Within the definitions of the suits, harmonies, and scales of the Muzoracle, there are a few concepts and terms that are continually referenced and should be made clear. First among them is the Harmonic Series.
The Harmonic Series is a map of the way objects vibrate in space, and the sound waves they consequently produce. The sounds we perceive as singular are actually combinations of many sound waves produced by fractional vibrations at the source. A plucked string, for example, vibrates at its entire length, producing what we perceive as its pitch; it also, however, vibrates to a lesser degree at half its length, one-third its length, one-fourth its length, and so on. Each of these smaller, quieter, inner vibrations creates its own set of waves, which intersect with the larger, louder one. The prominence or lack of these smaller waves -- called harmonics -- gives a sound its unique color. Sounds that contain prominent harmonics sound bright to us, like a string or a saxophone; sounds that contain only a few quiet harmonics sound dark, like a flute. Which harmonics are produced by a source and at what volume is determined by the physical attributes of that source: a vibrating string produces one pattern; a vibrating column of air within a horn, another; a struck drumhead, another still.
The larger, louder wave within a sound -- the one that for us defines its pitch -- is called a fundamental. While the differences in volume between a fundamental and its harmonics vary depending on the source, the relationship between them in terms of pitch is consistent no matter what the source. If a string, for example, is vibrating along its entire length at 440 times per second, its first harmonic, produced by the string vibrating at half its length, is vibrating at twice that speed: 880 times per second. Its next harmonic, produced by the string vibrating at one third its length, is vibrating at three times the speed of the fundamental: 1320 times per second. This pattern of relationships can be found in the sound of a trumpet as well as string, and in the sound of a drum, and in the sound of tires screeching on the road. What were looking at, what were hearing, is the Harmonic Series, those consistent frequency relationships between a fundamental and its harmonics that are present in all sound. The Harmonic Series can be simply expressed in ratios like so:
Fundamental, 1:1; 1st Harmonic, 2:1; 2nd Harmonic, 3:1; 3rd Harmonic, 4:1
Octaves in the Series. Musically, if we hear two instruments each playing a note at the same frequency -- at a ratio of 1:1 -- we obviously can say theyre playing the same note. Oddly, though, if we hear two instruments playing at frequencies separated by a ratio of 2:1, they also sound like theyre playing the same note, although one is higher than the other; this paradox is the phenomenon of the octave. Hearing the doubling of a frequency as the same note is universal, and the names of musical notes and the pattern of keys on a piano reflect this: they repeat every octave. In the Harmonic Series, a great many of the harmonics arising from the fundamental are octaves: 2:1, 4:1, 8:1, 16:1, etc. all sound like the same note, only higher. The harmonics in between the octaves, however, are a different story -- in them we find brand new notes in relation to the fundamental: harmonies.
Harmonies in the Series. The first harmony to arise from the fundamental, the first harmonic that is not an octave, is the harmonic at 3:1. This harmonic has a relationship to the harmonic directly below it -- that of 2:1 -- at a ratio of 3:2 (see below.) We call this harmony a Perfect Fifth. The second harmony to arise from the fundamental is that of 5:1. Its related to the harmonic directly below it at a ratio of 5:4, and is called a Major Third. A fundamental or one of its octaves, a Perfect Fifth, and a Major Third sounded together make a Major Triad -- arguably the most sonorous, ubiquitous, and satisfying chord on Earth.
The existence of the Harmonic Series demonstrates that all matter vibrates in a consistent pattern. And at a molecular level, at a quantum level, everything is always vibrating. That we like Major Triads is more than just a matter of acquired taste; they are a pure expression of our vibrating universe. Indeed, music as a whole -- harmonies, melodies, scales, and even rhythm -- arises from the permeating physicality and lawfulness of the Series, and so is a core expression of all that is within and without us. No wonder music affects us so; no wonder it can heal.
Probably the chief allegory in the Muzoracle system lies between the Harmonic Series and the Law of Three as defined by G. I. Gurdjieff. The Law of Three states that there are three primary forces at work in our world: the Affirming, the Denying, and the Reconciling, called in the Muzoracle the Initiating, the Receiving, and the Conciliating.
The Initiating and Receiving Forces. The Initiating and Receiving Forces are analogous to the Taoist concepts of Yang and Yin, respectively; they are sometimes referred to as active/passive, positive/negative, and masculine/feminine, although those terms -- all terms, really -- sell the concepts short. The Yin or Receiving Force refers to the passive action of that which is preexisting and receptive. It is the darkness from which existence springs, and the nothingness into which something-ness enters; it is the is-ness, the eternal aspect of things. The Yang or Initiating Force is that which springs forth from Yin, and penetrates it as well: it is active, bright, and moving; it rises and falls and actuates change. The Receiving and Initiating Forces can be seen in the Pagan concepts of Goddess and God, as they relate to the cycles of life, and in our many myths of death and resurrection: the Goddess is Earth eternal, while the God, the Year King, comes and goes, seeding the future upon his death.
The Conciliating Force. The third force, the Conciliating Force, is that which brings the first two together and allows phenomena to manifest. In electricity, for example, the first two forces exist as positive Yang and negative Yin currents -- both of which are moot without the presence of the third force, alive in the conductor. The third force can also exist within a catalyst, as when flour and water become bread with fire, or two sides of a case are resolved by a judge. It can also sometimes exist within a result, as when a teacher and pupil ensure transmission of a teaching.
While we can observe the effects of this third force and sometimes see what brings it about, the force itself is ultimately a mystery to us. Electricity is a classic example -- we dont really know what it is. We can measure the activity of fire on flour and water, but the true how and why of that activity is a mystery (and so, by extension, is bread). We can see a judge resolving two sides of a case, but the actual activity of resolution -- what is that?
Slippery as the Conciliating Force is to define, it is easy to see when its lacking: the first two forces play off one another endlessly, and nothing is resolved. Lack of the third force can readily be seen, for example, in war: regardless of either or both parties intentions or roles, it inevitably winds up a game of pass the gun.
Three Forces and the Major Triad. In the Muzoracle, the three forces are equated with the Major Triad. The Initiating Force resides at 3:2 in the interval of the Perfect Fifth, which marks the initial appearance of harmony in the Series. The Receiving Force is found in the space between the Perfect Fifth and the Octave just above it, in the interval of the Perfect Fourth at 4:3. The Conciliating Force appears in the sonorous Major Third, which arises just above the Perfect Fourth at a ratio of 5:4. These correlations play a big part in the way the harmonies are defined in the Muzoracle, and influence the meanings of the scalepoints as well.
Notes on their own or in harmony occur at once and, in the Muzoracle, refer to states of being; scales occur over time and refer to points in a process. The meanings of these process points -- the scalepoints -- are associated with another concept presented to us by Gurdjieff, the Law of Seven.
Ascending and Descending. The Law of Seven posits that the course of any process can be plotted over seven points analogous to the Major Scale. Descending scales refer to the downward flowing processes of nature: the things that happen around us and to us. Ascending scales refer to the upward flow of will, to intentional processes: the things we make happen, or try to.
Diatonic and Chromatic. Both ascending and descending scales are plotted in the Muzoracle on the seven familiar points of the Diatonic Scale: do, re, mi, fa, so, la, ti. These points are like rungs on a ladder; they have a different significance, a different meaning for us, depending upon which direction we are traveling. The bottom rung of a ladder, for example, marks the beginning of an effort when ascending, and the end of a journey when descending. Thats why we determine the direction of a casting at its outset: the points we reach mean different things, depending on whether were going up the scale or coming down.
The Diatonic Scalepoints, shown on a piano keyboard in the Key of "C"
There are, of course, twelve points on each die. The other five scalepoints -- the Chromatic Scalepoints, shown on the black keys in the diagram below -- do not have meanings separate from the Diatonic points; instead, they are mirror images of them. The Chromatic Scalepoints allow ascending meanings to appear in a descending casting, and vice versa.
The Diatonic and Chromatic Scalepoints
The Ray of Creation. The focus of the Law of Seven, as presented in the Gurdjieff literature, is not so much about generally defining each point in the scale; its more about the differences in vibration and density between the points, and how we might navigate those differences. (The Muzoracle, of course, does define the points not in any ultimate kind of way, but in a way that suits its processes and purposes, which are those of divination.) Gurdjieff does, however, provide us with one point-defined example of a very large descending scale: the Ray of Creation. In it he plots the ancestry of the cosmic beings of our world galaxies, suns, planets, et al. and our place among them. The highest point in the scale, of course, vibrates the fastest; it is also the least dense, and levels of increasing density and slowing vibration cascade downward from it, through the cosmos to our relatively law-bound world. The fastest and finest, however, permeate the slow and coarse: the cosmic ancestry that we are contained within is contained within us as well. Through conscious effort, through becoming that which we already deeply are, lies the possibility of individual evolution: the downward and outward flow of nature provides the possibility of inward and upward ascent. We can climb the ladder by virtue of being on the ladder. This magnificent allegory, so interconnected with the reality of music, brings additional meaning to the scalepoints and much of the Muzoracle system as a whole.
The Ray of Creation as it interfaces with the Muzoracle System.
Decrements. Most pertinent to the Ray of Creation -- and the Law of Seven in general -- are two unique intervals that occur within the Major Scale, described in the Muzoracle as decrements. The space between mi and fa, and between ti and do, is less, in terms of frequency, than is the space between the other steps. This can be seen in the scale diagram above: looking at a Major Scale in the key of C on a piano, we can see there is no black key between mi and fa and ti and do. According to the Law of Seven, the decrements in a scale require a different brand of energy to navigate; exactly which brand depends on the process at hand, and whether were going up the scale or coming down. In the descending scale that is the Ray of Creation, the first decrement -- the one between do and ti, between the Absolute and the Universe -- is filled by Divine Will. The second decrement -- the one between fa and mi, between the Planets and the Earth -- is filled by life on Earth, by us.
The meaning and function of each step in the Ray of Creation as it relates to the Muzoracle is further explored on the Scalepoints and the Ray of Creation page.
In order to absorb the significance of the Ray of Creation, one must first realize that the Major Scale is not an arbitrary collection of pitches. The interval of the tritone arises at 7:5 in the Harmonic Series; this tritone pulls us by the ears to a new key, a key whose do is a Perfect Fifth below where we started. This new do then spawns its own Harmonic Series, which in turn leads to another do a fifth below it, and so on. Students of Music Theory will recognize here the emergence of the Circle of Fifths, the basis of all twelve keys in our chromatic system. What also emerges are two interlocking Major Scales a tritone apart from each other, one going up while the other comes down. It takes some Theory chops to wrap your head around this; its explained in much greater detail in the Harmonic Engine pages. The point, though, is this: scales are just as much a result of natural law as harmony is. Indeed, scales are harmony, flattened and pulled through the dimension of time -- much in the way that experience derives from being.
The Ray of Creation is a mythic map of Nature unfolding, a Jacobs Ladder of density and vibration, a living history of the worlds within and without us. It implies an astrology of vibration. The scalepoints as defined in the Muzoracle derive from that astrology: they are particular, momentary views of level; they are snapshots of density in time.
Here and there in the Muzoracle -- particularly in the Harmony definitions -- there is mention of a pull upward or a pull downward. This refers to a pull toward a new key center, usually either a fifth higher or a fifth lower than the one of our casting.
Key centers have an order just like scales do, and like scales their order may be ascending or descending. Rather than being separated by the stepwise ratios found in a scale, though, key centers are separated by fifths. While the points in a scale refer to points in a process, movement between key centers refers to shifts in density and vibration, to shifts in paradigm.
Understanding the way key centers interconnect and their intimate relation to scales requires some music theory chops. One neednt be a musician, though, to understand upward and downward pull. In both scales and the order of key centers, downward movement means a move toward that which is more dense, more solid, and lower in vibration. Being pulled downward might, for instance, refer to a longing for something we know and trust; to being pulled away from something we wish to attain; to being dragged down into something beneath our dignity; or to becoming more grounded in our bodies. Upward movement is a movement toward that which is less dense, less solid, and higher in vibration. Being pulled upward might refer to a higher calling; to an ascent into airy-fairy fantasies and delusions; or to being drawn into the unknown. Upward can also simply refer to the future; and downward, simply to the past.