Klavdia Klangfarben and the Golden Section of Doom

a Chambered Nautilus

Yesterday, we reached the “turning point” of my novel, The Labyrinth of Klavdia Klangfarben.

Most stories have one moment in their progress that can be described as “the point where the story turns,” having developed from the initial material (the “exposition”) and now proceeds more purposefully toward an eventual resolution.

While such plot-points are different from “the climax,” very often we are told these occur at or about the “Golden Section” of the novel, a division which occurs frequently in nature and is often used consciously or subconsciously in architecture or art and can be used to describe, for instance, perfect proportions or the perfect face.

And that is where yesterday's installment of The Labyrinth of Klavdia Klangfarben ended: the Golden Section of the entire novel.

How do I know this? Because I put it there.

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Simply put, whether it's called the Golden Section, the Golden Mean, the “Divine Proportion” or Phi (according to its Greek-letter designation, the way Pi refers to the ratio of a circle's circumference to its radius), it was defined by Euclid around 300 BC: "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser."

Or that point where you can divide a line so that segment (a+b) is to segment a as segment a is to segment b.

Like pi, this ratio is an irrational number which is usually described as 1.618. If you want to find the “Golden Section” of a line or a number, you multiply it by 0.618.

“Da Vinci himself,” one writer explains, “used the Golden ratio to define all of the proportions in his Last Supper, including the dimensions of the table and the proportions of the walls and backgrounds. The Golden ratio also appears in da Vinci's Vitruvian Man and the Mona Lisa.”

The Last Supper by Leonardo da Vinci

Arguments are made for and against the idea this significant proportional ratio occurs – or almost occurs (in which case, it doesn't occur, does it?) – in such things as the various proportional subdivisions of the Parthenon's rectangle, or the ratios between the sides of Giza's Great Pyramid. Unless an artist says he was employing the Golden Section, however, does the fact someone sees it or can measure it in a work of art become a significant fact of its creation or a natural coincidence?

Certainly, it occurs in nature frequently enough – the famous nautilus shell; the way seeds spiral out from a sunflower's center – that its occurrence in art can be a human approximation of naturally observed patterns.

At any rate, you can read more about it, for example, here; or here; or in Mario Livio's book, The Golden Ratio, here. I should point out, however, that's it not necessary to go into such detail to "get" what I'm writing about, in this instance.

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The Labyrinth is the final novel in a trilogy that includes The Doomsday Symphony and The Lost Chord. While this post isn't about what they're “about,” giving you a synopsis of each story – let's just say they're all “classical music appreciation comedy-thrillers” – it's more about a structural feature you may or may not have noticed. And it has nothing to do with whether or not someone may enjoy reading it (or not).

When I began the first one, it started as a challenge. Now I'm finding it difficult to change. I admit it's tedious, a time-consuming procedure that I could easily abandon and rapidly increase the number of words I could produce in a day (after all, I have written 4,000-word posts in a day but sometimes find myself stuck trying to get 144 words in the novel).

It's called a “cognitive constraint” – that is, a pre-ordained restriction rather than free-flowing creativity – which could be perceived as a “gimmick” or an integral part of the finished work, depending on how it was intended and how it is perceived by the reader.

Poetic structure is a kind of “constraint” whether it's a sonnet or a limerick. A haiku, for instance, is a pattern of numbers, so many syllables divided in such a way in only three lines, though many people think they're creating haiku simply by writing three minimalistically brief lines with a kind of disembodied grammar.

In the various coded messages in The Labyrinth that poor Frieda has to laboriously work out, I employ something children's writer Greg Pincus originated on his blog and called a “Fib,” based on the numbers of the Fibonacci Sequence (I'll get to that in a moment or three), though I used a number of words rather than syllables as he does.

You may not be aware of this, but even Dr. Seuss's Green Eggs and Ham is an example of a writing constraint: he wrote the book on a $50 bet from his publisher he couldn't write a children's story using only 50 vocabulary words.

I first read French writer Georges Perec in 1989 when I picked up a copy of his Life: A User's Manual where the odd structure of the book is based on the way a knight moves across a chessboard. Basically, the plot, if one can call it that, centers around a man who's spent his life painting 500 watercolors which he then has turned into jigsaw puzzles so he can spend the rest of his life solving them and thus recreating the experience of painting them (and then destroying them, leaving no trace of his life's work). He dies suddenly, almost completing the 439th puzzle, and the novel, rather than telling his story in a normal arc from start to finish, is instead a snapshot of everyone who lives in his  apartment building at the moment of his death.

The ordering of the individual stories, however, seems to have no consistency and certainly no continuity: instead, Perec superimposes on a diagram of the building's various rooms and their tenants a chessboard over which a knight, with its odd pattern, moves in such a way it will eventually land on every block without landing on any one twice. This is called a "knight's tour," actually only one of the constraints Perec employs, but let's leave it at that.

When I began planning my dream sequence that is the opening Intermezzo: The House of dePaula Escher, I thought, since dreams are usually discontinuous and often non-consecutive and unresolved, unlike a standard straight-through narrative, I decided to map out in chronological order the different episodes of the narrator's dream (in this case, Dr. T. Richard Kerr, my main character in all three of these novels) and then superimpose on them a similar knight's tour to determine in which order they should appear. The challenge was how to proceed when some later events occur before earlier ones, and how to create some kind of transition from one to another and still maintain the semblance of a narrative arc in which the tension leads toward, as often happens in a real dream, a sudden interruption, leaving the story unfinished: in this case, Kerr simply is awakened at a key point. It is only later that some of these – the frequent sense one location is somehow familiar to him, especially the fascinating crystal globe at the bottom of Phlaumix Court's grand staircase – begin to make what might be perceived as sense. Or not.

I have not, however, gone as far as Perec did in his 1969 novel, translated into English thirty years later as A Void. In this case, the constraint is he cannot use any word that has an “e” in it. This makes for some odd grammatical nuances and sometimes stylized-sounding if not downright stilted vocabulary – avoiding articles like “the” or pronouns like “he” or “she,” past tenses formed by adding “-ed” or substituting words like whilst for while. It makes for curious reading and I admit, barely getting 20 pages into its 300-page length, feeling more aware of the “gimmick” than I am of any story being told. Yet there are times the sheer virtuosity of it is sufficient to hold my interest but again at the expense of the story. I must admit, the Wikipedia entry for the book's plot synopsis is masterful in that it too contains no “e” but reads infinitely more naturally. In fact, if you'd read it first, I doubt you would've even noticed the constraint!

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So, what, you're probably not asking, was my constraint?

In each of the previous novels, I had a pre-determined length – The Doomsday Symphony was going to be a novel of 150,000 words. Not about 150,000 words – exactly 150,000 words. But beyond that, the whole novel would be subdivided proportionally until each part of the book, each climactic point, each chapter, each paragraph, each sentence and even most phrases of those sentences would reflect the proportions of the Golden Section within those 150,000 words.

I did the same again with The Lost Chord, set at 180,000 words.

But with The Labyrinth, I wanted to use the Fibonacci Sequence and have the house where most of it is set – Phlaumix Court, one of those grand English manor houses like the fictional Downton Abbey – reflect the proportions of the Golden Section in its architecture, even (to the dismay of most everyone) the tiled patterns of the floors and the decor of the various rooms. It was even designed by an Italian architect named Philippo Nacci (“Fipo” for short), a pun on the name Fibonacci.

In the case of Phlaumix Court, everything looks slightly off-center. If you look at da Vinci's Last Supper (above) and re-imagine it with the central figure of Christ being moved over to the Golden Section point to the right of center, that is how the different doors, fireplaces or stairs of Phlaumix Court might appear to the viewer.

a Fibonacci Spiral with number sequence in Golden Proportions

In that sense, it seemed perfectly natural to have the proportions of the novel reflect the numbers of the Fibonacci Sequence.

Originating in a mathematical problem concerning the offspring of a pair of rabbits, this sequence begins with 1, again 1, then starts adding the last two numbers to arrive at the next, and so on. So, then, 1+1=2, then 1+2=3, then 2+3=5, 3+5=8, 5+8=13, 8+13=21 and so on.

The numbers of the sequence, then, are 1  1  2  3  5  8  13  21  34  55  89  144... and so on.

The relationship between each pair of numbers is similar to the subdivided line in the earlier illustration above: for the line 8, the division is 5+3, 5 being a and 3 being b. This dividing point is the Golden Section: not 4+4 or 6+2, each one another possible way of subdividing 8, but 5+3.

Technically, the complete novel is divided into the “novel proper” and its preface, the seemingly independent short-story, an “Intermezzo” called The House of dePaula Escher. Therefore, the “novel proper,” The Labyrinth of Klavdia Klangfarben, is exactly 121,393 words long, a Fibonacci number if you continue the sequence to larger and larger numbers (it divides by the Golden Section at 75,025+46,368).

Unfortunately, since I hadn't planned on The Lost Chord being anything but another novel involving the adventures of Dr. Kerr and his assistant, Cameron Pierce, the idea of turning them into a trilogy didn't occur until I reintroduced Klavdia Klangfarben into the cast fairly late in the story (and well after I'd finished the original planning). In order to make the novels vaguely proportional in comparison to each other, I needed an additional 27,689 words (not a Fibonacci number) to make a particular event in the second “half” of The Lost Chord – the presumed death of Dr. Kerr – the Golden Section climax of the entire trilogy. This, then, became the “introduction” to the third novel, though really The Klangfarben Trilogy is technically a trilogy of three novels and a short story...

Yet all of this third novel is overlaid by a unified structure where climactic points, chapter divisions and subdivisions, down to paragraphs, sentences and most phrases occur at various numbers in the Fibonacci Sequence.

This tends to give a certain sense of rhythm to the structure: in a line (a+b), the a-section is longer, the b-section shorter. As the paragraphs and sentences become shorter – or “tighter” – there's a feeling of being propelled to a point which underlies the increase in tension or anticipation.

And after the major climactic points, I insert something that gives us a chance to breathe, while postponing the resolution a bit. I noticed in several books I'd been reading how this rhythmic device would occur: you see it all the time in television dramas – they never take a commercial break in the midst of a ho-hum conversation between the characters; it's always after some build-up has been reached and you're waiting (“damn!”) to find out what it will be, making sure you're going to stay tuned through all those commercials for the resolution!

In The Lost Chord, those were the points where I inserted the flash-back sub-plot of Harrison Harty and his Harry Potter-esque journal about his summer at the Schweinwald Academy in 1880 with his friends, Mahler, Hans Rott and Ethel Smyth. In The Labyrinth, it's the extended excerpts from Knussbaum's “The Tale of the Master and His Belovéd” (Rainer Knussbaum being a main character in Harty's journal). They may seem like interruptions but they add new information and insights as a story-within-the-story. (By the way, note how the title (8 words) subdivides into The Tale of the Master (2+3=5) + and his Belovéd (3).)

These establish their own rhythm, beginning the process of building up to the next point-of-tension.

Whether one senses that or not – that yesterday's post is the Golden Section of the “novel proper” – is not the point: like listening to music, you know that passage, that harmonic resolution might be the climax, but you have no idea it might or might not be the Golden Section of the movement or the piece since we cannot perceive time – and music is “sound-in-time” – the way we can perceive a painting or a building.

We could look at a person and say “he is well-proportioned” (whatever that means) without measuring limbs or the distance between head-and-navel and then navel-and-feet to find out if they fit the idea of the Golden Section or the “Divine Proportion.”

But we can't read a novel and know “this is the Golden Section” unless you've looked at the last page and made your calculations – number-of-pages x 0.618 = approximate Golden Section. (And then, after all, the paging is fairly arbitrary, compared to what the author may have written).

And certainly in a serialization like this, you have no idea when and where the end might (finally) come, since you don't even have an idea how many pages are involved.

But it's there. I know it's there, like I said, because I made sure it was there! Frankly, it doesn't matter if you know it's there or not: it's all in how you perceive getting there and how the rhythmic build-up, the plot-tension and the overall sense of an arc reinforces that. It's not for you to reach this point and gasp “aha! it's the Golden Section!” when Frieda tells Dr. Kerr Toni is descended from both her twins (meaning the Old Gypsy's prophecy could come true and young Toni could grow up to be as great as her famous ancestor, Beethoven); but because you realize at this point something important has happened, something perhaps unexpected that begins to tie various seemingly unrelated plot elements together: the stories from Harrison Harty's journal in Book II and Knussbaum's Tale in Book III; what the murderer may have been looking for when various characters like Schnellenlauter have been killed; what Frieda's secret means; and how the Guidonian Hand may be involved in all of this. Not, I should mention, that all of those things point to the obvious solution... but it's where things tie together and from here, the tension builds toward the revelation. There will be more twists and turns to go. After all, we still have 46,368 words to go!

Therefore, if you've been reading this novel at all, you've been reading lots of sentences where the word-count resembles [(8+5)+(5+3)]+(8+5) = a sentence of 34 words divided into two phrases of (21+13) words. Or some such configuration – sentences could be 13 or 21 or 34 or 55 words long, maybe 89 words or more; longer sentences are at the beginning of sections, shorter ones at the end. Phrases might “mirror” these subgroupings as (3+5) or (8+13), but the basic point is everything's divided according to the Fibonacci Sequence (there are sentences where an 8-word phrase is divided as 4+4 or 6+2, but any complete sentence fits the mold). And from there, they build to paragraphs and chapters and dramatic structural points.

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(By the way, for years I have been using this asterisk-configuration as a dividing line between segments of my blog-posts. Now you might recognize it as a Fibonacci palindrome: 1+1+2+3+5+8+5+3+2+1+1.)

I suppose the first thing a reader might be thinking would be “why would you do this?”

Partly to see if I could – and if I could use it in such a way it didn't point to itself and say “see what I'm doing? Isn't that clever?”

Trust me, there are many times when I feel “you know, a few words more would make this sentence so much easier” or “would anyone notice if this sentence had only seven words?” But having once started it, I feel part of the challenge is keeping it going.

That I've written three novels already in “proportional word-counts” is enough to prove my initial point – yes, I can! – but yet, as I'm approaching the Golden Section Point of Novel IV, another adventure for Dr. Kerr and Cameron called In Search of Tom Purdue, I'm still writing according to the Fibonacci Sequence even though the location (the Philadelphia suburb of Marple) has nothing to do with visual manifestations of the Divine Proportion (perhaps it is best to leave Phlaumix Court as a building unique in its architectural style).

So let us continue after the Golden Section with the continuation of The Labyrinth of Klavdia Klangfarben. Having reached the “turning point,” what would you expect the next chapter to be about?

Dick Strawser

Phi Day: A Post about the Golden Section

Many people may be aware that March 14th is “Pi Day” but did you know that today – June 18th – is “Phi Day”?

And what, may you ask, is that?

Not that I'm a math geek – math, in fact, was my least favorite subject in school – but I am fascinated by “Phi” and its relation to the arts, especially music.

Phi, basically, relates to the Golden Section, a proportional ratio that is not two equal halves but rather two slightly different sections, not quite two-thirds to one-third. It occurs frequently in nature – the whorl of a nautilus shell, the divisions of a leaf – and may be found in architecture (for instance, one could argue, the Parthenon) or in the placement of objects in a painting (rather than being stuck squarely in the center, no pun intended, is the rectangular shape subdivided by its focal point into something other than equal halves?).

In fact, Phi can be described in the number .618 - and so, that becomes June 18th.

In mathematics, there's a famous sequence of numbers called the Fibbonacci Series where certain numbers can be divided by phi. In other words, 8 could be divided in half as 4+4 or, according to phi, as 5+3. Likewise, 8 could be half of 16 or it could be the “phi” part of 13 – as in 8+5. The interlocking sequence thus becomes

(3+2 = [5)+3 = (8]+5 = [13)+8 = (21]+13 = 34) etc.

and so on, multiplying like Mr. Fibbonacci's rabbits (which, curiously, is where the sequence originated, theoretically).

When I was in graduate school, I often heard how Bela Bartók's music frequently divided along the lines of the Golden Section, especially his Music for Strings, Percussion and Celeste and “very likely” other works from the same period like the 3rd String Quartet.

Usually, someone would point out the climax of the piece didn't happen ½ way through or ¾'s of the way or even 87% of the way through but at the Golden Section or 61.8% of the way through. Take the number of measures and multiply by .618... – that's what we call “phi” just as we call .314... “pi” – and there it was.

Or, in other pieces, wasn't.

Maybe it was a measure off, or even several measures off. Oops.

Now, we don't perceive music the way we do a painting or a building which we see in self-contained spaces in front of us.

Music unfolds over time.

If I'm listening to Bartók's 3rd Quartet, one of my favorite pieces, it may go by so quickly, I'm disappointed when I realize it's over already, while the person usually sitting in front of me is so bored, he thinks it will never end.

(That's another issue, completely, but hey...)

I remember asking my professor “if we listen to music in time, wouldn't the Golden Section be figured according to its duration rather than the number of measures, since the meters and tempos change?”

Everybody looked at me like I was... “one of those” and the topic was dropped.

The question is, since this happened occasionally in certain other pieces even by composers like Beethoven, was it something these composers consciously plotted or was it, like the way that leaf in nature divides, something that happened naturally – accidentally?

Did Bartók use it consciously in determining where the music's climax should be?

Bartók never wrote anything about his use of the Golden Section anywhere, that I'm aware of. But he was particularly close-mouthed about almost any technical aspects of his style and very few of his sketches survive. Who's to say he didn't consider it consciously?

A couple seasons ago, when I got to interview Peter Bartók, the composer's son, who was a toddler when the Music for String, Percussion & Celeste was written, I asked him if his father ever talked about how he composed music and he said “No, I was just a child – he didn't even talk about that with his colleagues!”

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It began as an experiment. Remembering the discussions about the Golden Section in Bartók's music, I started working it into my own music (which I've discussed elsewhere in this blog.)

Then I read a novel by English author, David Mitchell, Cloud Atlas, to my thinking one of the most innovative novels since James Joyce's Ulysses (oh yes, and Saturday was Bloomsday, the celebration of the day on which Joyce's novel takes place: you can read a post about that, here.)

Anyway, Cloud Atlas has a rather unique structure, six nested stories that, once interrupted, resume in a mirror pattern – that is, picking up where the stories left off in reverse order. I wrote about possible structural issues, particularly pointing to the Mirror-Form Golden Section.

It occurred to me later that, like Bartók's music being listened to “in time” rather than measure-by-measure, Mitchell's novel wouldn't be divisible by pages but rather by the number of words.

Thinking of Georges Perec's novel Life: A User's Manual which the author describes as “novels” in the plural – it also is a collection of stories interwoven in a particularly highly structured way, using a “Knight's Tour” to order the chapters,I came across his use of creative constraints, especially in another novel, The Void as it translates into English, which is written without the letter “e.”

Without getting into how the Golden Section and Phi apply to the music I've been writing over the past decade, suffice it to say when I started writing novels, it seemed logical to want to figure out where, in the overall scheme of things, my major climactic points would fall.

Then I just kept subdividing the proportions further and further down from the larger viewpoint (the macro-structure) to the smaller details (the micro-structure), down to the chapters, sections, paragraphs, even sentences.

Like I said, it was an experiment.

Composing aside, I've been enjoying writing “music appreciation thrillers” the past few years, starting with Dr. Dick and his sidekick Buzz Blogster in a parody of a mega-hit by Dan Brown which I called The Schoenberg Code and then continued with a thoroughly original story (insofar as stories are 'original') which I'm in the process of posting now, The Doomsday Symphony.

At the moment, I'm working on another one, The Lost Chord which began life a few years ago as a parody of Dan Brown's next thriller but which I abandoned because I didn't like it. However, I did like the essence of my version of the plot and most of the characters' names (no way I was going to abandon Yoda Leahy-Hu, Iobba Dhabbodhú and LauraLynn Hardy, but that's another matter...).

I am over half-way through it – in fact I'm well on my way to the PHI POINT, the Golden Section of the entire novel.

Considering what I said before – about how we listen to music unfolding over time – how do I know this?

We read the same way we listen to music, whether you're a speed reader or you can only take in a page or two before you fall asleep.

In this case, I made the conscious decision to say “okay, The Lost Chord will be 180,000 words.”

Here's a section of Chapter 27 which I wrote yesterday as an example. It's only 905 words, so read through it before you continue.

To explain, there is Dr. Richard Kerr (a thinly-veiled manifestation of myself) with his assistant Cameron Pierce and LauraLynn Hardy whose cousin, the composer Robertson Sullivan (the son of Gilbert N. Sullivan), was just murdered on the eve of the first rehearsal for his new opera, Faustus, Inc., at the Schweinwald Festival in Bavaria. She herself has been involved in scientific research into the study of musical creativity, by the way. Her and her cousin's great-grandfather, Harrison Harty, was a composer who left behind a journal about his studies one summer at the legendary Schweinwald Academy in 1880 where a fellow student was Gustav Mahler and where Brahms was a visitor. For some reason, at one point the journal breaks into code and somebody else (known to them as musicologist Rothbart Girdlestone) tried to kill LauraLynn to obtain it. The “artifact” mentioned briefly is something that also, presumably, has some important clues.

Now, the presumed killer (known to them as psychiatrist Dr. Iobba Dhabbodhú) needs Kerr's help in finding some specific fountain and while there are other plot-threads twisting around here, suffice it to say that Kerr and Company have found their way to the home of composer Howard Zender, pushing 90, who presumably is going to have some answers for them. (By the way, he lives in an elaborate late-19th Century chalet added on to what was originally a 14th Century castle outside Garmisch-Partkenkirchen, okay?) Oh, the Will mentioned briefly is Zender's nephew, Will Schlegel.

(It is unnecessary to know that Girdlestone and Dhabbodhú are one and the same, two disguises of the composer who calls himself Tr'iTone who is only one of the villains. The other one is a SHMRG operative named Garth Widor, but I digress.)

In this scene, Howard Zender and LauraLynn Harty have gotten into a discussion about creativity.

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Curiously, Zender had twelve different kinds of tea in his kitchen cupboard, making the choice, reaching any consensus, more challenging. I decided, given the hour, something decaffeinated, less exotic, would be preferable. The kettle (a watched pot) took forever to come to a boil – Zender detested boiling water in a microwave. It surprised me he'd even given into the modern convenience of tea-bags, ugly tails hanging over the cup's rim, but maybe Will had made the substitution and just never told him.

For living in a century-old German chalet appended to a 14th-Century castle, Zender's kitchen was like any suburban home's, even if considerably more organized and efficient, whether his doing or Will's. I let the tea steep for three minutes before removing the bags, preparing a tray with cookies and crackers.

Cameron had been burying his nose deep in Harrison Harty's mysterious notebook, carefully writing out a translation of the code, progressing more quickly as he gradually became more accustomed to the substitutions. It would be a slow, daunting task under the best of circumstances: who knew what secrets it might yield?

He barely looked up, nodding, as I placed the teacup beside him: I'm sure he would have preferred coffee. He took a sip, then bent over the page, back to work.

"So far, the problem is dealing with something objectively that's primarily subjective," LauraLynn said, continuing her conversation with Zender, "deriving facts from various series of data, eventually distilling certain common patterns, not like applying inductive reasoning where scientific observation yields consistent facts over frequent repetitions to something that's more deductive. We've spent the past few years accumulating lots of data in interviews with various composers from around the world, only starting on ways of filtering that data to discern certain thought-patterns."

"You're talking about codifying inspiration?" Zender asked, sounding more amused than argumentative, something of a twinkle in his eye. "Sounds kind of contradictory, applying science to something as mystical as inspiration."

Knowing better than to get involved here, I picked up the artifact, checking out the scratchings on its back.
"What I'm hoping," she said, "is, if we can replicate the process, can we trigger creative responses in someone who's..."

"Perhaps suffering from writer's block? Or," Zender responded, "uncreative to begin with?"

He nibbled on a cookie before continuing, apologizing for this guilty pleasure. I only assumed he meant the cookie.

"How can they create something without any knowledge of what they're creating? Wouldn't they need some kind of set-skills? The language of music is little different than that of any science."

He also asked if there's a distinction between blindly following these set-skills or breaking the rules to create art, wondering if any of her scientific variables could take that into account.

"There's something else Schoenberg said," Zender added. "A craftsman creates because he can – an artist creates because he must."

It started again, always falling – floating, a flying squirrel not yet Icarus – this dream that invariably began the same way, coming to him unbidden in that indefinable state between consciousness and unconsciousness, where he was most open to inspiration, suspended between Reality and Art: Time stopped, unimportant, what he had most. Lips in the palm of his hand, lips he wanted to kiss but was afraid would bite his face. He splashed through a mirror, past the firing squad, the armless statue...

"No," LauraLynn said, carefully sipping her tea, looking into the valley below, "that's like having one hundred chimps writing Hamlet. We can't take people off the street and say 'Write a symphony!' I'd so much rather have a term we could use that's not quite as loaded as 'inspiration' is, frankly."

She thought a moment before she continued, "Though maybe it's like this: let's say you hand someone a violin, train them to hold it and, eventually, to play a simple tune."

Turning around, she hadn't noticed Zender was in some kind of trance, not that he was inattentive or rude.
“There're thousands of hours of hard work before making her professional debut.”

Still, teaching someone how to write a simple tune or a symphony wasn't the point, just a starting place.
"But teaching someone set-skills," Zender resumed, "and having them compose by rote is not like turning them instantly into composers, though the world's already full of com-poseurs who genuinely think they are. Science," he admitted, "has never explained the difference how creative artists work, defining what made Mozart different from Beethoven.

"Copland told me he saw everything in a flash, everything whole, complete, but not every composer works that way. I can't find the light till I'm well into the tunnel, sometimes.

"There is, if you'll pardon the [Socratic?] argument, something each of us possesses that resonates within – but in different ways. Our inner child not withstanding, it's something I call our Inner Chord. For people who are tone-deaf or for whom all music sounds alike, it is silent though perhaps only impaired."

I found it impossible not to listen, deciding to put the artifact down on the table for the moment just as Cameron chewed on his pen after pushing the journal aside.

"How it resonates, creating overtones, determines our becoming performers, composers, or music-lovers, how we respond, form our stylistic preferences. But we can also lose that connection with it after a time.

"It becomes this thing, then, that we will always be searching for, what has now become our 'Lost' Chord."
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If you look at the Fibbonacci Series (see above), you'll notice a pattern: alternating segments of larger and smaller numbers. Translated to musical beats or a novel's words, they create a kind of rhythm. Now, when I subdivided my 180,000 words down to the chapter level, Chapter 27 turned out to be 2,368 words long, its internal Golden Section being 1,463 words. The second 'half' (or section) of this chapter, quoted above, is 905 words long.

This further subdivides into two segments of 559 words and 346 words. Each of these can be divided by Phi into (345+214) words and (214+132) words.

You can see that there is a rhythm at work here, longer segments followed by shorter segments, an internal lower-level climax (a short segment) then followed by a longer segment and so on.

Since not everything in a thriller needs to be “Action” (though some seem to be almost all action) there is often some contrast which might be created through longer paragraphs or sentences building up to shorter and shorter paragraphs and sentences.

Not every paragraph or sentence is completely self-contained. Dialogue, for instance, doesn't often move this way, but the topics around the dialogue or the focus of each segment might fit within a section's “boundaries.”

So, the “Golden Section” for this excerpt occurs after the surreal sequence about the lips on the hand biting his face, the firing squad, the armless statue (incidentally, a reference to Jean Cocteau's famous film, Blood of the Poet a kind of quantum challenge to the standard perception of time and chronology). That opening portion is 559 words long. The remaining portion is 346 words.

Why did I do this?

For one thing, the chicken climbing Mount Everest aside, I wanted to see where these points of arrival might fall and to space them proportionally, from the major climax-points down to the subtler changes that might happen within a given scene.

Have you ever read something and felt the pacing was terrific or that section just went on too long? One of the problems I had with my initial run-through with The Lost Chord was that, like its model, it had this enormous epilogue, actually epilogues within epilogues and I felt the pacing was all wrong – actually, it was all “out of proportion.”

Have you noticed, when you're reading a mystery or a thriller, after it builds to a climax, the next scene is often a contrast, more low-key, often longer, perhaps more slowly paced? But that as you get closer to the ending, these segments get shorter, are faster-paced and start tying what before seemed like unrelated elements.

This is why chapters turn into page turners, leaving you at a cliff-hanger; then you turn the page and start reading about Aunt Katie. But as you progress toward the conclusion (and your own thoughts about how it's going to work out), you realize there's something about Aunt Katie that's going to be important.

But if the author resolved the cliff-hanger, it would be over too soon and the sense of anticipation weakened: you want to find out what's going to happen, now you have to keep reading.

So when I started writing this fully revised version of The Lost Chord, I wanted to extend this sense of proportion down to smaller and smaller elements.

When I wanted to figure out where my climaxes should be, according to the Golden Section, I multiplied 180,000, the pre-determined length, by .618 and found that the chapter ending with the novel's “turning point” (not the actual dramatic climax, but a point where the action takes a definite turn toward the climax) would be at 111,240 words.

Taking it from there, there would be “sub-points” building in the tension that would be slightly lower high-points, so I divided each of the two segments on either side of “Big Phi” by .618 and placed the ends of chapters there.

I would begin with a general outline of the plot – basic premises, major occurrences, specific dramatic high-points. These, I stretched out over my word/time-line.

As I filled in the chapters, I began writing summaries of the action and generic views of expository scenes. Very often I found these broke quite readily into four sections. I could figure out, by constantly subdividing it – sort of like deconstructing the plot down to the molecular level – similar proportions at not just the chapter and section level but at the paragraph and sentence level as well.

Like I said, it was an experiment: I wanted to see if I could make it work. Curiously I found myself having to do very little editing to come up with the right number of words, or the balance of phrases.

It felt odd writing it almost sentence by sentence rather than full-steam-ahead from one chapter to the next. But I'd already taken care of most of that in the outline: this was like creating a painting with pencil outlines in a sketch, then figuring out what colors went where before filling in the individual brushstrokes that make up the textures and details you would only notice on closer inspection.

In fact, I discovered, in order to pace it toward the focal point, I often would begin writing at the end of the section, then work my way, sentence by sentence, backward to make sure I ended up where I needed to be when I needed to be there. This also helped me be, in one sense, more precise but also at times showed me I needed more time to let this idea expand: the biggest problem, working within the outline, was realizing if I wasn't careful it come off reading like a series of bullet-points rather than continuous, unfolding prose.

So I created an outline template (each chapter having four sections, each subdivided further and further into four subsections) and filled in the necessary word-count according to Phi, the Golden Section.

So, going back to Chapter 27 (the above example), I broke the 346 words of the 4th section into two sub-segments of 214 and 132 words, down to four smaller segments each to get

436 = (132+82) + (82+50)

then took the 132-word segment and divided it into (82+50) words or [(51+31)+(31+19)] words. And so on.

So if I take that last section from my example, rather than going through the whole thing, and look at it in my sketches, it looks kind of like this: unfortunately, the outline format and indentations is all screwed up, transferring from a Word Document to blogspot, so you'll have to bear with the profusion of numbers – but basically the larger numbers break down into pairs of proportionally divided numbers and so on from 346 words for the D-Section of Chapter 27 all the way down to clauses of 7 or 5 words.

*** ***** ******** ***** ***
Chapter 27: D-1 = 214 = ((i.) 132+ (ii.) 82) = [(82+50)+(51+31)] =
i. = 82 = (51+31) = [(32+19) + (19+12)] =
a''. = 51 = (32+19) =
32 = (20+12) = [(12+8)+(7+5)]
[20 = (12+8) = [(7+5)+8]] "No," LauraLynn said, carefully sipping her tea, [7] / looking into the valley below,[5] / "that's like having one hundred chimps writing Hamlet. [8]
[12 = (7+5)] = We can't take people off the street [7] / and say 'Write a symphony!' [5]
[19] = I'd so much rather have a term we could use that's not quite as loaded as 'inspiration' is, frankly." (this should break into (12+7) but it doesn't...)
(Ah, so on second thought, how about this revision which fits the pattern?)
I'd so much rather have a less loaded term we could use [12] / without quite the baggage 'inspiration' has, frankly." [7] (actually, I like that better)

b''. = 31 = (19+12) = [([7+5]+7) + (5+7)]
[19 = [(12+7)+] She thought a moment before she continued [7], "Though maybe it's like this: [5] / let's say you hand someone a violin, [7]
[+12] ...train them to hold it [5] / and, eventually, to play a simple tune." [7] (In this case, the 7+5 is reversed...)

ii. = 50 = (31+19) = [(12+7)+(7+5)] + [(7+5)+7)]
[31 = (19+12)] Turning around, she hadn't noticed Zender was in some kind of trance, [12] not that he was inattentive or rude. [7]
[12] “There're thousands of hours of hard work [7] / before making her professional debut.” [5] (I'm still not satisfied with this one: doesn't flow conversationally...)
[19 = (12+7)] Still, teaching someone how to write a simple tune or a symphony [12] / isn't the point, just a starting place. [7]

1b. = 82 words = (51+31)
i'. = 51 = (32+19) = [(20+12)+(12+7)]
[32 = [(12+8) + 12)] = [] "But teaching someone set-skills," Zender resumed, "and having them compose by rote [12] / is not like turning them instantly into composers, [8] though the world's already full of com-poseurs [7] / who genuinely think they are. [5]

[19 = (12+7)] Science," he admitted, "has never explained the difference how creative artists work, [12] / defining what made Mozart different from Beethoven. [7]

ii'. = 31 = (19+12)
[19 = (12+7)] "Copland told me he saw everything in a flash, everything whole, complete, [12] / but not every composer works that way. [7]
[12] I can't find the light [5] till I'm well into the tunnel, sometimes. [7] (Originally, this was 'Sometimes, I can't find the light till the end of the tunnel' but that breaks into 6+6; I fixed the wording but also placed the 'sometimes' at the end, balancing the proportions.]

2. = 132 words = (82+50)
a. = 82 words = (51+31)
i'. = 51 = (32+19) = [(20+12)+(12+7)]
[32 = (20+12) = [(8+12)+12]] "There is, if you'll pardon the (Socratic?) argument, [8] / something each of us possesses that resonates within, but in different ways. [12] / Our inner child not withstanding, it's something I call our Inner Chord. [12]

[19 = (12+7)] For people who are tone-deaf or for whom all music sounds alike, [12] / it is silent or perhaps only impaired." [7]

ii'. = [31 = (19+12)] I found it impossible not to listen, deciding to put the artifact down on the table for the moment, [19] / just as Cameron chewed on his pen after pushing the journal aside. [12]

b. = 50 words = (31+19)
i'. = []31 = (19+12) = [(12+7)...] = [19 = (12+7) = [(5+7)+7]
"How it resonates, creating overtones, [5] / determines our becoming performers, composers, or music-lovers, [7] / how we respond, form our stylistic fingerprints. [7] /
But we can also lose that connection with it after a time. [12]

ii'. = [19 = [(5+7)+7]
"It becomes this thing, then, [5] / that we will always be searching for, [7] /
what has now become our 'Lost' Chord." [7]
*** ***** ******** ***** ***

This excerpt was chosen more or less randomly – largely because I wrote it yesterday, so it's still fresh and editable – and it only demonstrates the method behind my phi-oriented madness. I gave you the whole 905-word excerpt so you could follow the rhythmic pacing through a longer span (I could demonstrate the structure of a Beethoven symphony movement by playing a couple phrases (a few seconds of music) but instead gave you, say, part of the exposition (several minutes of music).

If you're wondering how it works in the long run, if you've been following the progress of The Doomsday Symphony on the installment plan, here, you will already have an idea. Earlier today, I posted the PHI POINT of The Doomsday Symphony, a 130,000 word novel, on PHI DAY, June 18th (6-18) – if you haven't already noticed, each chapter is posted at 6:18am – and the same structure applies here, as it does in The Lost Chord.

Except, being 130,000 words as opposed to 180,000 words like The Lost Chord, the proportions are all different and the numbers will be adjusted accordingly (the sketch files are all locked in a dead computer, for what it's worth). I didn't always break it down to the sentence level, sometimes just the paragraphs were enough, but the idea is basically the same.

You can read an earlier post that “analyzes” the opening of The Doomsday Symphony, here.

Yes, it's very abstract and terribly left-brained and I may seem like a terminally OCD geek to anyone reading this (though I assure you my house is a mess, my life is terribly disorganized and I'm basically a slob).

The whole point for an artist is to create something out of these patterns we have around us and find ways of challenging ourselves to perhaps do something different (if not original) with them that somehow combine elements of structure (all language is structure) with elements of spontaneity (telling a story that engages both the mind and the heart).

"Phi Day" may not be as catchy as "Pi Day" because we can't bake pies with the Greek letter 'pi' on it, but it seemed an appropriate day to post the "Phi Chapter" of my novel and write about its significance in the way I think about writing.

Do you need to understand that to appreciate it?

No, of course not, just as you don't have to understand the implications of 19th Century Tonality to enjoy the really cool music Richard Wagner composed for his operas, The Ring of the Nibelung.

If you do understand it, then you can appreciate the music on an entirely different level.

I should mention, the name for my 90-year-old composer Howard Zender (loosely based on Elliott Carter), who describes the "Lost Chord" in this excerpt, comes from one of my favorite novels of all time, Howards End by E.M. Forster, not just because of its famous scene describing listening to Beethoven's 5th Symphony but because of its recurrent theme: "Only connect."

It is the artist's job to "connect" with the audience whether it's a single listener or millions of readers. How the artist does that, how the audience responds to it is one of the great mysteries of art if not life.

The great thing about Art is you can keep coming back to it and discovering new things about it each time, things that very often you had no idea were there the first time you encountered them.

- Dick Strawser