What’s So Significant About 64 Variations?
The Ciaccona has 64 variations, and I immediately called that evidence of Bach’s larger, impressive structure for the Ciaccona. What’s so important about the number 64?
Musical phrases usually come in groups of four or eight measures, and they certainly did so in 1720’s German music. The Ciaccona is based on both threes and fours. Each measure of the Ciaccona has three beats, and each has four measures. That’s common for pieces in three (think of your favorite waltz). And though each measure has three beats, each quarter-note beat is evenly divided into eighth notes, sixteenth notes, and thirty-second notes, in all but two variations – not divided into triplets, as it could be.
The fact that beats are evenly divided into halves, quarters, eighths, sixteenths, and thirty-seconds means that those powers of two are particularly relevant numbers. They are more relevant than just any multiple of two, such as 60, or even just any multiple of 16, like 96.
Bach could have just aspired to write a large number of variations and stopped anywhere after fifty. 51. 52. 60. Why 64 variations? To start, it’s an even number. There’s nothing significant about the number of variations being even. Of course, there’s a fifty-percent chance of that. But there is something significant about the number of variations being 64. Having the number of variations be a power of two, in this case, two to the sixth power, would allow the entire piece to be evenly subdivided six times (32, 16, 8, 4, 2, 1). That’s not true for other numbers. Take the number 60. 60 is a multiple of 4. Do I think that would be amazing, too? 60 variations could only be evenly divided twice (30, 15). Sets of 15 variations, or musical units, would be unusual for traditional, European music, because this piece is based on threes and fours, not fives.
Though having 64 variations would allow the piece to be neatly subdivided multiple times, it isn’t. The piece has three sections, each one shorter than the previous, and that don’t have tidy numbers of variations. The first section, in D-minor, is 33 variations long. It’s followed by an 19-variation major section, then by a 12-variation minor section.
Analyzing the larger structure of the Ciaccona is a large task that others have tried to tackle. I think that they mostly end up speculating about why Bach organized it the way he did. Here’s my speculation.
The opening theme recurs more and more frequently throughout the Ciaccona. I may be influenced by Arnold Steinhardt (whose book, Violin Dreams, I just finished) when I say that the opening theme reminds me of the call of death, the call for the end of the partita. The Ciaccona begins by saying, “It’s time to end the partita,” then, its whole life flashes before its eyes, but in the end, the Ciaccona theme keeps coming back more and more frequently until the end of the movement. It’s like in stories where death is a shrouded figure you sometimes see and worry about, then say, “Oh, it’s nothing.” Then the figure comes back. In the middle section, in D major, you think that you’ve escaped the end of the Ciaccona and that it’s going to keep going forever. Then the opening theme comes back, and the last section is the shortest of them all. I think it’s the way childhood seems to last forever, but then life speeds up during middle age, and before you know it, it’s gone.
Friday, April 2, 2010
Natural Order in the Bach Ciaccona
The Ciaccona from Bach’s D-minor Partita For Solo Violin comprises 64 variations on a four-measure theme. Every variation follows or references one underlying bass line and one rhythmic pattern. To listen to the piece, which lasts about 15 minutes, one might not realize that the number of variations is so round. In places, it feels like the Ciaccona will keep going forever. When the Ciaccona does end (always a letdown!), it sounds as though Bach happened on a conclusion and stopped. But he didn’t stop there by chance. He stopped at the end of the 64th variation on his theme. A strict structure can underlie music that sounds creative and spontaneous.
It’s a surprise to learn that the Ciaconna has exactly 64 variations on a theme. The music feels so free and even rambling in some places, particularly where there are many 32nd notes. There are so many surprises, like the key changes, the transitions to new sections, and the introduction of new themes, which seem spontaneous, rather than conforming. The parts flow together so perfectly that it’s hard to believe that Bach wrote them to fit a mold. The Ciaccona sounds like the model from which a mold might be cast.
Perhaps it is wrong to assume that what is natural and flowing is unstructured. That may be a more modern outlook on things. Form and flow aren’t necessarily opposed. Could the structure help the piece flow?
In the past, people thought that what was natural was orderly. In Elizabethan England, people believed in the Great Chain of Being, in which God ruled men who ruled animals. People who practice Islam have great structure to their lives, praying five times per day. These are two examples that come to mind, but there are many other examples of the way humans lead structured lives.
Whether or not we humans choose to discipline ourselves, nature imposes order on our lives. Our days, weeks, months, and years are precisely patterned. Every day has 24 hours, the time it takes the earth to rotate once around its axis. Every year has 365 and 1/4 days, the time it takes the earth to orbit the sun. Our months correspond roughly to orbit of the moon around the earth. The lengths of our days and nights and the characters of our seasons depend on the movement of the sun and the earth.
Perhaps it’s not so surprising that Bach built his Ciaccona on a large and regular framework. The world is filled with structures, hierarchies, and repeating themes, from the planets in the universe, to our seasons, to our sunrises and sunsets, to our generations. Life is a series of variations on a 24-hour theme, each featuring the same sunrise, sunset, and motions of the planets and stars. Unlike Bach, we can’t plan ahead how many variations we are going to write.
It’s a surprise to learn that the Ciaconna has exactly 64 variations on a theme. The music feels so free and even rambling in some places, particularly where there are many 32nd notes. There are so many surprises, like the key changes, the transitions to new sections, and the introduction of new themes, which seem spontaneous, rather than conforming. The parts flow together so perfectly that it’s hard to believe that Bach wrote them to fit a mold. The Ciaccona sounds like the model from which a mold might be cast.
Perhaps it is wrong to assume that what is natural and flowing is unstructured. That may be a more modern outlook on things. Form and flow aren’t necessarily opposed. Could the structure help the piece flow?
In the past, people thought that what was natural was orderly. In Elizabethan England, people believed in the Great Chain of Being, in which God ruled men who ruled animals. People who practice Islam have great structure to their lives, praying five times per day. These are two examples that come to mind, but there are many other examples of the way humans lead structured lives.
Whether or not we humans choose to discipline ourselves, nature imposes order on our lives. Our days, weeks, months, and years are precisely patterned. Every day has 24 hours, the time it takes the earth to rotate once around its axis. Every year has 365 and 1/4 days, the time it takes the earth to orbit the sun. Our months correspond roughly to orbit of the moon around the earth. The lengths of our days and nights and the characters of our seasons depend on the movement of the sun and the earth.
Perhaps it’s not so surprising that Bach built his Ciaccona on a large and regular framework. The world is filled with structures, hierarchies, and repeating themes, from the planets in the universe, to our seasons, to our sunrises and sunsets, to our generations. Life is a series of variations on a 24-hour theme, each featuring the same sunrise, sunset, and motions of the planets and stars. Unlike Bach, we can’t plan ahead how many variations we are going to write.
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