Reflections on Water

 

 

 “'I’m touched by your impatience over the Images. What happened was this: the first piece, ‘Reflets dans l’eau,’ doesn’t satisfy me at all so I decided to write another based on different ideas and in accordance with the most recent discoveries of harmonic chemistry…My apologies for this slight delay—which in any case won’t last beyond the end of the week. I’m starting to see things clearly again in my imagination and my thinking machine is gradually getting back into gear.'

Nothing in the composition of the piece has been written without consideration for phi and Debussy is unconcerned whether or not anyone, aside from himself and Durand, listens for the ratio unpacking, building itself, and then deconstructing itself over 94 measures and 375 beats. The new Reflets dans l’eau is an andantino molto that is almost as quiet as a droplet of water falling into a silvery lake. The piece divides asymmetrically into a beginning that stretches to the climax at the fifty-eighth measure and a smaller stretch that ends the piece. The climax, marked double fortissimo, is at the exact point of phi in the song, the mathematical equivalent of the golden ratio."

- Excerpt of an article found here regarding Debussy's use of the Golden Ratio (Phi) in Reflets dans l'eau,

The video is a re-mix of Reflets dans L'eau, (Reflections on Water) from Images I by the French composer, Claude DeBussy. It was created for electronic media by CJ Images and designed by CJ (Christopher John) for the game Flowscape. I chose this video (from numerous others) because some of its electrical sounds actually bring to (my) mind the golden spiral. To your right is the pentagonal golden spiral constructed by its 2 golden triangles.

"Among the mysteries of the irrationals, one number holds a special place: the so-called golden ratio. The golden ratio’s value is about 1.618 (but not exactly 1.618, since then it would be the ratio 1,618/1,000, and therefore not irrational) and it’s also referred to by the Greek letter φ, which is pronounced “fee” if you’re a mathematician and “fie” if you are in a fraternity. If you want an exact description, the golden ratio can be expressed as (1/2)(1+√5.)

People have been making a fuss over this number for centuries. In Euclid, the proportion goes by the more mundane name of “division into the extreme and mean.” He needed it to construct a regular pentagon, since the golden ratio is the proportion between the diagonal of such a pentagon and its side. A golden rectangle is one whose length is φ times its width; it has the agreeable quality that if you cut it crosswise so that one of the two pieces is a square, the other one is a smaller golden rectangle."

- Via the Slate article: The Most Irrational Number. Inset left is a beautiful photograph (found online) of the chambered nautilus, featuring a spiral similar to the golden spiral.

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Well, it took me long enough to write this post (!), but, then, I was somewhat intimidated by it. In terms of this blog, it's an important one; revealing just exactly where I've been at (creatively) for the past 2 years. Never mind that the past 2 years have been for myself and, I imagine, most people, a regular mind-f*ck. (After all, who amongst us did not in some fashion get sick?) However, the show must go on. And, for an artist, to create is to live... and to live is to create. Nothing changes this equation.

My creative journey began during 2019 and was referred to in this April interlude, upon the creation of the Rose Pentacle graphic. Later that year I began sculpting a 3-dimensional version of that image in clay for a ceramic casting (which is still in progress). I also began to envision a series of paintings which might bring the Night Garden to life while, at the same time developing a mythology relative to both the garden, the Rose Pentacle and the inherent mysteries I sensed were involved.  It's a big project.

But, as the Pandemic fell into place, I lost my place in the journey. The dream went on hold, and I turned, instead, to the one component of the Rose Pentacle that could be investigated in two dimensions on a computer monitor: the pentagram, its history, but, most importantly, its geometry... from which a series of diagrams eventually emerged (a few of which appear in this post.)*

(More after the jump...)

Why geometric diagrams? I think it was an effort on my part to maintain sanity in a world gone mad. Geometry is nothing if not sane. Triangles, squares, circles, are fundamental entities which do not change. They have no expiration date. They are not owned by anybody. They are what they are and you can trust them. So, In a world where history is inaccurate, the future is uncertain, and no one can agree upon what is presently true, geometry is like a vacation on a deserted island. It's just you, the sky and the ocean waves.

Most of my diagrams (such as the 3 presented here) involved the Golden Ratio (φ), which I didn't realize till late last year was actually an important property of the pentagon and the pentagram and is quite possibly where the ratio was first perceived.** I was familiar with the golden rectangle and the golden rectangle's spiral; I suspect that most people are. It certainly is the main reference you'll find on the web. Conversely, mention of the golden pentagram and its spiral is generally vague and/or incidental... as if it was of no account and didn't matter. Well, for a mathematician maybe. But, for artists (and architects), I think it's important. Not only does the pentagon and pentagram construct a better golden spiral, but the entire operation is at once more elegant, refined and profound. And, not only that, but I believe that all the investigators searching for evidence of the golden ratio in the world's ancient and historical art are barking up the wrong tree. Rectangles represent the least of it.

When it comes to music, however, the presence of the golden ratio is more difficult to ascertain; especially for those of us who can't write music! But, I wasn't surprised to discover French composers Claude Debussy and his friend, Erik Satie, both made use of it. Satie's involvement is said to have lasted from 1892-1897 during his alliance with a Parisian Rosicrucian group: the Ordre de la Rose-Croix Catholique du Temple et du Graal, Several compositions written at that time, particularly his 3 Sonneries de la Rose+Croix allegedly embody the golden ratio. (I have featured music of Debussy and Satie at the end of this post.)

Anyway, I have come to the end of my introduction for a new series of posts on Trans D, wherein I will weave the tale of the pentagram, dispel a myth or two, feature a number of diagrams, and present new speculation regarding a mysterious object which inspired my journey, and more speculation about the presence of the golden ratio in Renaissance art. Yes, there's more gold in the Dutch Golden Age paintings than you may have realized... and that's just the tip of the iceberg!

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* Regarding the 2 b/w diagrams I've included in this post... well, the originals, created on my Mac in full color, failed to translate into a PC format. The colors looked hideous. So, unless I can fix the disaster, they will remain in b/w, as will future diagrams from that group. No one is more sorry than I!

** (3/31/22) Correction: I most certainly did know about Phi and the pentagram... I mentioned it in a 2016 post! I think what I meant is that I had never seen Phi represented in pentagonal form. Then again, maybe somewhere between 2016 and 2020 I somehow just forgot.