semitone E-F, the third and fourth of its octave scale, the minor responsively in the descending genesis is producing the semitone B-C, the second and third of its octave scale. In this view of them, therefore, the semitone E-F belongs genetically to the major, and B-C to the minor; and this claim is asserted in the major tonic chord C E G, in which its own semitone is [Scientific Basis and Build of Music, page 64]

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

The great Genetic Scale, major and minor, the seed-bed and nursery of all, is that from which first of all the natural scale of the fifth arises into existence; and three fifths are generated in the major ascending side and three also in the descending minor side of the twofold genesis, giving us six fifths in all. At the top of the ascending genesis we find the major octave scale standing solid and in its perfect order and proportion; and at the bottom of the descending genesis we have the minor octave. [Scientific Basis and Build of Music, page 66]

generate D and B; D is the highest note in the chord-scale, but B is the last-born note, and has a higher vibration-number in the genesis. [Scientific Basis and Build of Music, page 67]

Music, and mathematics have nothing more to do with it. Already the Law of Position has guided the genesis upward in the major; and while mathematical primes were generating the chords one after another in precisely the same way and form, like peas in a pod, the Law of Position was arranging them one over the other, and so appointing them in their relative position each its own peculiar musical effect bright and brighter. And when the major had been thus evolved and arranged by ratios and position, another law, the Law of Duality, gave the mathematical operation its downward direction in the minor; and while the primes which measured the upward fifths of the major also measure the downward fifths of the minor, the Law of Position is placing them in their relative position, and appointing each its own peculiar effect grave and graver. [Scientific Basis and Build of Music, page 68]

The peculiar effects are exhibited when the chord-scale is next set forth. We have seen that there are six chords evolved in the genesis upward and downward, 3 in the major form and 3 in the minor. In the fifths of the minor the semitone is always in the lower third, occurring between the second and third in the subdominant and tonic, and between the first and second in the dominant chord; whereas in the major it is always in the upper third, between the fourth and fifth in the subdominant, and between the third and fourth in the tonic and dominant chords. While the thirds which the fifths contain are thus so varied, the fifths themselves have always one magnitude, whether major or minor. [Scientific Basis and Build of Music, page 68]

All compound and double compound chords are made up of notes already developed for the simple chords; there is no genetic developing of compound chords. Simple chords are all begotten in the genesis; they are true species; compound chords are only varieties of them. [Scientific Basis and Build of Music, page 70]

If the minors are to be developed by sharps in an ascending series of fifths, then the mathematical process must be, as in the majors, by multiplying the top of the dominant by 3 and by 5, and they will then follow the majors. But the Genesis must first necessarily be produced by the descending process. [Scientific Basis and Build of Music, page 84]

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

The intervening chord between the Diatonic and Chromatic systems, B, D, F. - This chord, which has suffered expatriation from the society of perfect chords, is nevertheless as perfect in its own place and way as any. From its peculiar relation to both major and minor, and to both diatonic and chromatic things, it is a specially interesting triad. F, which is the genetic root of all, and distinctively the root of major subdominant, has here come to the top by the prime 2. D, here in the middle, is diatonically the top of the major dominant, and the root of the minor subdominant; and on account of its self-duality, the most interesting note of all; begotten in the great genesis by the prime 3. B, the last-begotten in the diatonic genesis, top of the diatonic minor, middle of the dominant major, and begotten by the prime 5, is here the quasi root of this triad, which in view of all this is a remarkable summation of things. This B, D, F is the mors janua vitae in music, for it is in a manner the death of diatonic chords, being neither a perfect major nor a perfect minor chord; yet it is the birth and life of the chromatic phase of music. In attracting and assimilating to itself the elements by which it becomes a full chromatic chord, it gives the minor dominant the G# which we so often see in use, and never see explained; and it gives the major subdominant a corresponding A♭, less frequently used. It is quite clear that this chromatic chord in either its major phase as B, D, F, A♭, or its minor phase as G#, B, D, F, is as natural and legitimate in music as anything else; and like the diatonic chords, major and minor, it is one of three, exactly like itself, into which the octave of semitones is perfectly divided. [Scientific Basis and Build of Music, page 101]

THE GENESIS.


In Fig. 1, the mathematical framework of the scales major and minor, is shown the genesis of the scale. F1, in the top figure, is multiplied by 3, and that by 3, and that by 3, which brings us to D27, top of the major dominant. F1 is the root of the whole system. C3 is the top of the first chord, and from that grows the next, and from that the next; and so we have F, C, G, and D, the tops and roots of the major system of chords. When these 3 roots are each multiplied once by 5, the middles of the chords are found, as shown - A, E, and B; so B is the last-born of the major family. When B is taken 4 octaves higher at the number 720 and divided by 3, and that by 3, and that by 3, we get the notes E, A, and D, which are the roots and tops of the minor system of chords. Dividing B, E, and A each by 5 once, we get the middles of the 3 minor chords, as shown. [Scientific Basis and Build of Music, page 103]

WITH THEIR RATIO NUMBERS.


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 # 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]


There are 42 intervals exclusive of the octave interval with ratio 1:2. There are seven seconds of three magnitudes, so determined in the genesis of notes - two in the ratio of 15:16; two, 9:10; and three, 8:9. There are seven corresponding sevenths - two in the ratio of 8:15; two, 5:9; and three. 9:16. There are seven thirds - one in the ratio of 27:32; three, 5:6; and three, 4:5; and there are seven corresponding sixths - three in the [Scientific Basis and Build of Music, page 109]

ratio of 5:8; three, 3:5; and one, 16:27. There are seven fifths - one in the ratio of 45:64; one, 27:40; and five, 2:3; and seven corresponding fourths - five in the ratio 3:4; one, 40:54; and one 32:45. These are the ratios of the intervals in their simplest expressions as given in the second outer space above the staff in the plate. In the outer space the intervals are given less exactly, but more appreciable, in commas. The ratios of the vibration-numbers of each interval in particular, counting from C24, are given in the inner space above the staff. These vibration-numbers, however, are not given in concert pitch of the notes, but as they arise in the low audible region into which we first come in the genesis from F1, in the usual way of this work. The ratios would be the same at concert pitch; Nature gives the numbers true at whatever pitch in the audible range, or in the low and high silences which lies out of earshot in our present mortal condition. [Scientific Basis and Build of Music, page 110]

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

Ramsay


This is a twofold mathematical table of the masculine and feminine modes of the twelve scales, the so-called major and relative minor. The minor is set a minor third below the major in every pair, so that the figures in which they are the same may be beside each other; and in this arrangement, 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 minor being always a comma lower than the major. 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 sixth of the preceding masculine scale in every case, except in the first, where the note is D26 2/3. D is the Fourth 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 minor is always left this comma behind by the comma-advance of the major. 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 genesis 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 masculine. Compare Plate II., where the whole twofold yet continuous genesis 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 arrangement. The unit from which to begin may be any number; it may, if he chooses, be the concert-pitch-number of F. But let him take good heed that when he has decided what his unit will be there is no more coming and going, no more choosing by him; Nature 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 major are the numbers of the vibrations in the minor. We have, however, to see that we use the proper notes and numbers; we must know the secret of Nature. This secret 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 genesis 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 number, as we see in the great genesis, corresponds to 1 in the major, 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 number 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 number in the dual system. All the notes in the masculine development are above F2; and all the notes in the feminine 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 number 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 Music's mystery 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]


Hughes
The following scheme endeavours to show that the development of the musical gamut and the colours of the rainbow are regulated by the same laws. I wish it to be clearly understood that I have gained the evolutions from the mysterious type of Life—a golden thread running throughout the Scriptures, from the first chapter of Genesis to the last of Revelation;—life developing around us and within us from the Almighty, who is its Eternal Fountain. My youthful impressions included the belief that the views of Dr. Darwin, my great-uncle, contradicted the teaching of the Scriptures, and I therefore avoided them altogether. Having endeavoured for years to gain correctly the laws which develope Evolution, I suddenly discovered that I was working from Scripture on the same foundation which he had found in Creation; and as Creation and Revelation proceed from the same Author, I knew that they could not contradict each other. It is considered by many that my cousin, Charles Darwin, gained his first ideas of Evolution from his grandfather's works; but I know from himself that he was ignorant of them, and that his theory of Evolution was arrived at by his close experiments and observations of the laws of creation alone. Only a few months since, after reading his work on "the Movements of Plants," published in 1881, and wishing to be certain that I had not an incorrect belief, I asked the following question—"Did you gain your views on Evolution by your wonderfully acute observations, ignorant of your grandfather's ideas?" The reply was, that he had done so entirely from his own observations. [Harmonies of Tones and Colours, Introduction1 - Harmonies, page 9]

See Also


2.10 - Beginning
2.11 - Beginning as Undifferentiated One
3.6 - Differential Densities Begin to Form
beginning of expansion
beginning point
beginning points
Bible
birth
bottom of the descending genesis
cathode beginning of matter
Figure 2.5 - Non-Point of Proto-Beginning
First Cause
genesis of music
genesis of octaves
Genesis of Polarity
Genesis of the Scale
genesis
God
inverse genesis
major genesis
minor genesis
parthenogenesis
Ramsay - Duality in the Genesis of Music's Scales
Ramsay - Nature's Inverse Process for the Minor Genesis
Ramsay - PLATE II - The Genesis
Ramsay - The Genesis of the Chromatic Scale
Ramsay - The Marshalling of the Host of the Lower Heavens20
top of the ascending genesis

Created by Dale Pond. Last Modification: Monday February 8, 2021 03:40:15 MST by Dale Pond.