SACRED MUSIC AND SACRED NUMBERS Excerpt from Return to Meaning by Dr. Andrew Cort Who was Pythagoras? His life and teachings are shrouded in mystery. He was born around 500 B.C.E., presumably in Syria. According to legend, his birth was foretold by Apollo’s prophetess, who was known as the ‘Pythia’, at the Oracle at Delphi. She revealed to Pythagoras’ father, Mnesarchos, that the boy would "surpass all others who had ever lived in beauty and wisdom, and that he would be of the greatest benefit to the human race in everything pertaining to human achievements." Mnesarchos named the child Pythagoras, to thank and commemorate the Pythia. Other sources suggest that "Pythagoras derived his name from the fact of his speaking truth no less than the God at Delphi." Some even said he was the God’s own son. As a young man, he went on a long voyage of discovery - much as Plato would do some two hundred years later. Piecing together a plausible history from the fragments we have, Roger Lipsey writes: "When he came of age, Pythagoras set off on a voyage of study, lasting decades, that took him to all of the great centers of learning in the ancient world. His first master was Thales of Miletus... one of the Seven Sages. After many years, Thales sent him on to Egypt to study with the priests and learn the mysteries…. He spent the next twenty-two years in Egypt, according to legend, after which he was captured by Persian troops and transported to Babylon." Rather than regarding this as a setback, Pythagoras took the opportunity to study with other wise men from diverse societies who were also held captive in Babylon. Finally, at the age of fifty-six, he was able to return to the Greek world. In Greece, it was said that he studied in Delphi with the Pythia of his time, even that he derived his ethical doctrines from her." Eventually, after his many wanderings, he established a school in Crotona, in southern Italy, where he instructed his disciples in the secret wisdom that had been revealed to him, as well as in sacred mathematics, music, and astronomy. Two centuries later, when Plato came to southern Italy, followers of Pythagoras still lived and studied together in brotherhoods. More than two millennia later, the twentieth century mathematician and philosopher, Bertrand Russell, would say of Pythagoras, "I do not know of any other man who has been as influential as he was in the sphere of thought." Like his personal history, Pythagoras’ actual teachings are also an enigma, partly because he evidently preferred the oral method of teaching and had no ‘Plato’ to later write things down, and also because his disciples had the frustrating habit of attributing their own work and discoveries to their master, even centuries after his death. We do know that he placed great value in mathematics, and that his mathematical achievements were prompted by a discovery in the field of music. Working with a monochord (comparable to a guitar with one string), Pythagoras discovered that the note produced by plucking a string of a certain length could be ‘reproduced’ one octave higher by plucking a string exactly half as long, or one octave lower by plucking a string exactly twice as long. The way in which these different musical notes (e.g., what we now call a high ‘C’ and a low ‘C’) sound in some sense the same, is of course an inner, subjective, experience, and a universal one. The Pythagoreans discovered that this experience is associated with a kind of beautiful symmetry of strings and vibrations that are in mathematical proportion. He then discovered that several other very simple mathematical proportions also account for the familiar pleasing harmonies that we hear when the right notes of the musical scale are played together as chords, and that harsh, dissonant sounds occur when notes that are not in these proportions are played together. This, too, of course, is a subjective experience: we feel a sort of ‘pleasant agreement’ between some notes when heard together, while other combinations of sounds do not seem to get along at all and somehow give us a disagreeable experience when we hear them. Pythagoras found that the pleasing harmonic proportions, that is, the relative lengths of the musical strings which produce pleasing sounds when plucked simultaneously, can be expressed quite simply as ratios of the numbers 1, 2, 3 and 4. Other ratios of string length produce irritating disharmony. Thus Pythagoras discovered that ‘Number’ somehow underlies the phenomena and experience of music. He then wondered whether ‘Number’ might somehow underlie other aspects, or perhaps even all, of reality. Like other Greek philosophers of his era, he was looking for a fundamental ‘something’ that could unify and explain life, mind, and nature. But rather than a primary physical substance (e.g., water, air, or atoms), he discovered a primary idea. All things, he concluded, in their essence, are ‘Number’. He found that the motions of the heavenly bodies follow regular patterns which are understandable and predictable in terms of the same numerical principles of harmony and proportion - and thus was born the ancient notion of ‘the harmony of the spheres’; he saw that the various surfaces of tangible objects can be viewed as examples and illustrations of the perfect figures of geometry; he saw that beauty and physical health are dependent upon a harmony of material elements, and he saw that psychological health was also to be achieved through temperance or moderation, again requiring a proper harmonious balance. The Pythagoreans would eventually conclude that the perfection of a soul requires the restoration of inner harmony, and that achieving this is not dissimilar to achieving the perfect attunement of a musical string. The One and the Many Just as Creation begins with Unity before evolving into Multiplicity, so numbers begin with One. One represents the principle of absolute unity, God, the source of all Creation, prior to and pervading all things. It is symbolized in philosophical geometry by the ‘Point’. Like God, a point has no material substantiality (we are not speaking of a dot on a page used to represent a point, but of a true geometric point), it has no dimensions, it cannot be seen or touched. It is Everything (everything lies nascent within the One) and Nothing (for nothing as yet is differentiated) simultaneously. It is the Beginning from which all will come (the ‘First’), and the End to which all will return (the ‘Last’). For Plato, ‘One’ symbolized the transcendent level of the ‘Good’. Two marks the appearance of Duality: the first inkling of Multiplicity, the potential for ‘the Many’ that will come. Two is not the ‘sum of two ones’: there is only one One. Rather, Two issues from One, from the Creator, in much the same way that a single cell divides itself into two cells - the One becomes Two of its own Will, by reflecting upon Itself. Thus the One experiences dichotomy, it perceives and it is perceived, and thereby self-generates into Two. It is with this Duality that the idea of Opposites makes its first appearance: above and below, male and female, day and night, all the Taoist distinctions between Yin and Yang. But this is only at the level of abstract archetypal Ideas. Two is represented in geometry by a ‘Line’, the distance between two points. A line has a dimension - but only one. Thus, like a point, it still has no substantiality in the material sense: it cannot be seen or touched. The mind knows that it exists, but it is invisible to the eyes. For Plato, ‘Two’ represents the level of the eternal Forms. Three, a number imbued with exquisite symbolic meaning, appears next. Three is represented by a ‘Triangle’, the geometric form that is created from three invisible points and the three invisible lines that connect them. A Triangle now combines two dimensions (left/right and up/down), and this gives it a unique, peculiar, and immensely significant quality. Like any flat surface, it can be seen - if it is facing you in its upright position. But if a triangle is flipped horizontally so that its side is facing you, then there is only a line facing you - and a line is totally insubstantial and invisible. This means that a Triangle can ‘appear’ in the Sensible world and then ‘disappear’ out of it. In other words, the ephemeral number Three lies curiously in between the Intelligible world of Spirit and the Sensible world of Matter. Three represents a ‘Threshold’ between them, a passageway that links the manifest with the transcendent. This ‘Threshold’, as we shall see, is the locus of the soul. It may also be thought of as the dwelling place of angels and demons, beings that are partly of the earth and partly of the heavens. For Plato, this is the level of Dianoia, the level of abstract principles, mathematics, and pure reason.
a triangle made of three points, and now add a fourth point (not within the plane of the triangle, but somewhere in front or behind it), then each of the three corners of the triangle can be connected to this fourth point - and this creates a geometric figure called a ‘tetrahedron’ (looking rather like a pyramid, made of three triangular walls and a triangular base). The significance of this is that we now have a three-dimensional solid figure (so it turns out that four points are required for three dimensions to be created). And because the tetrahedron exists in three dimensions, it exists in our tangible, sensible, visible world - Plato’s Pistis. Four is therefore the number of material manifestation, and it also thereby symbolizes the four instinctive components of material nature (earth, water, air, and fire, or, stated in modern terminology, solid, liquid, gas, and energy). |
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