Home Page The Work of Mitzi DeWhitt Make an enquiry The Arousing of Thought Ancient Mysteries Ancient Egypt and Greece: Aristoxenus, Plato, Pythagoras Scales Of Creation Glimpses of Truth Essays and Fragments Aristoxenus's Ghost Nearly All and Almost Everything Gurdjieff, String Theory, Music The Meaning of the Musical Tree The Reality of Being Decoded Music - Performances & CDs About Mitzi DeWhitt Helios Internet Systems
Chinese Puzzle Indian Magic Greek Canon All Together Now
A Chinese Puzzle - The Lu Scale

In our modern world we have developed a language of science to support what we hope will be novel and  valuable insights into "reality".  Why not look through, and even past, our modern conceptual tools at the subtle and far-reaching insights derived in ancient times from a very different world-view.  Modern science deals comfortably with oscillation, energy transmission, chemical interactions via resonance, and harmonic mathematics.  Let us look through the "tescooano" of these modern concepts at what the Ancient Chinese "musician-physicists" are able to tell us.

The concept of motion is first conceived of, and applied, within a literally obvious and tangible mechanical context, when we are children.  In our modern world we have no difficulty in extending this idea of "motion" to less visible electrical or electronic phenomena, and even (with less justification) into the domains of "light" and "thought".  We easily move on from considering linear mechanical motion, to the idea, so central to modern physics, of "oscillation" - movement back and forth. 

 We regard the primary phenomenon of "sound" as a simple oscillation or vibration in air, usually extending our treatment of sound to considerations of the nature of vibrations in material objects which in turn "cause" the air to vibrate.  We use electronic instruments to allow us to "see" into this world of sound vibration, and one such instrument we call by the evidently apt name of "oscilloscope" - "viewer of oscillation". 

Everyone knows that "sound" is the basis of "music", which we realise involves "higher laws of relationship" between individual sounds.  It is easy to hear that, as "real-world" objects vibrate, more than one individual "sound" is engendered.  This multiplicity of sounds is governed and structured by the possibilities for co-existence or mutual suppression when individual sounds interact.  Ultimately, if you strike an object so that sounds "ring out", the vibrations will settle into a mutually supporting and sustaining group, and the laws by which this happens are the subject of the science of harmonics or harmony.

Sound may indeed be "broken down" and treated by scientists as simple individual vibrations, treating each on its own merits.  However, what we call "music" brings an additional layer of deliberate organisation, or "relationship-between-sounds", imposed by human "musicians" who generally work by intuition rather than necessarily following purely intellectual rules.  The "science" of music quite probably came later than the act of making music or singing, but that does not mean that such a musical science is a "late comer" into the world of science as a whole, considered historically.  It seems that in the ancient world science took its first steps within the context of the study of musical and harmonic laws, and we can learn from the achievements of ancient scientists who worked with a different technology but with no less insight and intelligence.

Science tells us that atoms become organised into molecules ("relationships-between-atoms") before becoming objectified as tangible material substance, and that oscillatory relationships determine these interactions.  The dynamic forces, tensions, and structures of "music" have their own special form of "physics", but this "musical physics" is one step further removed into the abstract than the more familiar physics of material objects.  The physics of music deals with a new type of  "super-matter", or meta-relationship, the very structure of relatedness.  The relationships with which the science of music and harmonics deals are no less real for being less "physical".  These musical "meta-relationships" between centres of energy, lead us into a magical world where "entities" relate to each other, move, are born, live and die.  Musical entities even (and especially, as we directly confirm by our personal experience) impinge on consciousness and the sensitive feelings of living creatures, or "bio-sensors" to use a scientific term. Music is thus a meta-science, extending to the core of our very being, but based nevertheless on the science of vibration for which we have, already available to us, useful technological tools and concepts. 

Why not apply ideas of electronics and our oscilloscope to the musical discoveries of Ancient China.  Let us build a ladder standing on the "earth-ground" of modern electrical science and use our technology to explore the higher realms of harmonic relationships.  Reviewing the Ancient Chinese Lu Scale, we can perhaps imaginatively employ an electrical analogy to shed a modern light on an ancient puzzle.

Look first at the table below: when the tones are confined by the numerator and denominator of the Pythagorean  Comma, what we might call a “magnetic field” is established as the two powers wind up and down, confined between the “poles.”    The “coil of wire” is the musical string itself, stretched tight (after all, opening up the fraction 531441/524288 produces a huge amount of tension).  Now the string is able to produce the dynamics of the chromatic scale.
The Chinese Lu Scale
 
THE CHINESE LU SCALE
Click table above to enlarge


 

Now lets us apply our "oscilloscope" to this scientific "data". The picture below, describing the movement of musical tones, is derived from our table of values retating to the Ancient Chinese Lu Scale..  From a physical sciences point of view, it looks very much like the lines produced by an oscilloscope, a device that graphs the oscillation of electric current in an electronic circuit. 

Scientists and technicians who use oscilloscopes are in general more concerned with the time-relationships revealed by the instrument.  Absolute levels of signal magnitude are rarely of great interest.  What is most important is the way that peaks and troughs in the "waveform" interact, and the timing of "signal spikes" in relationship to the overall progression of the group oscillation.
 

The Musical Oscilloscope
 
THE MUSICAL OSCILLOSCOPE
Click image to enlarge


 

Approached from a biological standpoint, the figure above resembles an EKG or EEG chart that shows electrical impulses, or rhythms of the heart or brain.  The word “rhythm” sounds similar to the word rhizomata.’  For the Pythagorean brotherhood, rhizomata (or “root”) had a very specific meaning: it signified the human psyche.  The root is mentioned in their sacred oath sworn at the time of initiation: “I swear by him who has transmitted to our minds the sacred four, the root and source of ever-flowing nature.”  

There are 22 tones in Figure 2 above.  In the Hindu scale, they are called “srutis.”  One may see here, also, a skeletal framework - “bones,” as it were.   It may be of interest to note that in the mythology of Greece, Pelops, the son of Tantalus and grandfather of Agamenmon, is associated with bones.  Having been fed by his wicked father to the gods at a dinner party, he was then put back together, bone to bone.  Pelops had twenty-two children, the number of bones in the skull.  Sacred geography relates the geographical area of the Peloponnese with the skull.   

Pelops became famous as a charioteer who defeated the king’s own chariot in a race and won the hand of the king’s daughter.  But it was said that he won race because he bribed Myrtilus, the royal charioteer, to remove the lynchpins from the king’s chariot before the race.  Because Pelops refused to acknowledge this assistance, the father of Myrtilus, who happened to be a messenger of the great god Hermes, cursed the descendents of Pelops.  Here we see direct correlations with the musical picture.  The lynchpins are the two ratios of the Pythagorean Comma which are removed (and to this day remain unacknowledged), and which come directly from the hermetically sealed scale of the gods.  

Musically speaking, the “fundamental entity,” the blue line running through the middle of the graph, is the Chinese Lu scale.  From this celestial lineage come the offshoots: the red “comma dieses” [81/80] and the green “just-chromatic-semitones” [25/24].  The pattern of scale points, marked by limma, comma diesis, just-chromatic-semitone, comma, [l-c-jcs-c], is called the “Word.”   

In the graph, the notes shown above the blue line (the ones highlighted in pink) are the basic Lu tones which have been divided down by eight octaves [28] to allow them to be perceived aurally by man.  (The word “sruti,” after all, means “that which is heard”).  Of these twelve (reduced) Lu tones, five (those with decimals) have been omitted, and only those having whole numbers are taken into account.  The remaining tones form a diatonic scale of Perfect intervals, shown below.  Beginning with 364.5, taking this note as F#+, the alphabetical names are F#+ G A B C D E F#+.  
 


According to Chinese scholar Joseph Amiot, the fundamental standard pitch of the ancient Chinese pitch pipe (“lu”) was F#.  (He estimated it at approximately 708 cps).  This fundamental pitch was called the huang chung and represented the “eleventh month” of the calendar.  For reasons that will be shown, I believe the elusive “lu” is the F#+364.5 and its octave double, F#+729.  My reasoning is as follows.  When the “power” of 364.5 is increased by 8 (364.5 x 28), the resulting frequency is 93312, the first “official” note ascribed to the ancient Chinese Lu scale.  

I believe that the line, “bent into an octave circle (364.5/729), represents the infamous “Tyrant” imprisoning the white hexachordal notes in between its black sharp clutches.  The confinement takes on intriguing implications as the confinement within the octave of electromagnetic “light” waves: 93312 to 186624 (the speed of light generally conceded to be “approximately” 186000 miles per second).  

The reason is obvious: there is no such tone resulting from powers of 3 or powers of 2.  Even though this thirteenth tone may indeed complete the full “octave-year,” it is essentially “bogus.”  It “comes in from outside,” it brings in a “foreign” element that “taints” the purity and perfection of the perfect system.  The perfection of powers of 2 and 3, the perfect octaves and perfect fifths, is sacrificed, so that movement can occur; there can be flow from one level to another: fagologeria.

The derivation of the Lu scale from the “lambdoma,” the result of powers of 2s and 3s, is elaborated in Gurdjieff, String Theory, Music; while the explanation of the srutis as the “Word” is explained in Nearly All and Almost Everything.  Time and space do not permit the “reinventing of the wheel” at this point.  However, the reader is urged to review these fundamental organizational foundations in order to understand what follows. 
 

Another view of the Chinese Lu Scale
 
ANOTHER VIEW OF THE CHINESE LU SCALE
Click table above to enlarge


The Lu scale, I believe, has correlation with “April Fool’s Day.”   Some say this day, supposedly dedicated to joking, originated in France in the 16th century, when there was the shift to the new Gregorian calendar.  In the old calendar, the week of the New Year ran from March 25th to April 1st.  There were some who would not count by the new and revised calendar.  Perhaps they forgot (calendars were not the commonplace they are today).  Perhaps they could not count.  Or, more likely, perhaps they flatly refused to acknowledge the weekly celebration of the New Year which had been arbitrarily changed by the king from the last week in March to the first week in January.  From such a change in the laws, the beginning of the New Year could no longer blossom in the springtime (March, the vernal equinox); and the seventh month would no longer occur in September (sept, seven) at the autumnal equinox.  Instead, what was formerly the eleventh month, January, would now originate the new calendar months.  (This sounds suspiciously like the Chinese Lu Scale which, according to ancient texts, begins at the eleventh note).  

Since a revised calendar would make the times and seasons “out-of-whack,” one sees how there could be very valid objections to such arbitrary overruling of Nature’s plan.  Those unfortunate dissidents, the resistors, who continued to abide by the old calendar dates were derided as “fools” by the power-possessing beings of the period.  

The resistor is the simplest of all electrical components, and constitutes the cornerstone of electronic circuits.  Its resistance is measured in ohms (or is it OMs)?  The behavior of a resistor, said to be passive and linear, depends upon the instantaneous value of current flow now (flow of electric current is simply a stream of electrons moving through a wire; the word “current,” in fact, means “happening Now”).  There are two magnitudes: the current itself, measured in amperes, flowing through it; and potential difference, measured in volts, defined as difference between elements.  

Derision being a valuable political tool for effecting rapid change in the populace, a whole day was set aside for the sole purpose of ridiculing fools, and was called April Fool’s Day.  (However, one may also realize that even dubious “honors” effectively serve to implant into subsequent generations the hint that something important happened here, should one care to look).  Since the termination of the old celebration (the “tail-end”) was April 1st, the jokes played on these resisting simpletons, or April fools, usually focused upon the posterior, the “tail.”  

Jokes and fools go together.  The “fool” is a “joker,” one who is thought to be stupid.  In some languages the “j” is pronounced as “y” (or vice versa).  A “yokel” is a contemptuous term used for a country bumpkin, an apparently stupid, simple man who resembles the “The Fool” in the ancient and mysterious Tarot deck, represented by card 0.  Not unlike the “Joker” in an ordinary deck of cards, the “Fool” (0) has a certain ambiguity.  It is the “extra” card, one that can be used as trump in any suit; one that can win no matter what regime is in power.  History and literature indicate that the medieval court jester, or wit, (de wit, again) played the part of the “fool,” and often transmitted crucial information through the subterfuge of hilarity.  His jokes were used as the means of trickery and deception.  In governmental legislation, clauses called “jokers,” by trickery, render a bill ineffectual, or make it serve some cause for which it was not originally intended.  

For those of Gurdjieffian persuasion, the “joker” clause sounds a whole lot like the organ Kundabuffer.  Placed in man by the legislative authority of the Most High Commission, this maleficent organ grew at the root of the tail.  By means of this inserted “clause” (claws?), as it were, man (originally intended to serve something Higher) was tricked into “feeding the moon” (something Lower) without rebelling at the knowledge of his plight.  The organ Kundabuffer, it was said, caused man to see reality “topsy-turvy.”  
 

Topsy-Turvy Derivation of the Twelve Lu
 
TOPSY-TURVY DERIVATION OF THE TWELVE LU
Click image to enlarge


There is another card in the Tarot deck that now comes to mind, the one called “The Hanged Man.”  To see the connection between it and “joker” (or “Fool”) requires taking a new look at what I have called “The Musical Tree,” now viewed as a man hanging upside-down:  The real Master, the root of the system, is invisible.  The “grounding” comes from the region at the foot of the Tree, not its head.  

The words in Ouspensky’s Symbolism of the Tarot about “The Hanged Man” are apropos.

"In his own soul appears the gallows on which he hangs in suffering, feeling that he is indeed inverted.  He chose this way himself.  For this he went over a long road from trial to trial, from initiation to initiation, through failures and falls.  .  .  . he seeks for Truth in a desert.  Now he has found Her."

 

The Hanged Man
 
THE HANGED MAN
Click image to enlarge
 


Obviously the three parts of the tree show the places where the three kinds of food enter the organism: ordinary food, air, and impressions.  In musical terms, they show the “compounds” required, and how they must be mixed in a definite proportion as determined by nature.  Only the correct relationships, or ratios, enable the proper “laws of passage” between the parts.  The connective links that integrate the component parts are found on the central column: Octave to Tone; Tone to Pythagorean Comma; Pythagorean Comma to Diaschisma.  From the Diaschisma, there is no “direct line” to the Prime.  Here one must take a “leap of faith.”  The three segments, in musical terms, are the three scale genera.  In terms of electricity, they are the three components of an electrical circuit.

An electrical circuit consists of three interconnected components, called resistor, inductor, and capacitor, that are confined between two extremities (bipolar).  These three components are the three “passive” building blocks upon which the whole of electronics is predicated.  Where one component is connected electrically to another component is called a “node,” (sounding suspiciously similar to a “note”).  Mathematicians use integration and differentiation to solve the complex behaviors of the three components.

What is really at stake here is man’s whole evolutionary potential (and “potential” quite literally refers to the electro-magnetic potentialities within the brain and spinal column that exist to a great extent unused).  Man has to learn how to “hook himself up” so that he can connect to the Greater Circuit, the Large Accumulator, the Prime Mover, the Master Controller.  (This idea is elaborated in The Meaning of the Musical Tree).  

The Tree has a curious connection with the change in the calendar, and with those April Fools, those resistors, who refused to abide by the new time-keeping.  Remember, the April Fools wanted the month of March and the vernal equinox to originate the calendar.  Keeping to this scheme, the month of February, having 28 days, would be the twelfth month, and January the eleventh.  December, the tenth month, would end the decimal year, November would be the ninth, October eight, September seven, August six, July five, June four, May three, April two, and March one.  

The first month, March, may show the derogatory connotations associated with the word “yoke.”  For example, in ancient Rome it was a device made of two upright spears across which was laid a transverse piece under which conquered armies were forced to march.  Yoking of animals kept them subservient and under the task-master’s whip.  In Scotland a yoke is the amount of time in which a yoke of oxen can do a specified amount of work.  Although the old calendar year beginning with March conveniently corresponds with the word-definitions of the months, and with the observed seasonal changes of nature, it has disadvantages.  One might say there are “leakages” in the system causing difficulties to arise in keeping accurate records.  These difficulties accrue as succeeding years become more and more out-of-phase.  The heavens and the earth no longer correspond.  Mere observation of the stars brings no relief.  In fact, the natural law of perception has become a “stumbling block.”  Something more is required.  Man must use Reason, must calculate how to make the connection between the Higher and Lower realms.  What did the ancients really mean by this word, Reason?  Would it not apply to mental calculations regarding the tonal frequencies?  

There is more to be discovered from our musical “QCD” chart.  For one thing, the further connection of black diagonal lines produces the Just diatonic semitone [16/15].  
 

Integration
 
INTEGRATION
Click image to enlarge


This Just diatonic semitone is the product of Limma x Comma [256/243 x 81/80 = 16/15].  Curiously, the “right-angled” triangles that appear on the graph above are now a “fit” with the Pythagorean Theorem: the “sum” (in terms of musical ratios, the “sum” is the product and requires multiplying, not adding) of the squares of the two legs of the triangle is equal to the square of the hypotenuse.  

Now there are three Just ratios: Just-Diatonic-Semitone [16/15], Just-Chromatic-Semitone [25/24], and Just-Enharmonic-Semitone (the “comma diesis”) [81/80].  These are the same three Just ratios which naturally occur from the 16 x 16 grid, the result of the HARMONIC OVERTONE SERIES.  (The explanations and calculations regarding this crucial information are given in another of my writings, The Just System of Srutis).  The Perfect and the Just systems are becoming integrated.  

The integration of the two incommensurate musical systems becomes even more apparent when yet another line is added to the graph.  This new line calculates to be the Just Minor Whole Tone, or 10/9.  This
 

Rhythm
 
RHYTHM
Click image to enlarge


The distance “across” each rectangular “diamond” in the figure above calculates to be 32/27, the minor 3rd (Major Whole Tone plus Limma, or 9/8 x 256/243].  This pink “diagonal” multiplied by the other green “diagonal” of 25/24 (Just-Chromatic-Semitone) equals 1.2345679. [32/27 x 25/24 = 1.2345679, a repeating decimal].  When inverted, the number becomes 0.81 i.e. the One divided by the parts [1 ÷ 1.2345679 = 0.81].  

There are five rectangular diamonds in all, each divided vertically in half, making a total of ten triangles.  The perimeter of each triangle also sums to 1.2345679, or inverted, to 0.81. [10/9 x 16/15 x 25/24 = 1.2345679].  The whole thus divided within by the ten triangles, each division equals 10 x 0.81 = 8.1.  The length of the pipe of the the huang-chung, 8.1 ts’un, was the fundamental measure of ancient China. (The ‘ts’un” is also discussed in prior writings).   

(This is 90/81.  Mathematicians and engineers may find it interesting to follow through with an investigation of “Fibonacci Ladders” and “power of 10 attenuators,” the latter which divides the input voltage by successive powers of 10 such that m2 = 81/10 when series arm resistance, r = 81ohms; parallel arm resistance, 1/p = 10ohms; terminal impedance, 9ohms; input impedance, 90ohms.  I have drawn freely from the illuminating book, Gnomon: From Pharoahs To Fractals, by Midhat Gazale, Princeton Univ. Press, 1999.  Any misinterpretations of the scientific material are my own.)

The picture above looks very much to be the description of the sound Parmenides mentions in his poem, where he speaks of the huge doors that spin open, rotating in hollow tubes or pipes.  The Greek word for pipe is syrinx, and syrinx and hissing and serpents and kundalini go together.  Parmenides must be telling us that this hissing is the sound of the universe being created.  

The picture may also describe the “siren” mentioned in the chapter, “The Bokharian Dervish,” (p. 890-1) about which Gurdjieff says “The construction of this childish bauble consists in this, that a current of condensed air is directed from a pipe, on to a revolving disc drilled with little holes, each hole exactly coinciding in size with the opening of the main air pipe; and as this disc revolves, the passage for the current of air, entering these holes form the main pipe, is alternately opened and closed.  And thus during the rapid revolution of this disc, successive shocks of air are obtained in the holes, and these produce an even-pitched tone of sound, and the number of revolutions recorded by the clock mechanism, multiplied by the number of the holes of the disc, should give the number of the vibrations of that sound made in the given interval of time.”

Recognizing that my expertise in the field of electricity and magnetism is so lacking as to be non-existent, nevertheless I must mention remembering seeing pictures about generators and electric motors in which loops of wire (looking very much like the “diamonds” in the graph above) are mounted on a cylinder between two poles and are caused to turn by an induced current.  In terms of tones, the slight discrepancy of the Pythagorean Comma ratio is what induces the current to flow.  What we may have, so to speak, is an “induction motor,” which can convert electrical energy to “Work.”  Maybe someone with real knowledge in this area will be able to see how musical frequencies and their “rhythms” are the actual causal connections, the “first principles,” by which “loops” of string-wires generate motive power.  Music, it will be found, really does keep the universe humming.  

What may also be described here, albeit in musical terms, is a “three-phase alternator.”  There are not one, but three currents, which may be obtained, each a little out-of-step with the other.  In musical terms, these three different currents, each from different sources, are shown below.  
 

The Musical `Three-Phase Alternator`
 
THE MUSICAL `THREE PHASE ALTERNATOR`
Click image to enlarge



Obviously the middle row is the Lu scale itself, whose tone of origin is 364.5.  Every tone in the row below it, beginning with 360, is lower by the interval of the Just-Enharmonic-Semitone, the comma diesis, 81/80.  In the row above the Lu scale are the Perfect dieses, recognized as being exactly one schisma [1.0011292] above the lineage of Chinese Lu tones.  

Mathematically, the intervals relate as follows:

The comma diesis [1.0125] multiplied by the schisma [1.0011292] equals the Pythagorean Comma[1.0136433].  The integration of vertical rows I and II, and II and III, produces this interval.

The proportional division of the comma diesis (1.0125) by the schisma (1.0011292) produces the diaschisma (1.011358), the lowest circle on the trunk of the Musical Tree.  

The region in between the two “hemispheres” is Middle C, forming the bridge.  
 

The Solid
 
THE SOLID
Click image to enlarge


The picture formed by the Chinese chromatic scale depicts an “axis-based” tonal structure with “tonic” as B124416.  The two separate “boxes” encapsulate the lower sub-dominant tetrachord (F# to B, the ratio 4/3) and the higher dominant tetrachord (C# to F#, also the ratio 4/3).  These two enclosed tonal regions are separated by the whole tone (B to C#, the ratio 9/8).  However, there is the more central division that occurs at middle C, the tritone.  The middle C divides the octave F# exactly in the middle: seven semitones above, and seven semitones below.  The exact halving of the whole tone (i.e., taking the square root of 1.125) results in the ratio 1.0606602.  

If the F#360 is assumed to be the F# above middle C256 on the piano keyboard, then the note “middle C” on the above chart will fall at 2.8284269.  This number, according to Fuller, relates to the cube.  “It is the cube formed by a uniform width, breadth, and height of v2 is v23, which is 2.828428.  Therefore, the cube occurring in nature with the isotropic vector matrix, when conventionally calculated, has a volume of 2.828428.” (Synergetics, p. 589)  Fuller says this cube is “exploratorily noteworthy.”  

2.8284269 is what Fuller calls “humanity’s conventional mensuration cube with a volume of one.”  He says that “to have a conventionally calculated volume of 2.828428, this same cube in the relative energy volume hierarchy of synergetics has a volume of 3.  “To correct 2.828428 to read 3, we multiply by the synergestics conversion constant 1.06066.”  (Synergetics, p. 590)  

                3 ÷ 2.828428 = 1.06066.  

Geographically, the Isthmus of Corinth divides the mainland of Greece from the Peloponnese, a large peninsula with water on two sides.  

Fusion has to do with integration.  What, exactly, is it that needs to be integrated?  The answer is: man’s two brain hemispheres that otherwise have little in common.  The “integration” of these two separate entities must have something to do with the corpus callosum (“hard body”), the thick bridge of neural tissue in the middle of the brain whose role is to convey information from one side to the other, enabling each part to contribute its part to achieve integration of the whole.  The corpus callosum, neuroscientists say, maintains a balance between the arousal of thought and attention.  Those persons in which the corpus callosum is thin or non-existent (the technical term for partial or total absence is “agenesis of the corpus callosum”) are plagued with brain disfunctions such as attention-deficit-disorder and autism.  

The popular film, “The Rain Man,” has familiarized the general public with the effects of a missing corpus callusom.  This film is a true story about the idiot-savant, Kim Peek, whose phenomenal memory abilities have made him almost a celebrity.  Despite his monumental feats of data retention (which are not unlike the memory system of a computer and, at least in Peek’s case, seem to be one of the positive outcomes of agenesis corpus callosum), the fact is, he is retarded and cannot dress himself, brush his teeth, comb his hair—in short, he cannot take care of himself.  Peek cannot conceptualize, make analogies.  For him, “get a grip on yourself” means to grab yourself with both hands.  A literal understanding is all he knows.  As Gurdjieff implies, one of the important characteristics of human thinking is that of analogy (“a nail is like a requiem”).  For Peek, making analogies is beyond his capabilities. The middle C produces the scale of equal temperament.  


Chart: Middle C and Equal Temperament

F# 1.0000000 0
G 1.0594631 150
G# 1.1224621 300
A 1.1892071 450
A# 1.2599211 600
 B 1.3348399 750
C 1.4142136 900
C# 1.4983071 1050
 D 1.5874011 1200
D# 1.6817929 1350
E 1.7817975 1500
E# 1.8877487 1650
F# 2.0000001 1800

 



 “The Musical I Ching”

Gurdjieff certainly considered Morse code relevant in the Work, hinting of its importance in his “Morse “Movements.”  Look, for instance, at how the Morse letters below form the word “Amin,” which is indeed the name of one of the Morse Movements. 
 

1 0 = dot, dash A
0 0 = dash, dash M
1 1 = dot, dot I
0 1 = dash, dot  N
  0

Look, also, at how, with the addition of the “0” at the end of “AMIN,” the four-letter word transforms to become the five-letter word, “Amino.”   Amines are very interesting to contemplate.  For example, the ammonia molecule, NH3, is obtained by the dry distillation of nitrogenous organic bodies (bones, blood), and the solution of this gas in water is known as “hartshorn.”  Does “amino” signify the hart/heart’s “horn,” giving it the power of speech?   The idea might not be as absurd as it first appears.   The addition of the 0, tacked on, would be an “artificial something,” not an actual part of the genetic encoding.  Signifying “nothing,” it could be the very thing that afforded dumb animals the capability to use words, to name things.  I thought of another of Gurdjieff’s “Morse Movements” titled “Adam and Eva.”  It was the biblical Adam, in Genesis, who was given the capability to name.

Being a musician, naturally I began contemplating the musical possibilities.  

Looking (listening) to the primal poles of yang (dash, 0) and yin (dot, 1), it was only a matter of musical logic to assume the interval of a major third to be the male principle, yang, (0, “Adam”), and the interval of a minor third to be the female principle, yin (1, “Eve”).   Remember, it is always the third of the chord that determines the “sex” of the triad.  

Now things began to take on real sound, vibrate, make a “joyful noise,” to “leap as an hart.”  To him that hath ears, let him hear the musical sounds of the I Ching!

According to Chinese history, in the mists of time Fu Hsi created the trigrams, made up from the two basic elements.  Let us here assume these two “basic elements” to be the 1 and 0, the “two I.”    

These two forms produced the four Hsiang.  Geneticists know there are four different nitrogenous bases: guanine, adenine, thymine, and cytosine, abbreviated by the letters G A T C.  Musically, speaking, the dots and dashes, or four elemental principles, produce the four Hsiang, the four triad possibilities: augmented (A), major (M), minor (m), and diminished (m).   The four Hsiang again produced the eight Kua.  From the eight Kua ensued the great business of life.

Read more about the Musical I Ching here and here and here


The I Ching and DNA Chaos

DNA Chaos
 
The I Ching and DNA Chaos

Click image above to enlarge


 


 

Top of Page