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“He who has exercised his mind to the utmost, knows his nature.
Knowing his nature, he knows Heaven”

 Intriguingly, extant records show that Aristoxenus of Tarentum, who flourished c. 300 B.C.E., was the son of a musician named Mnesias.  Can it be only a coincidence that the name of the father comes so close to the “second sage” of Chinese philosophy, Meng Tzu, whose Latinized form is Mencius [c. 371 – 289 B.C.]? 

The fact that Aristoxenus was the son of a musician and not a “sage” has only a positive effect upon our argument.  In ancient China music was regarded as the image of the order of the universe, the very key to promoting the success of civilization.  Therefore the most important position in the empire, other than the emperor himself, was the court musician.   Of necessity, he must be a wise man of great knowledge, a mage or sage.  The very extinction of a dynasty was inevitably attributed to his failure to secure the “kung”, the musical tone, upon which the regulation of the universe, the society, the family, and the individual depended.  The sage would have known the musical laws that regulated times and seasons and calendrical calculations, as well as their effect upon political agendas and societal considerations.  Musical knowledge was also the essential aspect of treatises concerned with agronomy and agriculture, for it was considered to be the regulator of crop yield: famine in the land was blamed upon the court musician who did not have the proper understanding of his duty.  Last but not least, music was one of the ways of spiritual liberation for the individual who knew its vibratory laws. However, such laws were kept hidden, for they provided the necessary correspondences, the resonances, between notes and gods, and gave the one who possessed their secrets godlike powers and great authority.  Thus the knowledge of musical science was priestly knowledge, for king and sage alone.

The ideal state was called “the Kingly Way”.  Such a virtuous government required virtuous men who had developed the “four beginnings” inside themselves.  The sage Confucius maintained that the “four beginnings” are made manifest in the very structure and organization of human society.  All men have the “four beginnings”, which bring virtues human-heartedness, righteousness, propriety, and wisdom.  All men are possessed of them, but they are not fused into us.  To be a man is to fuse these natural powers into one’s being.  That fusion is the essence of humanity, and distinguishes man from the animals.  All men have the same “four beginnings”, but the Sage is the man who has developed and expanded and completed them.  However, the virtuous Sage does not practice them merely because they are beneficial to him, or even beneficial to society at large; he practices them because he wishes to be a man.  He wishes to be.

The “four beginnings”, their coming about, how they are fused into the enharmonic genus; how they become intervals and notes; how they develop into systems, and expand into the modes; how they bring about what is called “being” - all these things are to be found, albeit “encoded”, in the categories of musical writings of Aristoxenus’ On Harmonica.

The essence of man, his “being”, or that which distinguishes him from the animals, is the human mind.  To be a man means the ability to reason.  The sage, Mencius, held that a man who acts in accordance with reason follows that part of himself which is great.  If he does not, he loses his essential humanity, and becomes one with the beasts.  “He who has exercised his mind to the utmost, knows his nature.  Knowing his nature, he knows Heaven”.  Man’s special prerogative from Heaven, a mind capable of reason; is that part of man which is great.  The senses, being shared in common with the animals, constitute what Mencius calls the part of man that is small. 

The Greek philosopher Aristotle [384 – 322 B. C.] in his Ethics, says the same thing when he states that appetites and desires are part of man’s lower nature; what differentiates man from animal is his reasoning mind. 

The mind, in Chinese, is expressed by the same word that means “heart”.  The heart correlates righteousness (“i”) and morality (“tao”).  The way of righteousness was Perfect; the way of morality, weighing good and evil, was Just.  Human-heartedness was the Middle Way that linked everything together into a unifying harmonia, dissolving the division between other and self; filling up all between Heaven and Earth.  The pithy statement, “If you want to know whether a country is perfectly-governed and has just ethics, listen to its music”, attributed to the sage Confucius, contains deep meaning.  The musical knowledge of the Three Worlds - Heaven, Earth, Man - was called the Kingly knowledge.  Only those individuals who attained to this great and high state of mind - one both perfect and just - were called Man.  All others were only “men in quotation marks”, or “beasts”. 

A true Man is one “in relationship”.  As Mencius said “The Sage is the apogee of human relationships”.  To be in right relationship, one must know whom he serves.  He must have allegiance to a Sovereign, since “every man for himself” is overly yang, and will fail.  He must also have allegiance to the Father, for to be without the Father, following merely the principle of “love”, the pairing of opposites, is overly yin, and will also fail.  “Without Sovereign and without Father: this is to be the same as a beast”.

At about that same time, in ancient Greece, Aristotle said that man’s harmonious nature, if it is to be completely developed, requires a state and a society.  If a man says he is incapable of living in society, he is injuring himself; if he says he cannot serve his state, he is injuring his sovereign.  If a man is to be wise, he must be in relationship: ruler and subjects, parents and child.  If one pursues the novel idea that the great Chinese sage Mencius is actually the father of Aristoxenus, it would not be a surprise to find such close correlation between the words of Mencius and the Greek philosopher Aristotle, who is reputed to be the teacher of Aristoxenus.  In fact, if my supposition is right, Aristoxenus, the son of Mencius, is the teacher of Aristotle, not the other way round. 

By the time of Mencius, the greatness and richness of ancient China had degenerated, the old law codes, the sacred canon that ensured proper regulation of society had been abolished, and feudal rulers preyed upon and conquered one another in turn, each vying to be the greatest of all “power-possessors”.  Even a scant hundred or so years prior, during the time of Confucius, there was still one canon that measured all and everything.  However, by the time of Mencius, many philosophical divisions became known as “the doctrines of the Hundred Schools”.  Mencius himself said: “Sage-kings cease to arise, and the feudal lords give rein to their lusts.  Unemployed scholars indulge in unreasonable discussions”.

The unfortunate situation, threatening the entire fabric of civilized culture, was due, in no small part, to the fact that the feudal rulers had little patience with “the ancients” and their beliefs in a harmonious system of measures.  Caring nothing for “the four beginnings”, for “first causes”, howling and indignant that the king’s rule was “unjust”, the feudal warlords held to the motto: “Every man for himself”. 

Mencius, on the other hand, held to the old concept of the “i”: righteousness, duty, benevolence.  He deprecated feudal government and held to perfect rule by an exalted king.  Such a king, he believed, had a conscience, and could not bear to witness the sufferings of others, while a feudal lord had no conscience, and ruled only for personal gain: for name, honor, and profit, for “me”.

The hierarchical order in social distinction, Mencius held, must be maintained.  Human society requires both men of superior grade to rule the countrymen; and it requires countrymen to support the men of superior grade.  Distinction between ruler and ruled makes possible the cooperative division of labor.  A man who is capable of making pottery is made a potter.  One able to farm well is made a farmer.  One who has courage and can fight is made a warrior.  To rule requires a class of specialists of great value and worth who “spend their youth in studying”.  Therefore, “before a man can be Emperor, he must be a Sage”.

The division into castes was practiced in the whole of the ancient world.  Unlike today, when such a system is generally considered to be “unjust”, in antiquity such a system was believed to be essential to the harmony of society.  Difference and inequality between men is the source of progress for civilization; and mankind finds equilibrium only when the basic four castes - sage, warrior, agriculturalist, and artisan/worker - are themselves in harmony.  The leveling of power and privilege and resulting repression of the “elite” (today, a characteristic of so-called socialist and communist countries) lead to disastrous consequences for all. 

There is a scenario, in the pages of Beelzebub’s Tales to his Grandson, which seems related to these ideas.  Once upon a time there was a good King Appolis whose kingdom was in revolt.  This unfortunate state of affairs was brought about because the king made a wager with a young countryman who was indignant at the money and labor extracted (as he believed) unjustly from the people by the king to maintain his kingdom.  The “unjust” king agreed to follow the new “just” rules set down by the young countryman.  Soon the people stopped working and paying, and the result was a country in shambles.  To rectify the serious situation, the “Arch-cunning” King Appolis made a plan to replace the present so-called just administration with his own ministers who held to the old idea of a perfect governing hierarchy.  The change-over, as expected, created revolution and revolt.  During this dangerous but ultimately restorative process, King Appolis, to ensure his protection, resided outside the kingdom, in “one of his suburban palaces in the city of Samlios”.   (The word “Samlios” sounds suspiciously like “Samos”, a Greek island in the Aegean where the legendary Greek, Pythagoras, spent his early years).  The story ends by saying that eventually the earlier policy (the perfect system) of King Appolis was reestablished, and the community resumed its former tempo.  The unfortunate countryman who created the problem left, and became a bailiff (one who makes arrests and who puts people in jail).  The idea of a prison has to do with a system of justice, with balance scales of good and evil, with reward and punishment.  In musical terms, as we shall see, such a system of paired contraries is called the Just system.

Mencius believed the sole raison d’etre of the Emperor and his administration is to “gain the peasantry”.  If a ruler fails in this, he loses that which makes him a ruler.  The people are “the most important elements”. 

In the Perfect hierarchy of cyclic fifths, the musical representation of the “Emperor” (Kung) is C, 81/1.  The “People of the empire” (Chio) are “gained” at the fifth cycle, or 81/64, at the tone E: 

The Chinese Musical Empire


As musicians know, there are two ways of deriving the tone E.  One is by the calculation of cyclic fifths [C G D A E]; the other is by the simple superparticular ratios of the harmonic overtone series: [C C G C E].  Unfortunately these two ways diverge to create two musical streams.  Whereas the cyclic E can be calculated to be (3/2)4 = 81/16, the divisive E is short: (5/1) = 80/16.  The difference amount is calculated to be the syntonic comma: 81/80, or 1.0125. 

THE DIVISION INTO TWO STREAMS

The idea that mankind is split into two streams is an important concept in the Work.  Gurdjieff tells us that “the general life of mankind has been divided into two streams since the time of what is called the ‘Tikliamishian civilization,’ which directly preceded the Babylonian civilization”. Since this time man has been divided into “masters” and “slaves".  Or, one could just as well say, “royals” and “commoners”, or “kings” and “peasantry”.

One of the “streams”, the “masters”, is represented by the royal perfect fifths.  Expressed from a base of 8.1, they are the notes of the gapped pentatonic scale: C D E G A.  The numbers 81, 72, 64, 54, and 48, when multiplied together, the square root of their product gives the basis for the Hindu time measure called (depending upon the number of zeros placed at the end) the Year or Age of Brahma: 31104. 

  √ (81x72x64x54x48) = 31104

The perfection of the Brahmanic Year is seen in the fact that when the shortest measure of time, the second, is  multiplied out - from seconds to minutes to hours to days to months - it results in the base number of seconds per year: 60 x 60 x 24 x 30 x 12 = 31104 x 103.  The ancients considered time to be in the form of a perfect circle.  To keep perfect Brahmanic time meant to keep the Divine decree, the perfect circle of 360 degrees.  Taken from a base of 360, the number of seconds in one day amounts to 31104000: 360 x 60 x 60 x 24 = 31104000. 

The five “Chinese” pentatonic scale numbers have a curious relationship with the “Greek” (Pythagorean) scale tones, 384, 432, 486, 576, and 648.  When these so-called Pythagorean tones are multiplied together, the cube root of their product also gives the Year of Brahma: 31104. 

3√ (384x432x486x576x648) = 31104

These two sets of number - the one “Chinese”, the other “Greek” - forming twos, pair together, again becoming the “Hindu” Year of Brahma.

                                                            384 x 81 = 31104

                                                            432 x 72 = 31104

                                                            486 x 64 = 31104

                                                            576 x 54 = 31104

                                                            648 x 48 = 31104

  Yet another curious fact is that the five “Chinese” numbers (81, 72, 64, 54, and 48) whether squared or cubed result in the corresponding “Greek” ratios.  As shown, the intervals coming in between are those of the gapped pentatonic scale ratios 9/8, 9/8, 32/27, and 9/8.

 

These scale structures caused me to recall Beelzebub’s Tales, the chapter “Beelzebub’s Fifth Flight to Earth”, where Gurdjieff mentions “psychopaths squared” and “idiot-cubed”.

When the various squared and cubed tones are made into one line their resulting tonal ratios of major 2nd (9/8) and limma (256/243) describe those of the seven-tone diatonic Pythagorean scale.  Recall that in In Search of the Miraculous (p. 383), Gurdjieff had said to Ouspensky, “There, now make one line out of that”.  Was he hinting of this musical scale formation?

Figure 2: The Pythagorean Seven tone Scale

 384      432        486               512       576         648      729

       9/8          9/8        256/243       9/8          9/8           9/8  

  G         A              B                    C             D           E            F#

The addition of the eighth tone at the lower “end of the stick” (that is, the lower octave F#364.5) serves to confine the white keys to within the one-octave tonal limit.  Thus it is that the six tones of the musical hexachord, G A B C D E, find themselves “hexed”, imprisoned between the two black-key F#s.  The become the “slaves” of the “master”, F#. 

  Figure 3: The Two Ends of the Stick

 

It is no coincidence that, in musical terms, the F# is known as the diabolus in musica, the Devil! 

It should come as no surprise that in the Egyptian pantheon, Set (or Seth) is the dog-headed god of darkness and evil.  In ancient thought, chaos and evil are equivalent.  As the archetypal prison warden, Set shackles man and keeps him trapped in material considerations, the ever-dissipating material energies.  The word “set” itself, in one of its definitions, means “to act as a foil for; to trap”.  The homonym of Set is “sept”, meaning “seven” in the French language.  Omitting the first decimal F# (364.5), there are seven notes, the seventh being the devilish F#.

Gurdjieff apparently affords us clues about the evil “dog-god” Set (whom he names the “barber-surgeon”) in the story of the “dog catcher” who, in his “specially constructed carriage”, trapped the unsuspecting dogs in his net.  And given the fact that, in Egyptian myth, Set kept man trapped in instinctive animalistic behavior patterns that afforded pleasure and enjoyment but prevented him from evolving, the correlation between Set and Gurdjieff’s “dog catcher” is even more convincing.  For in Beelzebub’s Tales we read that at the moment when the poor dog is totally identified in such pleasurable matters (“wagging his tail and looking at a bitch”), the barber-surgeon throws his net upon the unsuspecting victim.  Only an occasional stray dog escapes the net.  The unfortunate dogs are kept for two weeks at the slaughterhouse and fed upon offal.  If unclaimed, they were then “solemnly driven down a certain passageway which led to a specially built oven” and soon became “useful substance for fertilizing”.  The trail left by Gurdjieff’s word-clues continues to proves intriguing: the word “septic” indeed pertains to “offal” and is etymologically related to both Set and sept. 

When the five Chinese pentatonic scale tones (81, 72, 64, 54, and 48) are multiplied by the numerator (2187, or 37) and denominator (2048, or 211) of that highly strange and secretive Pythagorean interval known as the apotome, ten of the twelve Lu scale notes already make an appearance. 

 

The two “missing” Lu tones are the B124416 and the F#93312 which, instead of the apotome (2187/2048), require the limma (256/243) for their calculation.  These two notes may be the enigmatic “nodes” of the moon” found in ancient Indian musical treatises, whose meaning is supposedly lost to posterity.  When the ten notes, plus the two additional “nodes” are set out in a line, the full-fledged Chinese Lu scale comes into focus:

  Figure 4 The Chinese Lu Scale

At this point, the reader may be asking: What does all this ancient music theory have to do with me?  Perhaps that question begins to have at least the beginning of an answer. 

Consider the human body as a 12-fold sequential progression: there are ten lines of action along the limbs to the fingers and the toes, plus the two lateral lines that divide the whole body, front to rear.  The interactive tones are tied together, and their mutual interactions produce more than the “digital channel” commonly considered by neurologists to carry information.  The line shows addition “analog functionality, less well known.  The “nervous system” described here displays changing analog fields that can be modulated.  (Music theorists know that modulation requires the twelve-tone chromatic scale).  The body displays energy potentials across axes of symmetry.  There are twelve channels defining the resonant structure of the human body, which may be universally fundamental to physical bodies.  These twelve channels can be mapped onto the skin.  This mapping is common to all human beings.

There appears to be direct connection between the Chinese scale, the skin, and with that other regenerator, the blood. 

In the vernacular, the skin is the “buff”.  To be in the buff means to be naked, to wear only one’s skin.  A buff is also a thick soft undyed fabric from the skin of buffalo (hence “buff”) or elk or oxen, and was (is) used as a lap robe by Native American Indians.  (Perhaps our “sorry scientists”, as Gurdjieff called them, would do well to don such a “lap” robe in their oh-so-sterile “laporatories”). 

However, the word buff has other very interesting connotations.  For example, a “buff” is a blow, and a buffer deadens the blow.  A buffer is a device for lessening the shock of concussion.  The word buffer, for a Gurdjieffian, recalls that maleficent organ Kundabuffer.  Given that “kunda” means “coiled”, and the kundalini is the fiery sex energy flowing between the poles (the base of the spine to the crown of the head), it becomes almost humorous that another of the dictionary definitions for “buff” is “a fireman, one who rushes to put out fires”.  Along the same line, a buffoon is a clown or joker, one given to crude pranks and coarse jokes.  In musical terms, the buffo was the bass singer in comic opera, the one playing the part of the coarse fool. 

A bufo is also a genus of toads.  In the fairy tale, the crown prince has been turned into an ugly toad by an evil witch, and must await the kiss of the princess.  It is obvious (for reasons previously discussed) that the “toad prince” (a cold reptilian creature reputed, if touched, to cause warts on the skin) must refer to the E# in the Chinese Lu scale (177147).  Those fools that rely on the toad, unable to reach capacitance, will never be able to modulate. 

The capacitor is able to store energy.  Also called a “condenser”, the capacitor is the second electrical component, and has the capacity (and presumably lacks the resistance) to work.  It consists of a non-conducting dielectric film sandwiched in between two conducting surfaces.  The capacity of the conductor is defined as the property of a body expressed by the amount of electricity required to give it a potential greater than its surroundings; or the ratio of stored electrical charge to the potential difference between the two electrodes.
 
Other dictionary definitions of “capacity” include (1) the ability to receive or contain; (2) cubic extent; (3) carrying power.  There is a “female” aspect here: a gravid uterus; pregnancy.  But before conception can occur, there must first be a build up of a strong electrical current between male and female.  And here I boldly and fearlessly (those who know about electronics might say ignorantly) come to the idea that capacitance concerns the kundalini energy, otherwise known as the “sleeping princess”.  To awaken this great force requires the “kiss” of the handsome prince.  So far, there is only the ugly toad.  As the ancient Chinese calculators well knew, things are looking pretty Grimm. 

Two things need to happen.  Put in Gurdjieffian terms, two shocks are needed.  The two “shocks” are the two limmas (256/243) coming into play at the notes B124416 and F#186624.  (Without this first shock, the scale fails to function at normal human capacity and is unable even to reach the E# 177147). 

  Figure 5 The Two Shocks

The second of the two shocks, F# 186624, affords octave completion.  However, without the first shock, the second shock is unreachable. 

The first shock may be what is meant by B-ing.  Under ordinary circumstances, man should attain the seven-tone heptachord: F# G# A# B C# D# E#.  This scale is the “birthright” of the human being.  Without such “being”, as Gurdjieff correctly states, man “cannot do” - that is, he cannot achieve his full capacity at the Do 186624.  However, there is no guarantee that this first shock of “being” will carry the energy to its full completion - far from it.  Octave completion is very, very rare and requires long work.  The ordinary use of the sex energy (the first shock), if used merely for satiation of desire (presumably the “desi” way of the Hindu musical system) quickly discharges and the higher energy remains “asleep”.  The yogic treatment of the sex energy (kundalini yoga) requires willing that the generative substance will produce “thought children” rather than physical progeny.  The second shock is thus posited to be the third aspect, “will”.  The three aspects - function, being, will - are part-and-parcel of the Chinese Lu scale. 

Only then, when the “crown prince” arrives on the scene, can the sleeping princess be awakened with the kiss of higher consciousness - man’s true love. 

Octave completion brings the “artificial light” that enables the modulation of consciousness to a higher level.  Unlike the “quickie” pleasures afforded by the first shock, the results of the second shock are long-lasting.  Instead of remaining on the old scale of animalistic nature, man can attain the “way of the gods”. 

There are many tales from around the world that tell of the “thirteenth fairy” who bodes evil, who brings bad luck. 

Recall that the “April Fools”, or resistors, wanted to keep to the old calendar, wanted the first month to remain March.  February (which evidently comes from the word that means “fever” and usually means an abnormally-high temperature) would remain the twelfth month and could be “adjusted” longer or shorter by adding or subtracting days as necessary.  But keeping to the old calendar, although it retains the “perfection” of the two powers (review the previous document) causes the cosmic cycles to become more and more out-of-sinc with man and his time-frame.  The new, revised version of the calendar “fixes” the problem by putting a “cap” on the octave at 186624.    Granted, it fails to achieve the perfection of the old system; nevertheless, it is able to harmonize and blend the incommensurates in such a way that the integrity of the whole system is preserved.  The “compromise” is apparent at the highest pitch, F#186624 which, when divided down by 2’s, is 364.5.  This puts it within the hearing range of man.  However, it also puts it slightly higher than the tone of origin, taken as 360, by the interval of the comma diesis: 1.0125, or 81/80.  The old Brahmanic system of time-counting is indeed compromised.  The new system set in place requires a whole new calendar.

The idea brings us directly to the change in the laws and the new Julian calendrical system.

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