In two separate articles -- one recent (Music, Math & Models) and another slightly less so (Phi -- How the Golden Ratio Determines Who is a Supermodel) -- Cash has demonstrated his point that music is math, clearly enough that even Al Gore couldn't get it wrong. As threatened, in this article, I hope to explore the implications that this 'music is math' truism has for the world of magic.
First we need to acknowledge the extent to which music is able to directly affect the centres of the brain which govern emotion; in and of itself a nearly magical result. People like legendary composer John Williams have been demonstrating this constantly since the birth of talking cinema. Who can forget the feelings of foreboding and even terror created by scores for movies like Pyscho and Jaws, or the soaring triumphalism of the theme from Star Wars?
Equally compelling is the martial spirit that music can invoke; John Phillip Sousa, father of the American march was one of the masters of this form. The examples go on and on, from the sublime (Mozart) to the ridiculous (Rick Dees and His Cast of Idiots). But these practitioners have approached music largely as an art, when -- as Cash's articles make abundantly clear -- there are legitimate scientific principles at work as well.
These same principles were well understood by magicians, alchemists and proponents of hermetic thought. Early hermeticists viewed the world in accordance with the principle "as above, so below". In their worldview, all of creation was a holistic, interconnected unit, whose binding element was the principle of harmony. This principle was one which they could easily test, through the use of stringed instruments. When two strings were tuned to the same frequency, when one was plucked, the other would vibrate in what appeared to be 'sympathy'. What we understand is that the plucked string causes the air surrounding it to vibrate, which then causes the second string to vibrate, assuming that both strings have been 'harmonically attuned.'
The various aspects of this holistic and interconnected universe were bound together through this concept of harmony and were related to one another through analogies or correspondences that could best be expressed through the use of symbols, in much the same way that modern mathematics expresses universal constants through formulae. To the hermeticist, a mathematical number could have a symbolic and analogous relationship to an element, to a mineral, to a chemical, to a chord or note in music or to a point on the human body (in eastern disciplines, these bodily points might be considered chakras) or even to . Any of these, then, could be interacted with to achieve changes in state; by changing a musical state, for example, it would be possible to change a man's physical state, or a chemical's state, and vice versa. This was the birth of the largely false notion that alchemists sought to use chemical means to achieve the transmutation of lead to gold.
So, to hermeticists, and their later inheritors, the alchemists, these symbolic constructs were not mere representation of concepts. As explained by authors Michael Baigent and Richard Leigh in The Elixir and the Stone, to them symbols were "repositories or storage cells of power, batteries holding a latent charge of energy...[these] symbols could be manipulated, like elements or molecules in chemistry, to form new compounds, new amalgalms of possibility. By virtue of such manipulation, change could be effected. The process whereby it was, was called magic."
Baigent and Leigh explain that to virtually all post-shamanic practitioners of magic, "the cosmos... comprised a single vast musical instrument in tune with itself, producing its own music, to which it incessantly vibrated and resonated. Humanity and the gods, earth and heaven, microcosm and macrocosm, were all linked by harmony and reflected the same harmonious proportions. These proportions could be defined and described in mathematical terms". As we recall, this is precisely what Cash was able to accomplish in the two articles we referenced earlier.
Probably the earliest known font of perspective on the world was the Greek mathematician and mystic, Pythagoras (circa 580 BC). Often regarded as the conduit for eastern mysticism into the western intellectual tradition, Pythagoras was the man who coined the term 'philosophy'.
One story about Pythagoras is quoted by author Colin Wilson in his landmark reference book 'The Occult'. This tale refers to his "passing by a blacksmith's shop, in which four smiths were striking anvils of differnent size, and producing four different notes. Pythagoras had the anvils weighed, and found that their weights were in the proportion 6, 8. 9, 12. He then stretched four strings from the ceiling and hung four weights of the same proportion. The strings, when plucked, produced the same notes." From this curious finding, Pythagoras built an entire corpus of mystical thought, which ultimately concluded that "perhaps all the harmony of creation is due to numerical secrets".
Christoph Reidwig, in Pythagoras, His Life, Teaching and Influence, describes how Pythagoras believed in "the harmony of the spheres", a notion that inferred that because cosmic bodies moved according to mathematical equations (today, we'd call this orbital ballistics), those equations could be translated into musical notes and thus produce a symphony -- one which would be far more harmonious than what he considered the cacaphonous state of contemporary music in his time.
Lastly, the degree to which the music was considered one of the prime tools of the alchemist is emphasized in an essay by chemist and writer John Read, 'An Intepretation of the Alchemy Lab Drawing', in which he notes: "the importance attached to music, harmony, number, and proportion in the operations of the Great Work [alchemy], already suggested by the symbol of the pentagram, is emphasized by the musical instruments and pair of scales lying on the central table; moreover, the attached Latin inscription indicates that sacred music disperses sadness (or alchemical melancholia) and evil spirits."
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