Letter on the relationship of harmony with numbers

1800

Author: Louis-Claude de Saint-Martin, Martinès De Pasqually

France

Subject: Theosophy

This text appears in first position in a collection of texts from theOrder of the Elect Cohens. The original of this collection is kept at theNational Library of Franceunder the name of the Manuscript of the Elect Cohens ( Ms. FM4 1282 ).

► It was Robert Ambelain who donated the collection to the library in 1993.

► The collection is still called the Green Book , the Grainville Manuscript or the Algiers Manuscript

You absolutely want, Sir, to see in writing my relationship between harmony and numbers. Here they are: all I will ask you is not to believe that I am giving you this as science, but only as one of the testimonies of science; and never forget that it does not consist in cold reasoning or ingenious observations, but in the virtuous desires of the soul and the use of all the forces of our being. It is only on this condition that I will write.

You know, Sir, that a sound cannot be heard without carrying with it, in rising, three other sounds of which it is the generator. Here is already the quaternary unit; here in one form is the central point and the three angles of the triangle; here is finally one of the traces of the law which directs all production, both particular and universal. I leave you to think if this law could be observed so regularly, so universally in created things, if it were not the same in the uncreated order, especially since it is recognized that what is sensible does not subsists only through what is not. Let us therefore try to rise to the insensible quaternary and we will have the principle of all things; principle which will enlighten us about ourselves and make us wise by making us seek if we are in conformity with our origin.

The three sounds relating to the main sound are with it in a relationship that the musicians have evaluated, the first under the name of the twelfth or octave of the fifth; the second of a major seventeenth or double octave of the third; and the third under the name of octave which is the repetition of the fundamental sound. Such are the relationships given by nature; such is the distance she established between the four corresponding sounds. But the major twelfth and seventeenth are only octaves of sounds which are in a closer relationship with the bass sound; thus, the major seventeenth responds to the major third above the low sound, and the twelfth responds to a sound which is two thirds above this same low sound. This is where the perfect chord is formed, composed, according to the received notion, of the tonic, the third, the fifth and the octave. I know that the octave being only a repetition of the low sound, I could eliminate it like the other sounds outside the octave, but I cannot avoid admitting it, because, without it, the range would not be finished, and that it is proof of unity. I will not go into detail about the other harmonic sounds that the masters of the art claim to discover in the resonance of the sound body. As these sounds are almost not perceptible and, moreover, they are only new octaves of the four primitive sounds given, I stick to those and I will consider the numerical relationships that I find between them in the perfect harmony that they compose.

Firstly, the perfect chord bears the number 1, in that it is the one and only, that it is entirely filled with itself and that it is unalterable in its intrinsic value like unity, because I do not do not take into account the sixth or the sixth fourth which are only a transposition of the same sounds of the chord and, consequently, do not change its essence.

Secondly, this chord is composed of four sounds which contain three intervals between them. You saw the unit produce its three corresponding sounds and slave them to itself. You currently see the quaternary somehow containing and linking this same ternary number, which already shows us a relationship of the quaternary to unity. Let us consider for a moment this ternary and this quaternary, both in their rank and in their particular action.

The first interval of the triad is a third, the second is a third, and the third a fourth: why should we not recognize there the number and the inferiority of the simple triangle and the double, as well as the true place of the quaternary constituted above both to preside over it and direct all its action? Once we have seen that it contains everything, why should we not also admit that it governs everything? Especially since we see it dominating by its natural rank on this double triangle, and it is always this quaternary and higher note which determines the nature of the perfect chord, which we could call the universal chord. It seems to me that nature itself establishes here the difference from the ternary to the quaternary or from the triangle at its center. We see limitation and dependence in the one, and we see omnipotence in the other. We see in the first two thirds of the perfect chord the double triangle, or the senary, factor of all lower things, whereas the quaternary is raised above them and rests there as on its seat. One is composed of two different thirds and thereby represents to us the perishable nature of all elementary things; the other formed by a single quaternary interval is a new image of the first principle, and both by its number and by its rank, it represents its simplicity, grandeur and immutability. It is not that this harmonic fourth is more permanent than all other created things; as soon as it is sensitive, it must pass, but that does not prevent, even in its passing action, it from affecting the intelligence, the essence and the stability of its source. It is therefore found in the assembly of the intervals of perfect harmony, everything that is passive and everything that is active, that is to say, everything that man can conceive, and it is there which shows this relationship that I established between the quaternary and the unity from which everything comes.

But to better understand this relationship, let us examine by what means this quaternary contains all things: it is because from its beginning to its end, there are really 10, as you have already noticed. In fact, from the unit or the low sound to the sound which ends the first interval of the triad, there is a third; from the end of this first interval to the end of the second, there is yet another third, which makes six. Finally, from this last interval to the end of the third, there is a fourth: 6 and 4 make 10, and everything is complete. Can you have more sensible proof of the power and divinity of the denaire? And is it not through this that the quaternary has all its virtue? Because, finally, it is the unity which, joined to its three correspondences, forms the quaternary and all that it contains. But, as this quaternary and all that it contains cannot do anything without the unity from which it comes, it approaches it and relates to it at the same time all things by the dudenary means which is the similarity and the most perfect image of this unit. You see from this that it is through its correspondence with unity that the quaternary acts; and that in truth, it is always the quaternary unity which contains and limits the ternary, both in its principle and in its divisions and subdivisions; that is to say in all the productions, actions and qualities of which the ternary is susceptible. This is also what the perfect chord does which contains the three intervals with all the divisions and subdivisions that can be made there, which produces all the tones of the scale, and from which come all the principles and all the possible effects of harmony.

However, it is only in a way hidden from matter that this denaire appears to us to contain all things; we only discover it through our intelligence; instead of it manifesting this truth to our very senses by means of the eighth which is its first action. So we have only eight sounds in our range, in which the last and the first are the same, or, if you like, the alpha and the omega; which indicates to us the universal power of the eight-year-old in creation. I don't need to tell you what this eight-year-old is, you know as well as I who is the one who bears this number; present observation confirms to us what we are taught, that it is he who made everything appear, and that it is he who will sustain everything for the duration.

We know this eighth better under the name of double power; well, the order of the notes of the scale (crossed out: divided into two equal tetrachords) still indicates it to us under this name, since this scale is divided into two equal tetrachords, both for the number of notes contained therein as for their intervals which are absolutely established according to the same ratio in the two tetrachords. Examine the natural intervals of the first four notes beginning with C, and those of the last four, and see if they do not resemble each other? Don't they each contain two full tones and a semitone? And this in the same order? I do not stop to examine whether these full tones are major or minor; I know that none of them must resemble each other since nothing resembles each other, but, in relation to my limit of matter, being reduced to being able only to feel their difference, I do not dare take it upon myself to estimate it, and I find that men have been very bold in fixing their relationships by numbers of vibrations from 8 to 9, from 9 to 10, etc. Because finally, on which A- mi-la did they take the tone? They don't have one of their own, they are obliged to make one for themselves. Now, as this artificial A-mi-la is not fixed, it follows that the relationships that we can draw from it are not fixed either and that what men give us as true under the numbers that they admitted, can also be under other numbers, depending on whether the A-mi-la will be more or less low. Moreover, this knowledge, if it were deepened, could well give me some instruction like the others, but, not having weighed it sufficiently to find certainty in it, I limit myself to the present observation on the two tetrachords and which is within the reach of the least trained ears: I limit myself to what my thoughts and my eyes tell me on this, that just as it is the eight-year-old who manifested the whole creature, so it is he who operates and maintains it; and, as we have seen that this creature was the assembly of the passive and the active, a power was necessary for one and a power for the other: now, this is what forms this double power that everyone can read like me in the two equal and quaternary parts of which the harmonic scale is composed. For you, Sir, you will be able to read there the power of what we must call the Church, and the material proof that outside of her there is no salvation, remembering however what I have said at the beginning, that the sensible only subsists through what is not, and that consequently it is only the material expression of the laws of an immaterial principle hidden for the eyes of the body.

Although we have recognized that the scale was composed of eight sounds, yet the last being only a repetition of the first, there are in fact only seven sounds different from each other; and if the ear does not find itself at rest on the seventh of these sounds, but only when it has reached the eighth, it is a new confirmation for me that all things must return to their principle, and that having born in unity, they are only at peace and in their place when they return to this unity. Nothing is clearer than this truth, since we see the notes of the scale only ending in the eighth, which, according to what we saw above, is only the sensitive action of the denary, which denary is the first spiritual action of unity. The seven notes undoubtedly seem to you, Sir, to contain a large number of relationships, and it is true that the closer we get to what is created and temporal, the more easily we must find analogies there since we live in the land of time. I therefore believe that without being imaginary, we can recognize the seven main agents of the universal creature whose corporeal names you know, all the products, virtues, divisions, signs and properties which belong to these seven agents, as well as everything that men use them every day to represent them without knowing either the principle or the effects. Finally, you will find proofs of this natural septenary in everything that composes and contains the creature in its temporal action, because it divides and occupies it entirely from the surface to the center.

Everything nevertheless indicates that this septenary is only a temporal or operating agent, and not a holy agent like the eighth which immediately touches the denary and which rests on the septenary like the Lamb on the seven seals. Observe that you cannot reach this eighth year without having passed through the seven lower degrees and educate yourself... Recognize our staircase and differentiate it from the apartment to which it leads; let this not prevent us from making the most of it and considering it as what we have dearest among created things, because ultimately we have only one way out of the land of Egypt, and I see nothing that prevents me from believing that it is the one. The Red Sea was the first step of the ladder, the forty-two camps were the other six, and they all had to be climbed to reach the Promised Land. I will say no more about the septenary, I leave the field open to your reflections on this and I have no doubt that by going deep within yourself, you will confirm yourself alone in a large part of the things that I just processed. Let's move on to other observations.

Until now, Sir, we have only considered the range in relation to what it is in itself and to the fundamental principles which compose it; we have not penetrated into the play and the particular movement that all sounds can take in harmony. Also, by examining only their natural order, we have only discovered the constitution of all things established by the Creator. Let us now find out if another point of view will reveal to us those which are not revealed by it; then we will feel if there is any power other than his, if there is any other truth, any other law, any other perfection than that which is due to his incommutable essence; finally if it is possible that there is more than one unit. For this purpose, let us remember, I pray you, what is the nature of the three intervals which we have recognized to be included in the perfect chord. It is the repeated third and the fourth which measures them. Their sum gave us ten. Ten begat eight, and eight sustains seven, so that we already have the six agents who carried out the six eternal thoughts that became sentient in temporal creation. I say these six eternal thoughts, not in relation to the creation whose cause and birth had a beginning, and which consequently will have an end, only in relation to the uncreated nature whose order has been and will eternally be the type of visible nature. These six agents are 1, 3, 4, 7, 8 and 10. You know that 6 is only 3. You also know that as long as we are in our bodily form, 3 will be all we can know; because its center will be forever hidden from created things, and darkness cannot understand light, so that no man has ever seen God.

But what I mainly propose to point out to you here, Sir, is that, in all the numbers that we have just found and which contain the two universes, the passive and the active, we have not seen the least trace of the three other numbers which are contained in the decade, namely, the binary, the quinary and the neuvary; well, I want it to be your ear that will still teach you their origin; he is a witness whom you will not distrust, and who must confirm to you the certainty of matters of intelligence.

You easily judge that if perfect harmony had always remained in its nature, order and just harmony would have subsisted perpetually; but this monotony seemed boring, and those who were trained to hear it, having become disgusted with it, determined to compose. Now, what course did they follow for this? They altered the triad by removing its octave and substituting the preceding note, from which comes what is known as the seventh chord; this is the source of all musical productions, which is for me an image of universal production, and where my mind discovers its principle as it discovered its constitution above. Let us therefore examine the nature of this seventh, and we will touch with finger and eye the causes and results of the confusion which generated the creature and which perpetuates it.

The design of creating another order of things than that contained in the perfect agreement, of placing another unity alongside the first unity, coming only from disordered thought, could only produce disordered effects, and by consequent who were in combat with the true essence of being, which can never be denatured. It was pitting principle against principle, power against power, what we call walking by the number two. Also this seventh chord is absolutely repugnant to any ear that is not disturbed, it keeps us in pain and anxiety until we save it by bringing us back to the perfect chord which is our principle . But why does this seventh shock our ears in this way? Is it not because the first and last notes of the chord are immediately adjacent to each other, and therefore carry this famous binary number, from which what we call a second is formed? ? We cannot therefore deny that this number two is the cause of disorder and that wherever it is found, there is dissonance, according to the language of musicians.

We find new proof of the irregularity of this number in the relationship of all the notes of the scale with the low sound, in which relationship we clearly find the accuracy and perfection of our quaternary. Indeed, I considered the seventh as a second in relation to the low note or, if you want, to its octave which is the same thing; but this seventh is not at all the only dissonance; any diatonic connection is condemned by nature; so, wherever I find two neighboring notes sounding together, I will be hurt. Now, as in the scale there are only the second and the seventh which can be found in this relationship with the low sound, this makes us see that the creation is formed of two dissonances, just as we have seen that it could only be a dissonance, or the number two, which would have given birth to it. We find on the contrary that there are only four notes, and that there are only these four notes which agree perfectly with the bass sound or its octave, namely the third, the fourth, the fifth and the sixth. Is this not a new and clearest proof of the relationship of our quaternary with unity? Did it not veil in another form our four universal correspondences and a new effect of the immutability of the principle? See then the difference between good and evil: the eternity, the impassibility of the one; the youth and instability of the other. Recognize that consonances, either by their quaternary number, or by their effects, announce order and perfection everywhere; and that on the contrary the dissonances, considered equally in their number and in their effects, produce directly opposite results. I will come back to this point to offer you a little image of yourself that may make you open your eyes. Let's continue.

It is on the dominant that the seventh chord is made, as the most sensitive of all and the most opposed to the natural tone, since it cannot exist for an instant without the latter taking over again. This dominant in the intellectual order being raised two thirds above the bass sound bears the number six, as you have seen: but, in the sensible order of the eight tones of the scale, it really bears the number five. As long as this dominant remains attached to the low sound which is its natural link, the consonance is perfect; but when she separated from it and wanted to walk alone, when she presumed to be able to do without the generating principle and put herself in its place, you saw the seventh that resulted. You therefore see that the quinary number could not appear alone without creating a dissonance with unity, and, consequently, without having an intimate connection with the number two. You could, I know, object to my own words and tell me that what I take for the fifth in the sensitive range of the eight notes is really the sixth in the intellectual denary which composes the perfect chord, as I have just described. establish it myself. But, just as the eighth scale is divisible into two tetrachords, so the denary scale is divisible into two quinaries, and in one or the other of these two scales whether [10] you take the dominant, it will always be the first note and as the source of division. If it is in the eighth, it will carry five by its rank, and by joining the number four which is found from this fifth to the octave, you will have the novenary which will remind you of the meeting of the animal part at the head of abomination. (I will speak later about this new number and will show you clearly that it makes the subdivision of matter). If you take your dominant in the denary, it will carry six by its rank, but making the division as in the eighth, there will be five from this dominant to the denary, which will make you eleven; thus, from whatever side you examine it, as soon as you divide the scale into either denary or eighth, you will always recognize that it is the quinary which has brought disorder and confusion everywhere. In the eight-year range, it is below; in the denary range it is above, that's all the difference.

What I have to tell you about the novenary is discovered perfectly in the seventh; is not this seventh composed of three thirds? I'll let you do it yourself on these three thirds, both together and separately, the application of everything you know about three, six and nine. I leave you to meditate on the origin and constitution of bodies, whether in the universal or in the particular, and draw for yourself the consequences of their incompatibility with what existed before them. Then considering this novenary in the sensitive range where it really bears the septenary number, you will see if this created nature can be supported other than by the action and reaction from which come the combat and the violence that you see there; mixture of regularity and disorder that harmony faithfully represents to us through the assembly of consonances and dissonances which constitute all musical productions.

I promised you, Sir, on the subject of dissonances and consonances, a small image of your being here below; we must give it to you.

You remember well that I pointed out to you that in the scale there are four notes, namely the third, the fourth, the perfect fifth and the sixth, which agree with the fundamental note, and that there are two , namely the second and the seventh, which do not agree at all. I only ask you to observe the place that these consonances and these dissonances occupy in the scale, both in relation to themselves and in relation to this fundamental note. Don't the four consonances occupy the center? Are they not limited by the two dissonances? And these by the low note and its octave? So read with me the quaternary or man in his dark form and which separates him from his principle; read the route you have to take to get there; read the horrible division that matter has brought into all spiritual nature; finally read both your misery and your duties.

There were wise men who put a veil on what I discovered about you here; they announced man under the name of the color red, in the color black, in the color white: physical image which is confirmed in this experience of light imbued with the three elementary colors. The harmonic order also represents their allegory to us in a natural way, and I am quite convinced that, if we wanted to take the trouble to search, there is not a being who would not also offer it to us in nature.

I only have one more article to deal with, Sir, it is that of the minor tone. I am sorry to be obliged to tell you that it is not in nature; the sound body does not give it, it is an invention of man who created it in imitation of the major tone. He transported below the tonic two strings mounted in such a way that one responds to the fifth or dominant, and the other to the minor third above, and, as the vibration of the tonic made them resonate, the man adopted his work and placed it among natural productions. This was all the less repugnant to him as he found this minor tone capable of almost the same harmony as the major tone. It also bears the denary, or perfect chord, having no difference except in the order of the thirds; it consequently extends and embraces like the other all the notes of the scale; the sensitive chord is the same for both, finally it has, like the major tone, advantages and pleasures which are particular to it, but which are however infinitely more limited and less outgoing.

Would it be an abuse of the right to compare to find in this the repetition of everything we know about the primary prevarication? I leave the matter entirely to your judgment, but I ask you to examine the reports. You see that the minor tone has double power like the major, since it is composed like it of two tetrachords; with this difference, it is true, that the two tetrachords of the minor tone do not each have an equal order in their intervals because of the sixth which is minor. You see that the note which forms the first third of the minor triad is only a semitone away from the second or dissonance, and this slight observation may mean something; you see the sensitive note of this minor tone generate a diminished seventh chord, from which this tone draws its greatest beauty, a chord which does not carry a single note of the triad, and which on the contrary carries the only four notes which are proscribed, a chord, finally, which bears nine, being composed of three thirds like all sevenths, but whose relationship is the tightest of all known relationships in harmony, since these three thirds are minor. Everything here announces the weakness and infirmity attached to the works formed by the hands of men.

Here, Sir, are all the connections that I have thought I have seen so far between the laws of harmony and the laws of numbers. I have no doubt that there would be infinitely more to discover if one wanted to consider in detail the structure of all the dissonant chords, the qualities and properties assigned to the different modes and different tones, the sequence of modulations by means of tones correlative to the main tone, the order which reigns in what composers call a sequence of sevenths, finally all these laws which the ear and the genius of man have discovered in the science of sounds, and which nature approves since its course is the same. Because I strictly forbid myself any research into the assumptions that have been accepted and that we admit every day in music. The ear, like all our senses, is usually sensitive. I am very convinced that there were our inventors who could have been deceived in good faith and who made laws for us about random things that time alone had made appear regular. But, even leaving aside all these forced productions, intelligent eyes would surely discover in all the rest a multitude of things which have escaped me and which I will not take the trouble to look for, given that there is a better work to do that one. It is enough for me to have glimpsed the connection of the fundamental principles; if the others come to me later, I will receive them, that's all I can and all I must do.

Thus, I am far from believing that I have clarified all your ideas on these matters, the point of view that I present to you is surely completely new for you. Besides, subject as a man to being deceived by my imagination, I will not flatter myself of having completely protected myself from this danger; I therefore urge you to distrust even the little that I advance and not to adopt anything that you have not weighed. I urge you even more, Sir, not to regard as solid food these kinds of research in which the mind sometimes shows as much its laziness and its distrust as its penetration, and to always have before your eyes only the most beautiful discoveries in this kind is not worth the least affection of the heart.