The Eight - Six (Philidor's Tale continued)

(Page 173) "I initiated myself," said Bach calmly. "Oh, I know that there are secret societies of men who spend their lives trying to unravel the mysteries of the universe, but I am not a member. I seek truth in my own fashion." Saying this, he reached over and plucked Euler's formulaic ches map from the piano. With a nearby quill he scratched two words across the top: Quaerendo invenietis. Seek, and ye shall find. Then he handed the Knight's Tour to me. "I do not understand," I told him in some confusion. "Herr Philidor," said Bach, "you are both a chess master, like Dr. Euler, and a composer, like myself. In one person, you combine two valuable skills." "Valuable in what way?" I asked politely. "For I must confess, I've found neither to be of great value from a financial standpoint!" I smiled at him. "Though it is hard to remember sometimes," Bach said, chuckling, "there are greater forces at work in the universe than money. For example - have you ever heard of the Montglane Service?" I turned suddenly to Euler, who had gasped aloud. "You see," said Bach, "that the name is not unfamiliar to our friend the Herr Doktor. Perhaps I can enlighten you as well." I listened, fascinated, while Bach told me of the strange chess service, belonging at one time to Charlemagne and reputed to contain properties of great power. When the composer finished his summary, he said to me: "The reason I asked you gentlemen here today was to perform an experiment. All my life I have studied the peculiar powers of music. It has a force of its own that few would deny. It can tranqulize a savage beast or move a placid man to charge in battle. At length, I learned through my own experiments the secret of this power. Music, you see, has a logic of its own. It is similar to mathematical logic, but in some ways different. For music does not merely communicate with our minds, but in fact changes our thought in some imperceptible fashion." "What do you mean by that?" I asked. But I knew that Bach had struck a chord within my own being that I could not quite define. Something I felt I'd known for many years, something buried deep inside me that I felt only when I heard a beautiful, haunting melody. Or played a game of chess. "What I mean," said Bach, "is that the universe is like a great mathematical game that is played upon a tremendous scale. Music is one of the purest forms of mathematics. Each mathematical formula can be converted into music, as I've done with Dr. Euler's." He glanced at Euler, and the latter nodded back, as if the two shared a secret to which I was not yet privy. "And music," Bach continued, "can be converted into mathematics, with, I might add, surprising results. The Architect who built the universe designed it that way. Music has power to create a universe or to destroy a civilization. If you don't believe me, I suggest you read the Bible." Euler stood in silence for a moment. "Yes," he said at last, "there are other architects in the Bible whose stories are quite revealing, are they not?" "My friend," said Bach, turning to me with a smile, "as I've said, seek and ye shall find. He who understands the architecture of music will understand the power of the Montglane Service. For the two are one." *********************************************************************************** David has listened closely to the story. Now, as they approached the fretted iron gates of his courtyard, he turned to Philidor in dismay. "But what does it all mean?" he asked. "Waht do music and mathematics have to do with the Montglane Service? What do any of these things have to do with power, whether on earth or in the heavens? Your story only serves to support my claim that this legendary chess service appeals to mystics and fools. Mucha s I hate to tie such appellations to Dr. Euler, your story suggests he was easily prey to fantasies of this sort." Philidor paused beneath the dark horse chestnut trees that hung low over the gates of David's courtyard. "I have studied the subject for years," the composer whispered. "At long last, though I've never been interested in biblical scholastics, I took it upon myself to read the Bible, as Euler and Bach had suggested. Bach died soon after our meeting, and Euler immigrated to Russia, so I was never again to meet the two men to discuss what I had found." "And what did you find?" said David, extracting his key to unlock the gates. "They'd directed me to study architects, and so I did. There were only two architects of note within the Bible. One was the Architect of the universe. That is, Gog. The other was the architect of the Tower of Babel. The very word 'Bab-El' means, is discovered, 'Gate of God.' The Babylonians were a very proud people. They were the greatet civilization since the beginning of time. They built hanging gardens that rivaled the finest works of nature. And they wanted to build a tower that would reach to heaven itself, a tower that would reach to the sun. The story of this tower is the one, I felt sure, that Bach and Euler alluded to. "The architect," Philidor continued as the two men passed through the gates, "was one Nimrod. The greatest architect of his day. He built a tower higher than any known to man. But it was never completed. Do you know why?" "God smote him down, as I recall," David said as he crossed the court. "But how did He smite him down?" asked Philidor. "He did not send a bolt of lightning, a flood, or a plague, as was His custom! I shall tell you how God destroyed the work of Nimrod, my friend. God confused the languages of the workers, which until then had been one language. He struck down the language. He destroyed the Word!" ************************************************************************************** This is the end of Philidor's tale. I would like to add one other Bible story in which "music" (sound) is used to destroy a civilization. Perhaps you will recall the tale of Joshua and Jericho. Joshua was instructed by God to have his army march around the seemingly inpenetrable walls of the city for a prescribed seven days: for the first six days the army and seven priests playing seven rams' horns marched around the city once; on the seventh day the seven priests once again played their horns as they marched around the city with the army seven times, but not a word was spoken, only the music of the rams' horns was heard. And then, at a signal, all the Israelites let lose a great war cry. And the walls of Jericho crumbled and fell down. Interesting...

The Eight - Cinq (Philidor's Tale Continued)

Philidor’s Tale continued (Page 171) Euler and I complimented the aging composer upon the cleverness of his work. I was then requested to play three games of blindfold chess simultaneously against the king, Dr. Euler, and the kapellmeister’s son Wilhelm. Though the older man did not play chess himself, he enjoyed watching the game. At the conclusion of the performance, where I won all three games, Euler took me aside. "I’d prepared a gift for you," he told me. "I’ve invented a new Knight’s Tour, a mathematical puzzle. I believe it to be the finest formula yet discovered for the tour of a Knight across a chessboard. But I should like to give this copy to the old composer tonight, if you don’t mind. As he likes mathematical games, it will amuse him." Bach received the gift with a strange smile and thanked us genuinely. "I suggest you meet me at my son’s cottage tomorrow morning before Herr Philidor departs," he said. "I may then have time to prepare a little surprise for both of you." Our curiosity was piqued, and we agreed to arrive at the appointed time and place. The next morning Bach opened the door of Carl Philipp’s cottage and squired us inside. He seated us in the small parlor and offered us tea. Then he took a seat at the small clavier and began to play a most unusual melody. When he’d finished both Euler and I were completely confused. "That is the surprise!" said Bach with a cackle of glee that dispelled the habitual gloom from his face. He saw that Euler and I were both totally at sea. "But have a look at the sheet music," Bach said. We both stood and moved to the clavier. There on the music stand was nothing other than the Knight’s Tour that Euler had prepared and given him the prior evening. It was the map of a large chessboard with a number written in each square. Bach had cleverly connected the numbers with a web of fine lines that meant something to him, though nothing to me. But Euler was a mathematician, and his mind moved faster than mine. "You’ve turned these numbers into octaves and chords!" he cried. "But you must show me how you’ve done it. To turn mathematics into music – it is sheer magic!" "But mathematics are music," Bach relied. "And the reverse is also true. Whether you believe the word ‘music’ came from ‘Musa,’ the Muses, or from ‘muta,’ meaning mouth of the Oracle, it makes no difference. If you think ‘mathematics’ came from ‘mathanein,’ which is learning, or from ‘Matrix,’ the womb or mother of all creation, it matters not…" "You’ve done a study of words?" said Euler. "Words have the power to create and kill," Bach said simply. "That Great Architect who made us all, made words, too. In fact, He made them first, if we may believe St. John in the New Testament." "What did you say? The Great Architect?" said Euler, growing a little pale. "I call God the Great Architect, because the first thing He designed was sound," Bach relied. "’In the Beginning was the Word,’ you remember? Who knows? Perhaps it was not only a word. Perhaps it was music. Maybe God sang an endless canon of His own invention, and through it, the universe was wrought." Euler had grown paler yet. Though the mathematician had lost the sight of one eye by studying the sun through a glass, he peered with the other eye at the Knight’s Tour that sat upon the clavier stand. Running his fingers over the endless diagram of tiny numbers inked across the chessboard, he seemed lost in thought for several moments. Then he spoke. "Where have you learned these things?" he asked the sage composer. "What you describe is a dark and dangerous secret, known only to the initiated."

The Eight - Quatre (Philidor's Tale Continued)

(Page 170) My work came to the attention of the German mathematician Euler. He’d read of my blindfold play in the French Dictionnaire published by Diderot, and he persuaded Frederick the Great to invite me to his court. The court of Frederick the Great was held at Potsdam in a large, stark hall, glittering with lamplight but barren of the artistic wonders one finds at other European courts. Indeed, Frederick was a warrior, preferring the company of other soldiers to courtiers, artists, and women. It was said he slept upon a hard wooden pallet and kept his dogs beside him at all times. The evening of my appearance, Kapellmeister Bach of Leipzig had arrived with his son Wilhelm, having journeyed there to visit another son, Carl Philipp Emanuel Bach, harpsichordist to King Frederick. The king himself had written eight bars of a canon and had requested the elder Bach to improvise upon this theme. The old composer, I was told, had a knack for such things. He’d already developed canons with his own name and the name of Jesus Christ buried within the harmonies in mathematical notation. He’d invented inverse counterpoints of great complexity, where the harmony was a mirror image of the melody. Euler added the suggestion that the old kapellmeister invent a variation that reflected within its structure "the Infinite" – that is to say, God in all His manifestations. The king seemed pleased by this, but I felt certain Bach would demur. As a composer myself, I can tell you it’s no small chore to embroider upon another’s music. I once had to compose an opera upon themes of Jean-Jacques Rousseau, a philosopher with a tin ear. But to hide a secret puzzle of this nature within the music…well, it seemed impossible. To my surprise, the kapellmeister hobbled his short, square body to the keyboard. His massive head was covered in a fat, ill-fitting wig. His foreboding eyebrows, grizzled with gray, were like eagles’ wings. He had a severe nose, heavy jaw, and a perpetual scowl etched into his hard features that suggested a contentious nature. Euler whispered to me that the elder Bach did not care much for "command performances" and would doubtless make a joke at the king’s expense. Bending his shaggy head over the keys, he began to play a beautiful and haunting melody that seemed to rise endlessly like a graceful bird. It was a sort of fugue, and as I listened to the mysterious complexities, I realized at once what he’s accomplished. Through a means unclear to me, each stanza of the melody began in one harmonic key but ended one key higher, until at the end of six repetitions of the king’s initial theme, he’d ended in the key where he’d begun. Yet the transition or where it occurred, or how, was imperceptible to me. It was a work of magic, like the transmutation of base metals into gold. Through its clever construction, I could see that it would go endlessly higher into infinity until the notes, like the music of the spheres, could only be heard by angels. "Magnificent!" murmured the king when Bach slowly ended his play. He nodded to the few generals and soldiers who sat on wooden chairs in the sparsely furnished hall. "What is the structure called?" I asked Bach. "I call it Ricercar," the old man said, his dour expression unaltered by the beauty of the music he’d wrought. "In Italian, it means ‘to seek.’ It’s a very old form of music, no longer in fashion." As he said this he looked wryly at his son Carl Philipp, who was known for writing "popular" music. Picking up the king’s manuscript, Bach scrawled across the top the word Ricercar, the letters widely spaced. He turned each letter into a Latin word, so that it read "Regis Iussu Cantio Et Reliqua Canonica Arte Resoluta." Roughly, this means a song issuing from the king, the remaining resolved through the air of the canon. A canon is a musical structure where each part comes in one measure after the last but repeats the entire melody in overlappin fashion. It gives the appearance of going on forever. Then Bach scribbled two Latin phrases in the margin of the music. When translated they read: As the Notes increase, the King’s Fortune increases. As the Modulation ascends, the King’s Glory ascends.