Music, Number and Divine Harmony
There is…an esotericism in music. One aspect of it is the science of speculative music, which searches out the principles and laws underlying both practical music and its reflections in the cosmos… The other aspect of musical esotericism is the experiential one, driven by the power of practical music over body and soul… Music, in short, contains all the requisites for a path of spiritual development.
– Joscelyn Godwin, “Music and the Hermetic Tradition”
Ancient tradition held that communication once took place by means of an interior language that was not dependent upon outward signs or sounds, and that when communication became an outward and external function, disparity began to exist (in the book of Genesis this theme is mythologically portrayed in the story of the Tower of Babel). From that time forward, communication between men was limited like everything else on the physical plane. Entrapped in his tomb of flesh, man still struggles to express himself through this lost spiritual language, and he attempts to communicate it to others. If he is a poet, he uses words that are full of beauty and vibrant with subtle overtones of meaning. If he is an artist, he uses colors and reveals the divine in radiant hues of light. If he is a musician, he sings or plays upon key or string with such inspiration and fervor that he may awaken his own spirit and the spirit of others to a recognition of infinite Truth. Thus, music and the other arts as modes of human expression are not merely incidental to human civilization but are intrinsic and essential to the human experience. Albert Einstein writes:
"Where the world ceases to be the stage for personal hopes and desires, where we, as free beings, behold it in wonder, to question and to contemplate, there we enter the realm of art and of science. If we trace out what we behold and experience through the language of logic, we are doing science; if we show it in forms whose interrelationships are not accessible to our conscious thought but are intuitively recognized as meaningful, we are doing art. Common to both is the devotion to something beyond the personal, removed from the arbitrary."
Music is one of the most sublime gifts of man. It expresses something that lifts man out of the active, noisy, materialistic rush of the world and recalls the part of his nature that transcends the physical and mental being. Pythagoras was among those great teachers who worked with music to disengage man from the “bondage of earth,” and he recommended its daily use among his disciples to help them experience the memory of their divine origin. Following in this tradition, Plato taught that is was through music that man can be attuned most quickly to the realm of the Archetypes. In the schools of both of these great initiates it was recognized that, through music, a definite purification takes place within the soul, and man’s regeneration is thereby advanced. Like love, the essence of music’s power cannot be known to the senses nor to the intellect. Its deepest meaning is experienced by the intangible nature of man’s being. As a mystery, music is a representation of the divine and puts man into direct communion with the Infinite Spirit of Truth. In fact, the origin of western music can be traced back to the initiate Pythagoras who, basing musical intervals on pure mathematical ratios, represented the relationships between divine concepts that were symbolized by numbers.
The most essential universal principles in Pythagorean thought are Limit and Unlimitedness. Limit refers to that which defines by imposing order or form; Unlimitedness refers to the undifferentiated, or that which is without order or form. Limit acts upon and provides order to the unlimited, or infinite (not finite), realm of space. The result is the phenomenal universe in which all physical manifestation represents infinite constants limited by local variables. The Greek word for this universe was kosmos, which means “ordered-world” and also means “ornament.” This was another way of saying that the universe is ornamented with order. However, it must be noted that Unlimitedness is equally responsible for the beauty that results from this ornamentation. Consider, for example, how the beauty of a musical composition relies on the harmonious balance of both order and randomness.
In the school of Pythagoras, Number is the formal manifestation of Limit. Therefore, in keeping with the role of Limit in providing order and definition to the universe, Number is believed to be “the principle the source and the root of all things.” Whereas modern man is inclined to think of numbers as defining quantity, the Pythagorean considers numbers as representations of archetypal and absolute truths. In this sense Number is a universal and divine principle, not merely a tool for quantifying material things.
Unity, signified by the number 1, is not considered a number itself, but rather represents the concept of Number. All other numbers originate from 1 and are contained within the concept of Number, reflecting the multeity that emanates from and is contained within Unity. Because Unity represents the concept of Number, and Number is the formal manifestation of Limit, Unity and Limit are one and the same. As previously stated, multeity emanates from Unity when Limit (which is the same as Unity) provides order to Unlimitedness. In other words, multeity emanates from Unity by the action of Unity upon itself. From this arises the image of a Divine Consciousness, which creates the material world out of itself by an act of consciousness. The number 1 therefore represents the source of all things, which arise by the action of that source upon itself. It is the archetypal representation of transcendent Truth.
Whereas the number 1 represents Unity and Limit, the number 2 represents multeity and Unlimitedness. The number 1 represents the spiritual plane, and the number 2 represents the material plane, in which there is force and resistance (at least two objects are required for a force and resistance). The number 2 represents division and the beginning of strife, but also the potential for a relation between two things; the number 3 is the number of harmonia (“joining together”) because it achieves that relation. The number 3 brings the opposites represented by the number 2 back into unity and also reflects the nature of 1 (both 1 and 3 are odd numbers). This sequence represents the archetypal model of cosmogenesis in which there is an undifferentiated Unity, followed by the emergence of opposites from that Unity, followed next by the reconciliation of those opposites into a unity that reflects the original Unity. This model should be considered not only as action that takes place over time, but also as different but simultaneous levels of consciousness. In the materialistic consciousness represented by the number 2, all things are perceived as individual units. Transcendent Truth (represented by 1) is beyond the realm of human comprehension, so the consciousness represented by the number 3 (which signifies the reconciliation of multeity into Unity) allows the individual to recognize that what appears as multeity on the material plane is a reflection of Unity on the spiritual one.
Pythagoras is often credited as being the first to discover the numerical ratios upon which music is based. In his hands the musical scale arose as a means of representing the action of Limit upon Unlimitedness and the harmonia of the resulting multeity into unity. The monochord, a one-stringed instrument with a moveable bridge, represents Unlimitedness by virtue of the fact that, theoretically, the string can be divided at an infinite number of points to produce an unlimited number of tones. Numerical ratios are used to define intervals, and thus Number provides Limit to the unlimited potentiality of the string to create the multeity of tones in the musical scale (Limit acted upon Unlimitedness to create multeity). Adding further significance, the Numbers that are used to provide Limit to the Unlimitedness of the monochord are 1 and 2, the very representations of Limit and Unlimitedness! In the ratio of 1:2, Limit and Unlimitedness are combined to yield the interval of the octave (if a string is divided in half, creating a 1:2 ratio, the half will sound one octave above the original pitch of the string). The numbers 1 and 2 are then combined according to the following formulae to yield the perfect fifth (2:3) and the perfect fourth (3:4):
Arithmetic mean: (A + C) / 2 = B. When the ratio of A:C = 1:2, the resulting ratio of A:B = 2:3 (perfect fifth).
Harmonic mean: 2 / ( (1 / A) + (1 / C) ) = B. When the ratio of A:C = 1:2, the resulting ratio of A:B = 3:4 (perfect fourth).
These intervals cooperate with one another in such a way that the relationships between them and the root are inversely reflected in their relationships with the octave. In other words, C to G is a fifth and G to C is a fourth, while C to F is a fourth and F to C is a fifth. The octave, the fourth, and the fifth are produced in the naturally occurring overtone series, demonstrating that the symmetry with which these spiritual principles interpenetrate one another is naturally reflected in the physical realm of sound. The 8:9 ratio that results between the fourth and fifth is the whole tone, the basis for filling in the remainder of the scale.
Two strings are needed in order to produce all of the tones of the diatonic scale, because the monochord cannot be simultaneously divided into ratios of 2:3 and 3:4. Therefore, one string is divided by 3 to produce fifths (2:3), while another string is divided by 4 to produce fourths (3:4). These strings represent Limit (1) and Unlimitedness (2), respectively, because the division by 3 reflects the odd faculty of the number 1, and the division by 4 reflects the even faculty of the number 2. The strings that give the primordial tones B and F are chosen to be divided in this manner because these two strings, developing in inverse directions either by fourths or fifths, produce two identical sets of tones. Starting on B and rising by successive fourths, obtained by shortening the string by a quarter of its length each time (3:4), produces the series B, E, A, D, G, C, F, B flat, E flat, and so on. Starting on F and rising by successive fifths, obtained by shortening the string by a third of its length each time (3:2), produces the series F, C, G, D, A, E, B, F sharp, C sharp, and so on. Thus, the two strings produce by opposite paths the seven notes of the diatonic scale, which owes its identity to the contrary unfoldings of the principles of Limit and Unlimitedness. These seven notes of the scale are the aural manifestations of universal Truth, just as the seven colors of the spectrum are the visible manifestations of Light.
We have seen that on multiple levels the musical system represents the combination of Limit (1) and Unlimitedness (2). It also reflects the principle of harmonia (the reconciliation of multeity into Unity), which is represented by the number 3, because the combination of 1 and 2 yields 3. The Greek word for this system was lyrai, derived from the same root as the Phoenician word sirah, which expresses everything that is harmonious and concordant. Over time the term was transferred by extension to the stringed instrument by which the musical system was demonstrated, and the word “lyre” came to refer to the instrument, rather than the system itself.
The principle of harmony represented by the musical system asserts that multeity is merely the physical representation of Unity; the material plane is a manifestation of the spiritual plane. Therefore, what appears to the material consciousness as individuality is in reality a lower manifestation of Oneness. By extending this concept to one’s relations with his fellowmen, one sees that all individuals are connected as individual cells in the organism of Humanity, separate in body and mind but one in spirit.
The principle of harmony governs the relation of every part to the whole, but as stated previously, this must not be misunderstood as a chronological sequence of events in which Unity becomes multeity, followed by multeity being brought back into unity. In other words, Unity and multeity are not physically or temporally separate, but rather exist eternally, in unison and within one another. Similarly, the assimilation of man into the oneness of mankind exists simultaneously with his individuality, and Unity does not undermine his independence.
Frater Plethon
March 1, 2002.
References:
Campbell, Joseph, and Moyers, Bill, The Power of Myth, ed. Betty Sue Flowers, 1988.
d’Olivet, Fabre, The Secret Lore of Music: The Hidden Power of Orpheus, ed. Joscelyn Godwin, 1987.
Guthrie, Kenneth Sylvain, The Pythagorean Sourcebook and Library, ed. David Fideler, 1987.