Béla Bartók's Music For Strings Percussion and Celesta, Movement I
Eerie and Aimless
This piece is eerie. It begins with a dark and eerie melody played without harmony. Each time it is repeated the dark harmonies slowly emerge and the music becomes louder and louder. But it is a slow build up, almost a perfect wedge of tension climaxing at exactly 61% through the piece, then a reversal as it wanders, seemingly aimlessly, until it ends on the note it started.
"Seemingly aimless" describes what you may think as you listen, but nothing could be farther from reality. The piece is actually a perfect fusion of math, form and passion.
Gold Ratio and the Fibonacci Sequence
The "golden ratio" is a math function (a+b)/a = a/b, which equals about the number 1.6180339887. The ratio is also related to the Fibonacci sequence, which is what you get when you start with 0 and 1, and add the 2 numbers. So 0 + 1 is 1. So you have 0, 1, and 1. Add 1 + 1, you get 2. Now you have 0, 1, 1, 2. Add 1 + 2 to get 3. Add 2 + 3 to get 5. Add 3 + 5 to get 8. It looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and on. Well, divide 13 by 8 and you get 1.625. Divide 21 by 13 to get 1.61538. 34 divided by 21 is 1.61904. All of these numbers divide to be the golden ratio. And if you divide 21 by 34, you get .61, the spot that this piece climaxes at.
This ratio occurs naturally in the spiral of snail shells, in plants (the count and arrangements of flower petals, pine cones, tree branches, the curve of fern leaves, etc), and it is even present in the ratios of the human face and body.
The ratio exists in man-made structures as well, from Greeks structures and even the Egyptian pyramids to the modern day. The ratio is simple to understand for non-mathematicians, yet it has captivated some of the greatest mathematical minds of all ages. It has fascinated biologists, artists, musicians, historians, architects, psychologists, and undoubtedly mystics.
"It is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics." - Mario Livio, The Golden Ratio: The Story of Phi, The World's Most Astonishing Number
The number is nearly always contained in anything striving to be beautiful.
Music is Communication
I do not give the ratio so much attention because it alone makes greatness. The ratio certainly helps, but music is not math. I studied music composition and we didn't use calculus, trigonometry, geometry, or even algebra at all, not once. Musicians use fractions all the time (quarter note, half note, you know, stuff I learned in 5th grade...) and it is true that the western music scale is based off of math ratios so there is math in music.
But don't let anyone fool you, music is communication. The human spirit says things through music. Some of the things that are said are easier to say through music than can be said with words. Music will often say different things to different people and different things than the composer intended. Sometimes musicians execute a flawless performance, but they don't say much to their audience. Those are often boring performances. Sometimes musicians stumble through a performance, but they don't let their faults distract from the message and the audience is often captured by it and enthralled and doesn't even notice the mistakes.
Just because Béla Bartók uses the golden ratio doesn't give this piece any special meaning. The music itself is a passionate expression of nature and the ratio is just a part of that. Unlike some strict "mathematical" music built solely on algorithms and formulas, this piece has a melody and a message. A good composer has 2 things. A good composer knows how to set a message to music and a good composer has a message worth setting to music.
The Moral of the Story
Listen for the eerie melody which moves between instruments and pitch ranges, sometimes high up with the violins, sometimes scraping bottom with the double basses. Try to hear Bartók's message. Maybe your mind wont understand it, but it should stir something inside of you.
When you listen to music don't give it respect by dutifully giving it your time and attention and attempt to understand the greater meaning. Instead, ask what does this music say to and do for you. When you answer that question you can decide for yourself what is worth listening to.
Honestly, you might not like this piece, or it might not be the type of thing you need to hear at this point in your life. But every once and a while a song says something that stirs you and you value it so much you tell your friends about it and even write about it so others will come across it and perhaps find something of value in it too.
Béla Bartók (March 25, 1881 – September 26, 1945)
Bartók is considered one of the greatest composers of the 20th century. He was a Hungarian composer, pianist and collector of Eastern European and Middle Eastern folk music. He was passionate about recording the music the common people sang, which was greatly misunderstood and undervalued and there was no record of before his day. He incorporated folk music into his own music, but not by quoting it. In his own words:
"We must penetrate it, feel it, and bring out its sharp contours by the appropriate setting... It must be a work of inspiration just as much as any other composition."
The following is from an article by Peter Hughes.
This multi-ethnic interest caused Bartók trouble, especially after World War I when Slovakians and Romanians were no longer part of Hungary. Areas in which Bartók had previously been free to explore and do research were no longer open to him. Moreover, he endured much criticism at home for his "unpatriotic" interest in the peoples of nations hostile to Hungary. Nostalgic for the ethnic diversity of the old Austro-Hungarian Empire, Bartók dreamed of the "brotherhood of people, brotherhood in spite of all wars and conflicts."
...
Béla Bartók Jr. later wrote that his father joined the Unitarian faith "primarily because he held it to be the freest, most humanistic faith." Although Bartók was not conventionally religious, "he was a nature lover: he always mentioned the miraculous order of nature with great reverence." Nature was Bartók's hobby as well. He collected specimens: plants, minerals, and, especially, insects. Later in life he expressed his philosophy using a homely image drawn from nature: "There is life in this dried-up mound of dung. There is life feeding on this dead heap. You see how the worms and bugs are working busily helping themselves to whatever they need, making little tunnels and passages, and then soil enters, bringing with it stray seeds. Soon pale shoots of grass will appear, and life will complete its cycle, teeming within this lump of death."
Bartók's personal philosophy was stoic and pessimistic. He held himself apart from others, independent of the ambitious struggle after "trifles." As a consequence he felt lonely... Bartók translated his own sense of profound spiritual isolation into music.