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."
This is brilliant stuff. I'm at just under 40 minutes to read one article and I read fast. Meticulously researched, terrific pacing - you may be too good for Newsvine.
Cash has demonstrated his point that music is math, clearly enough that even Al Gore couldn't get it wrong.
This, however, just never stops being funny.
People, get your asses in here and vote for this.
Are you 2 guys in love? I kid.
you may be too good for Newsvine
indeed.
Pythagoras was interesting because he created frequencies based on pure multiples of 2 and 3 (therefore including 4, 6, 8, 12, 16, etc.) but did not include the next prime - 5, which is in fact used in traditional music. For example, the major scale "me" (in so-fa) includes I think "me" at 5/4 ratio of the fundamental note, and "la" at 5/3.... or should that be 5/2 and 10/3?? I get confused and I lent my "bible" of this stuff out to someone who hasn't given it back - don't you hate that? (That would be "E" and "A" in the key of "C", by the way.)
Oh and you want to look at Indian Raga tunings - they get this stuff to a level of sophistication far beyond the west and they intend and understand the mystical side of the emotional effect of the notes.
You make a good point. At least in my articles when I was talking about overtones and their mathematical method I was specifically talking about western harmonic theory.
And then there's the question of the "Neanderthal flute" that was discovered in 1995, and later a mastodon "tuba" along with several other musical instruments that have been discovered. [The link is to a google search.]
Would Neanderthal man have had the intellectual and mathematical capacity to intentionally create a woodwind instrument capable of creating the musical scale? The jury is still out on that one.
There's a certain arrogance we are accustomed to, or perhaps a lack of perspective, which makes us think that "cave men" were unsophisticated. Look at the art in Lascaux... there's nothing "primitive" about it in the normal sense of the word (as art).
Western harmonic theory, as Cash says, is complex in ways Ragas and many other sorts of traditional music aren't (it has the ability to change key during a piece because the "E" in C Major is the same "E" as in A Minor), but it's also simple in ways other music isn't. Blues and jazz have tapped into some of that traditional sophistication and even extended it in places - now we're getting well outside my limited understanding of things, though.
there's nothing "primitive" about it in the normal sense of the word (as art).
I often think the same when I look at La Tène (pre-Celtic) design -- and that's even more modern than Neanderthal, but still rather astonishing, imho.
Just one last word: truly magical ritual *should* be exuberant, and engage creativity. Maybe that's why great music feels like it puts me more in touch with "god" than the church ever does.
Your mileage may vary ;)
I may be Catholic but I have instructions in my will that I get a whole group of large Baptist women singing at my funeral. They sure got that part right.
Heehee Synthesis - thanks for that visual.
My personal preference for funeral music is the New Orleans version, parade and all.
One story about Pythagoras is quoted by author Colin Wilson in his landmark reference book 'The Occult'.
Just curious, did you recently read, or re-read this classic?
great article!
Speaking of music and magic...
The toroidal model of tonal space is especially fascinating.
So, to hermeticists, and their later inheritors, the alchemists, these symbolic constructs were not mere representation of concepts.
It is brilliant and beyond me in the sense that there's a place all this theory goes to that pushes the limits of my mind to really integrate fully. To compensate I think I'll try to memorize your phrase and deliver it with a look of deep thought. That should work in lieu of real genius; it employs the best element of my career in venture finance stated as, "An ounce of facade is worth a pound of substance" the Wall Street accounting, correlation to math!
Facade is the face you put forward, very focused Pamela Drew, on such a humane cause, and substance is what's underneath. On my scales, substance is worth more in the long run.
Yet the numbers, though added, subtracted, divided and multiplied, plus more ad infinitum, are symbols that tell things. The substance of them is in and beyond the symbols -- gnostic.
Take, for a start, the vertical line 1, which points toward heaven from the linear plane of earth.
The bonesmen, and there are women among them, listen to the music they hear and march to the beats of their own drummers -- and the rest of us be damned.
But not me.
Synthesis greetings, first time poster here and very interested in your article(s). I come at this topic from two perspectives.
The first is that I am a Cymatic Researcher which is essentially what you are describing though you may not be familiar with this science given that it was not mentioned. Cymatics is itself merely a metaphor for a deeper understanding which is that sound is the closest phenomenal sense to the 'vibes' which permeate the entire cosmos, both matter and anti-matter for lack of a proper English word to describe such things. A Swiss scientist named Hans Jenny created many patterns using audible and inaudible sound as well there are others who have now evolved this work into medical delivery systems due to the electromagnetic constitution of the human body.
The other issue for me are symbols which traditionally I have attributed little merit though i am beginning to realize that symbols contain proportional relationships that embody and activate the intelligent data contained with matter and anti-matter, rather like a portal which is hat the word chakra essentially means. Symbols are activators if properly understood by the whole body, curiously, and not just the brain but as well these can stand on their own.
All that I say here is just the tip of an amazing iceberg. I think we are collectively waking up and myth can become factual again.
Synthesis hi and no problem on the response. I am not a regular here as yet though I am impressed with the concept and structure of Newsvine. I am an active member of Tribe.net which is thread-based providing clusters of people based on themes and not hairstyles! I find MySpace and Facebook and the like quite annoying. Being sociable ought to include a place to exchange intelligent ideas too. Imagine that?
You mention alchemy in relation to this thread which has become a very strong interest of mine recently. I was tuned into a most extraordinary book called The Dwellings of the Philosophers based (translated from the French text) the ideas of Fulcanelli (Pseudonym), a deceased Master Mason who describes both alchemy and the Gothic cathedrals from an alchemical perspective. The writing is brilliant in my opinion and touches up the very reasons that symbols are potent by examining the active ingredients of life rather than the sterile facts of conventional science. This is what has been lost over the ages. WE have become nouns and forgotten how to be verbs so to speak.
Underpinning all biological form is energy and this energy is structured on several simultaneously different scales of reality. Morphogenetic Fields persist as energy types if you will and more subtle than this is the Intrinsic Data Field (IDF) which is rather like the blueprint for physical form. Several different energy medicine modalities such as Cymatics and Rife Technology consistently show that disease exists in these data fields before it manifests in the body and the balancing of these energy fields nearly guarantees that illness and disease will have no place to proliferate. Further, these fields are structured in various geometrical patterns which can be animated by other harmonious frequencies. The source of the frequency does not matter (no pun intended), only the resonant harmony of the interacting energies. This is a response to your interest that genes may be affected by, let's say, remote stimuli, the answer is indeed yes, including the bad stuff like cell phones and television sets and junk food whose resonances are not healthy for us. Sadly, there are weapons that utilize frequencies for ill effect as well with HAARP being the most prominent example I know of (based on Tesla's achievements).
Thanks for your efforts, John Gil
Hello again Synthesis, yes, science is finally catching up with humanity and now we have forgotten our humanity! WE are often more friendly with each other when we have problems so I figure that w need to identify some real fun problems. All technology mirrors biological capability though generally with greater focus and amplification, and of course no complaining!
Rather than thinking of the body as a mechanism with replaceable parts, it is becoming increasingly understood that the eternal regeneration of biological material can be coaxed into a healthy state from a range of different modalities, some of which include inner self management and others which are remote and technological. The Asian arts incorporate a geometrical understanding of the human body within which the etheric body dwells. Technology accomplishes the same result though creates a dependency upon an external solution that diminishes transcendant wisdom.
It is my opinion that we are physical in order to resolve intellectual and emotional uncertainties whereby we can experience problems / opportunities until such time that we reunify and no longer need a physical experience to 'understand'. I am interested in subtle technologies like the symbols you describe above which carry energy and memory that can merge with the etheric body. Several years ago I would have thought this to be nonsense but the paradigm of all pervasive energy clearly suggests that like energy resonates like energy just as the dial on a radio reveals by tuning into a particular frequency and ignoring the rest. We know this intuitively but remain dependent on what our physical senses seem to be telling us.
It is frustrating when you approach this door and begin to see how easy life can be, and how peaceful, only to realize that the lack of inner unity requires that more time be spent investigating specific branches of knowledge to locate additional lessons. We are eternal but the physical experience to a great extent is a choice. There is great power in understanding this, as well, we will eventually accept the responsibility that our relationship to our knowledge and identity is the same as our relationship to our existence here on Earth. We are Co-creators and all of the knowledge we have mirrors this grand model. The current Green / Recycling movement is one step closer to a mass understanding of the eternal and cyclical (non linear) Nature of things for example. Gore promotes the trend and is rewarded despite his many lies about the subject.
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