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Music of the Spheres and the Harmonics of Being: The Search for Awakened Listening
"In the Beginning was a Vibration--or the Word, if you prefer..."
This remark by G.I. Gurdjieff, as well as other telling observations on sacred chant remembered by a young medical student in the 1920s, was followed by a practical demonstration: Gurdjieff chanted the Lord's Prayer in a special way, intoning the entire text in one long breath, on a single note, at the same time asking the student to place a hand on his chest. The young man reported feeling something like an electric current. Apparently the art of chanting was yet another sacred science of which Gurdjieff had a practical mastery.
I met the Gurdjieff Work and Lord Pentland in 1975, after 5 years of magnetized search, at exactly the same time my inner and outer ears were awakened by overtone chanting from Tibet, Mongolia and Tuva, by the Gurdjieff-deHartmann music, by overtone music in the west (LaMonte Young, Terry Riley, Tony Conrad). 1975, when I was 22, is the year I founded The Harmonic Choir in New York, following my first artistic incarnation in New York as a successful experimental filmmaker; it was for my film Moving Parts, which I showed at the Whitney Museum in 1973, that I first searched for prismatic sound.
In 1981, in Paris upon return from a research trip to Mongolia in search of fragments of forgotten teachings about primordial sacred chant and the music of the spheres, I had the good fortune to have an audience with the great Tibetan Buddhist master, Thuksey Rinpoche, thanks to a wonderful mentor, James George. After my offering Harmonic Chant to Rinpoche at his request, he remained silent for a moment, and then did a Mo divination to ascertain what 'security clearance', what level of teachings, he might share with us. Apparently we passed muster, and what followed changed my life. He began by saying, "Young man, it's very interesting what you've shared, but did you know that in our tradition, the art of sacred chant is just one chapter of the great art of breathing?" And he proceeded to guide us, under the vow of secrecy, through an utterly extraordinary series of contemplative breathing exercises. Rinpoche was apparently gravely ill, and yet there shone such a light from him as I'd seen only before in Gurdjieffian masters such as Lord Pentland and Michel de Salzmann. Afterwards Mr. George and I sat for a long time in a great stillness, bathed in the resonance of another dimension.
From that time on, following the songline into the harmonic world has been accompanied by the corresponding inner journey, back through the inner octaves of sound, breath, listening awareness, sensation, silence, space and light, back toward Holy Sun Absolute, toward the Dharmakaya primordial awareness, to the very heart of the innermost octave. The aim has always been to develop Harmonic Chant equally as both an approach to the music of the spheres and to development of the harmonics of being.
Lord Pentland brought me to Paris in 1977 to meet Mme. de Salzmann, Dr. Michel de Salzmann, Mr. Henri Tracol, and Mr. Peter Brook, so that I could share my music with them and, perhaps, offer music to the film, "Meetings with Remarkable Men." I was of course thrilled when this indeed came to pass. Over the course of many years, the awakened teachers and great artists in the Work remained great sources of inspiration, as are today the great Buddhist Dharma teachers at whose feet I sit.
Over the years, I gradually came to understand that harmonic presence is not just outer sound, not just inner vibration, but something universal in this cosmos, at all levels, in all octaves.
Here I focus mostly on relationships between the music of the spheres and the spheres of Being as expressed in the Gurdjieff Work.
Like light, musical sound energy is a blended spectrum of pure frequencies, which in music are called harmonics or overtones. This primordial scale governs the structure of every musical sound. Every note, whether chanted, sung or played, as well as any harmonic resonance, whether of a "string" of "String Theory" at the microcosmic level, of any of the infinite stars, or of the echoes of the cosmos itself, is a blend of these pure vibrations.
Within any such fundamental note, or '1', a particular series of these other notes appears, like light refracted through a prism. These higher sounds are from the harmonic series, which corresponds to the infinite series called the continuum, including all whole numbers and all whole number fractions from zero to infinity.
Besides being universal to musical sound, the harmonic series is innately part of the entire Creation, as much so as light, relativity, gravity and heat: harmonic waves-- the cosmic background radiation, or CBR-- were an integral energy in the earliest phase of the current Creation. All wave-like energies take the form of the harmonic series in responsive bodies and space, and the material universe is formed from the infinite internal relationships of this series. Study of these seemingly simple vibratory relationships can lead, in music and elsewhere, to enlightened and fruitful contemplation of the origin and nature of things.
Physicist David Bohm even suggested that this Creation was brought into being through energies coming together in the relationships of the harmonic series. In this view, such a harmonizing of disparate energies made possible a unified wave of summation which, in cresting, created the universe._ Thus, even the beginning of the universe, and therefore life, may not have been the random accident that science generally speaks of, but the action of harmonious forces on an infinitely vast scale. The echoes of that first moment still resound. Astrophysicists measure those harmonic echoes resonating everywhere in the Creation, from every direction. It's no coincidence that astronomers and physicists like Dominique Proust and Basarab Nicolescu find the terms we have proposed for the beginning such as the "Big Ring" or the "Great Sound" a better evocation of that initial "vibration" than the "Big Bang."
Perhaps there is not only a music of the spheres; perhaps musical laws helped serve their very coming into being. Music in this broader sense could be understood as the harmonic movement of energy, and musical laws, beyond their everyday uses in life on Earth, as the carrier waves of the Creation.
In music, through its interaction with what Gurdjieff called the "law of octaves," by which what is "above" and what is "below" can be related and attuned, the harmonic series becomes the source of melody, harmony and rhythm.
In the beginning of my work developing the Harmonic Chant with my group the Harmonic Choir, in the early 1970s, I was musically inspired by ancient sacred chanting with harmonics by the Gyuto and Gyume Tibetan Buddhist monks, by the hoomi singers of Mongolia, and by the overtone singers of Tuva, the Russian Central Asian republic adjoining Mongolia. Interest in harmonics, in "just intonation" (non-tempered tuning systems) is widespread in contemporary music, but this music from Central Asia seemed to go further.
I felt that the universality of the harmonic sound showed extraordinary possibilities which go beyond the usual aesthetic questions of culture, language and style. The development of these possibilities, which we call Harmonic Chant, could lead toward a new global sacred music, in the direction of what Gurdjieff called "Objective Music".
Gurdjieff's finely-tuned teaching makes very significant use of music. Music and musical laws were for him a perfect symbol of the structure and function of the entire Creation, and of the inner life of man. Gurdjieff had as his disciple the Russian composer, Thomas de Hartmann. Developed with Gurdjieff, the music they produced embodies magnificently Gurdjieff's teaching of what he called "the laws of vibration."
The Gurdjieff/De Hartmann music has a very special quality indeed, which we can feel, depending on the state we're in when we hear it. It is unmistakably a music of a certain time and place. But if one listens very attentively, within and beyond the music's inevitable and natural relationship to cultural circumstances, there are the harmonic vibrations of another kind of time, another kind of place --that of sacred listening, of inner work.
Krishnamurti said near the end of his long, extraordinary life that he felt he'd mostly been singing to the deaf. One positive way to interpret this comment, directed toward us, is to learn to listen. I feel work on listening to be the main opportunity that music provides. Work on listening seems to me to be an absolute key to the awakening we need to bring to life in ourselves and on this planet. Attunement, or work for harmony, depends first of all on a transformed listening.
Harmonics correspond, I think, to what Gurdjieff called "inner octaves," referring both to musical sound and to the vaster resonance of the cosmos. They are the genetic material of all musical sounds, and in their infinite combinations in the realms of scale, melody, harmony and rhythm, are the underlying basis of all music. The series is potentially infinite. But in any musical sound, only a certain number of harmonics are present and only up to a certain point in the series, depending on the quality and loudness of the sound and on the vibrating body producing it.
Very often, we do not really hear what harmonics there may be, because of our conditioned, habitual listening. The effect of this conditioned listening is we vary, as individuals, and even as whole civilizations, in our sensitivity to harmonics, and to harmony. Perhaps the range and magnitude of harmony obtaining in any particular sphere of activity is directly related to the quality of listening or attunement. In any case, what music or life can equally help us measure is to what extent there is a harmonic listening present in us, sensitive to different levels of harmony.
Harmony comes from above. Any two notes which are in harmony share a unison higher harmonic. In fact, all the notes we tend to sing or play as harmony can be seen quite literally as projections downward from a common higher 1 they all share. Harmony among different notes or vibrations can be made finer through awareness of this 1 above, the source note which is a shared higher harmonic common to each note below. A very deep harmony can be found also well below the actual notes, where they share a subharmonic root.
In bringing the harmonics more strongly to life through Harmonic Chant, the voice acts like a kind of sonic prism and lens, 'refracting' and focusing the harmonic notes, otherwise masked in the over-all timbre.
A chosen starting note, or DO, we call also "the first harmonic," the "fundamental" (note), or the "1". It is the tuning reference for the harmonics above (and the subharmonics below). As the whole number multiples of the frequency of the 1, they can all be expressed as fractions or musical intervals in relation to the 1, as for example 2/1, 3/1, 4/1, etc. In other words, they appear at frequencies twice as high, three times as high, four times, and so on... The harmonics of, say, a middle C, tuned to 264 cycles per second, are numbered and named by the whole numbers, beginning with 1 (for C itself), then 2, 3, 4, and so on... The first harmonic in the example given is the C itself at 264 cycles per second (cps); the second harmonic, or '2', is twice the frequency, 528 cps, and therefore an octave higher, i.e. C; the third harmonic, or '3', is G at 792 cps, and so on.
In many instruments, such as gongs and bells, the mass or tension of the vibrating medium actually pulls the harmonics sharp or flat relative to the pure proportions of the series. "Harmonicity" is the balance of three factors in vibrating bodies: sounding length or mass, tension, and diameter.
By the way, the tension is too high in the strings of the piano, pulling the harmonics sharply out of tune. Lowering the overall tuning even a half-tone dramatically improves the harmonicity. The harmonics of the voice, on the other hand, are absolutely in tune.
Mysteriously, there are no harmonics along the vertical axis between '1' and '2', measuring a perfect octave distance, a void. '1' and '2' are like the Below and the Above, like Earth and Heaven. The Egyptians had a saying: "All the Creation can be found between 1 and 2."
This observation can be studied musically in a practical way. All harmonics, even very high ones, can be transposed by ear and/or number downward into this basic 'prime' octave space between 1 and 2 and come to life as fundamental notes, thanks to what Gurdjieff called "the law of octaves". Given a 1 to be tuned to, every vibration has a place.
This provides an extraordinarily rich language of musical expression in terms of modes, scales, melodies, harmonies and rhythms. It is an essential key to appreciating the diversity of musical expression around the world. Its importance for music parallels that of the periodic table of elements for chemists, or that of the pure color spectrum for those who work with light.
One may think of the infinite variety of harmonics as falling into 7 main interval families, DO, RE, MI, FA, SOL, LA, and SI. The esoteric origin of these steps may be thought of as forming, according to Herbert Whone, a descending and ascending cosmic octave, beginning and ending in DO, Dominus-- God. RE is regina coeli, queen of the heavens--the moon. MI is microcosmos--earth and the human being. FA is fatus-- destiny; the planets. SOL is the sun. LA is the voie lactée--the Milky Way. SI is sideria--all the starry heavens. And again DO.2
In some traditions, for example in the raga singing of North India, patterns of melodic movement between 1 and 2 are understood as codes or maps for the relationship of energies moving through different scales and states in a human being. Of course, all that can only be real then, when every important aspect of how we listen, of how we receive sound in the body, the different centers of resonance, and so on, all interact... harmoniously.
The first ascending harmonic after the mysterious leap octave leap between 1 and 2 is 3, which sounds as SOL; 4 is DO; 5 is MI; 6, being twice 3 is therefore an octave of 3 and also SOL; 7, a SIb; 8, again DO; 9, RE; 10, again MI; 11, a note between FA and FA#; 12, again SOL; 13, a LAb; 14, same as 7; 15, SI; and 16, again DO; 17, a REb; 18, again RE; 19, MIb; 20, again MI; 21, an approximate FA; 22, same as 11; 23, FA##; and 24, again SOL.
There are ascending and descending harmonic series. The harmonics in musical sound are ascending, in the sense that as they increase in frequency, the pitch "goes up" above the fundamental note, but notes and inverse scales corresponding to the proportions of descending harmonic series (subharmonics) can be generated, and sung. For example, the musical distances of 2/1, 3/1, 4/1, etc., in the ascending series are mirrored perfectly by a descending harmonic series from the same note: 1/2, 1/3, 1/4, etc. The musical distances are identical, and of course the intervals are inverted (3/1 gives SOL, while 1/3, its inverse, gives FA). The two sets of harmonics are complementary, and the multiplication of any harmonic interval by the corresponding subharmonic intervals always gives 1/1 (3/2 x 2/3 = 3/3= 1/1, for example).
Even-numbered harmonics are repetitions of preceding harmonics, since they are divisible by 2, and therefore sound as octaves. The octaves of 1, for example, are 2, 4, 8, 16, 32, 64, etc. They are the same note higher up, or divided by powers of 2, lower down, as for example 1/2, 1/4, 1/8, etc. Odd-numbered harmonics are new notes, appearing for the first time.
The harmonics are the pure, non-tempered, truly in-tune versions of the much-reduced set of notes that, since Bach's time, has been enthroned in 12-tone equal temperament. Already in the 21 harmonics mentioned, we find notes both considerably different from their tempered versions (5, 7) and/or unknown in our usual scales (7, 11, 13, 14).
The major scale comes from the harmonic series. DO (1) , RE(9), MI(5), SOL(3), LA(27) and SI(15) come from the ascending harmonic series, and FA(4/3) from the descending, where "the 1 is above".
As one ascends into the harmonics (transposing/relating to 1 as one goes), after the harmonic void of the first octave, there are more and more harmonics per octave. In a next-higher octave of harmonics, there is always a new harmonic between every two adjoining harmonics from the preceding octave. For example, 3 falls between 1 and 2; 5 between 2 and 3; 7 between 3 and 4, etc. Finer and finer gradations of the basic notes are found, and the steps are closer and closer together. The musical difference between one harmonic and the next is more and more in the realm of extremely subtle microtonality.
The idea of intervals in music, of hearing one note with another and perceiving a specific harmony, can be seen as coming from the relationships of the harmonics series. Any given note can be understood as being a harmonic, and any given musical interval as the relationship between two harmonics.3 Their basic relationship can be transposed and expressed as a simple whole number ratio in the prime octave of 1 to 2.
All musical intervals, a higher note with a lower note, come about in one of the following three ways:
1. As the relationship between an ascending harmonic and the nearest 1 below as the lower note. Examples are 2/1 (the octave), 3/2 (the fifth), 5/4 (the perfect third). Mathematically, this can be expressed simply as h/1, where h is any positive whole number, and where the denominator is 1 or any of its octaves--2,4,8, etc.
2. As the relationship between a higher note corresponding to 1 or one of its octaves and descending harmonic of this1 above. Mathematically, this can be expressed as 1/h, where a note corresponding to 1 is the higher note, and the lower note corresponds to a harmonic projected downward from this 1. An example is 4/3, which defines the interval we call the fourth, DO-FA. 1/3 is the third subharmonic of a series projected downward from the 1. Since 3 is an odd number, it is the 1 that is transposed by octaves, to 4.
3. The third source of musical intervals, "when there's no 1," is the harmony between two notes, neither of which is a 1 or an octave of 1. This can be expressed as h1/h2. Examples would be the musical intervals 13/9, 7/5, 9/7.
Without transposing, the first group of intervals h/1, where h is any positive whole number, tends toward infinity as the harmonic number goes up. In infinity, one harmonic is as high as the next...a sort of silence in the Absolute. In the second case, intervals corresponding to 1/h, the expression tends toward 0, again, a sort of silence. And the third possibility, tuning non-1 harmonics to each other (h1/h2), the tendencies extend in both directions. With transposition, one can study all three "where one is" in the middle, in the prime octave between 1 and 2.
This possibility of attuning the harmonics to 1, to any other note, or to one another, means that the range of possible intervals and harmonies is as infinite as the harmonics themselves, encompassing any whole number ratio. The harmonics are the source of the reduced number of intervals we employ in our scales, where they are usually altered for the purposes of 12-tone equal temperament, in which no interval besides the octave is really in tune. The harmonics are also the source of many intervals we do not know or use, or have forgotten, of equally great musical interest.
Melodic harmonics at least as high as SOL 24 can be sung from the normal register; in the subharmonic chant, the harmonics can be in the 40s, some six octaves above the fundamental. There are other audible accompanying harmonics virtually to the limit of hearing. In the subharmonic chant, one can extend down to just about 0. It could be said therefore that the voice can extend from 0 upward as high as one can hear. One may hear as many as 7 sounds in the voice at any one time.
Harmonics too high to sing (in their original octave), but which represent factorable numbers, such as 25, 49, 63, 77, etc., can be found by first singing the fundamental note corresponding to a factor; the second factor, sung as a harmonic of the first factor, gives the harmonic in question.
In Mongolia, I was told a "different" story about harmonics than that provided by science: a sacred waterfall in the mountains of Western Mongolia was said to "sing" harmonics. Coming to that sacred place, people learned to sing harmonics from Nature Herself. The river below was called the Buyan Gul --Deer River-- because whole herds of deer were also attracted by the beautiful sounds and came to bathe in the waters. Singers of "hoomi", this Mongolian form of harmonic chant, were formerly said to be in contact, through the songs, with "supernatural forces." And so in Mongolia, as in Tuva, the Russian republic across the Yenisey River, there are historical connections between the chant and shamanism. For ourselves, we moderns, for the most part so out of touch with Nature within and without, we could understand that statement of contact, as being in touch, simply, with natural forces--the forces of Nature.
Understood in that way, the harmonics heard and felt, beyond words, are like the pure mountain source where the Mongolians say they first appeared. They are the direct expression of natural law--a stream of pure, communicating vibration. The harmonic sound seems sometimes to contain the seed of all music, a pure mountain stream nourishing all valleys below.
There is a direct references in Gurdjieff's book Beelzebub's Tales to a site, near "Gob," now covered by the Gobi desert of Mongolia, where the arising of special sounds in the atmosphere inspired construction of an astronomical observatory.
There are two stories about the origins of the Tibetan form of chanting very low notes with harmonics, which we call the subharmonic chant. The story I was told in Mongolia is that the Tibetan (and Mongolian) Buddhists adapted the more ancient shamanistic Mongolian hoomi singing. Hoomi singing is wordless, sung solo in a baritone or tenor register with melodic harmonics, whereas in the Buddhist liturgical chant, sacred texts are recited on extremely low (subharmonic) pitches by choirs of monks chanting generally in unison, and emphasizing generally one specific harmonic (SOL or MI). A Tuvan form of secular harmonic singing, the kargiraa, a sort of subharmonic hoomi, also may have been an influence on the Buddhist development. The other story is that the founder of the Gelugpa sect, Tsonkhapa, was taught that special chanting by a dakini (angel), while meditating.
Formerly, in the two leading monasteries of the Gelugpa sect, Gyuto and Gyume, where a form of harmonic chant is practiced, lamas would only be accepted after 20 years of preliminary training. Since the Chinese massacres and takeover of 1959, both monasteries exist, with difficulty, in India. The monks are mostly quite young.
My colleagues and I have brought a number of our own discoveries together with work with the sources of harmonic chant in Tibet, Mongolia and Tuva. In order to serve the possibility of a unified, global field of research, we have brought together this work along the following lines, which we call the 12 levels of harmonic chant.
The first seven concern specifically the basic acoustical fact of the harmonic chant, the possible co-presence in the human voice of a fundamental note and one or more harmonics, and the latter five, the extension of these in musical practice.
l. The singer produces a held note with one or several harmonics.
2. The singer moves melodically note and harmonics together in
3. The singer produces soaring melodies and harmonies
from the harmonic series above a held fundamental note,
which is the 'one' below for the notes above. This was inspired by Mongolian hoomi singing.
4. The singer holds a specific harmonic as a drone, all the
while singing melodies in the regular voice. These melodies will be formed among the notes of a subharmonic series below the held harmonic, which is the 'one' above for the fundamental
5. The singer moves melodically both the note and the harmonic,
in converging or diverging directions. That is, the fundamental note may go down as the harmonic goes up, or the fundamental note may go up as the harmonic goes down.
6. The singer holds a low fundamental note (C below middle c, for example) and 'refracts' the note downward by an octave, an octave plus a fifth, or (rarely) by another subharmonic multiple. This is subharmonic chant, inspired by the Tibetan monasteries Gyuto and Gyume. Resonated subharmonics, or undertones, replace the fundamental. This low note (approx. 45-80 hz) is now the acoustic fundamental, and 6 octaves of harmonics above this subharmonic are available. Subharmonic access is possible to Levels 1-5 and 7.
7. Vibration in the voice in addition to harmonics above the voice. Everything we otherwise call vibrato, tremolo and ornamentation.
8. Harmonic Modes. The generation and use of scales and modes from the harmonic series.
9. Harmonic Polyrhythm. The study and use of meters and rhythms from the harmonic series.
10. Harmonic chant in relation to chanted, intoned or sung text.
In many cultures it has been the role of music to help express a sense of the harmony of the universe in which we live, the sense of a harmonic order which one can aspire to in oneself, in spite of--in light of!--all shocks and daily contradictions. Could the fact of listening differently, we wonder, change one's ability to be open to the traditions, or to inner search?
The traditional idea of music as a real link to the sacred is in modern times mostly "hearsay". The measure of a music is in how it can help transform the state of our listening, focus it on essential communication, and make the idea of harmony real.
Here, Gurdjieff's indications as to the level of perception of truth obtainable through sincere study of music are quite striking. He embodied this principle even in the name of his center in France, the "Institute for the Harmonic Development of Man." His writings are full of indications concerning the science of vibration, and harmony, and even sound, but, as for all the other aspects of his teaching, there is no "manual," no "how-to". He knew that direct contact with a teaching is the only way to truly "hear" its resonance in the whole of oneself and one's life. His statements, even when they resound in the moment, guard symbolic meanings which only actual experience can illuminate.
In his Beelzebub's Tales, Gurdjieff discusses at length the possible ways one can research the fundamental laws of the universe and of the human being. He emphasizes just how far certain kinds of music, the science of "the laws of vibration," can help. And he widely employs musical metaphors to explain the action of these cosmic laws on every scale. He stresses that the real aim of research is the attainment of another level of being.
In his writings Gurdjieff praises the benefits of certain kinds of chanting, which he says bring to life a state of "echo" and "centralization" in one's being. He describes a "sacred, cosmic law of the universe,” given by the sounds "AIEIOIUOA": "There proceeds within every arising, large and small, when in direct touch with the emanations either of the Sun Absolute itself or of any other sun, what is called Remorse, that is, a process when every part that has arisen from the results of any one Holy Source of the Sacred Triamazikamno [Law of Three], as it were, revolts, and criticizes the former unbecoming perceptions and the manifestations at the moment of another part of its whole."
The art of chanting, when it is correctly transmitted, seems particularly suited to helping an inner listening, an inner attention, a state of greater presence to oneself, to appear.
Until I can listen better, there is no hope that I can hear a teaching. So many enlightened beings, so many sacred texts! But until I can hear what is being said, and can hear it working within, it is as Gurdjieff said--"like hearing a bell without knowing where the sound came from."
Our listening is often so conditioned, so filled up with thoughts and tensions, that it is as though we were deaf. The vibrations from subtler levels of our being, which Gurdjieff says are calling to us from within, go mostly unheard. However, these harmonics of the fundamental notes of our lives are necessary--they give quite another meaning to the deep tunings and mistunings which come and go, day after day, in ourselves and with others...to our coming and going itself.
What is harmony? What is listening? What do I need to hear? What should I listen to? Which direction is the right one? Will a listening help me steer? Will I echo when I'm dead? Listening is always in the present, and being one of our most vital energies, like breath it is replenished from the same source as the life force itself, with which it is intimately related.
An inspiring teaching is presented in Gurdjieff's written works regarding this universe, life, and our role, fate and place as human beings here on Earth. The basic language of this teaching, from top to bottom and from start to finish, is that of harmony, music, and vibration. And this on every scale, from the most vast cosmic processes, to their most silent and secret echo in the inner life of Man. Gurdjieff's vision of the cosmos, and of man, was that of a resounding scale or symphony of vibrations, which along an Axis Mundi, like a musical string, manifests every sort of transformation of the basic energy, from finer to coarser and coarser to finer. The finest, most harmonic and most complete primordial energy, the original Sound or Word of the universe, God saying BE!, in radiating outward in what Gurdjieff calls the "Ray of Creation," through a series of "descending" octaves, brings galaxies, stars, planets, and beings to life. In his view, this same primordial energy passing through everything finally rejoins its source, mounting through "ascending octaves" through finer and finer states of vibration.
In relation to the cosmos as a living, infinite system of circling, circulating and cyclic harmony, Gurdjieff saw the human being as both a small unfortunate dissonance, as regards his ego, his "little I," and as a microcosm of cosmic Being, which he called "real I." In helping us understand --that is, harmonize-- these two poles of our being, so tragically separated and fragmented, Gurdjieff brought to life a teaching with a very complete vibration, or as he said, a "wholly-manifested intonation," with many, many harmonics. That is, many levels.
When a new listening appears, everything changes...
1 David Bohm, Wholeness and the Implicate Order, Routledge & Kegan Paul, London:
2 Herbert Whone, The Hidden Face of Music, Garden City Publishing
3 With the sole exception of the notes of tuning systems, like our own, based on the (irrational) square root of 2.