To complete this fine task I have decided that I should dismantle and rearrange one of my (J.S. Bach) finest fugues! I decided to start with Fugue No. 12 in F Minor, from The Well-Tempered Clavier Book II.

The Fugue is a particularly difficult but beautiful form of contapuntal composition. A fugue is sort of like a round or a cannon, but with a lot more restrictions. One voice starts the piece and then other voices enter one after another. The difference is that the voices in fugues enter on higher and lower pitches. All fugues are built upon a small musical section called the Subject.

The subject for Fugue No. 12 (WTC II) looks like this


Fugues start with what is called the Exposition. In the exposition the subject being played in a single voice in the tonic key (F Minor For Us). After the statement of the subject, a second voice enters with the subject transposed to the key of the dominant. When the subject is re-introduced in a different key than it was originally written, it is called the Answer. While the Answer is playing, the voice that had played the Subject goes on to develop other melodic material.

Some fugues have a Counter Subject that plays along with the answer, this is like another small musical idea that is repeated throughout the piece. The fugue I chose doesn't use a counter subject, so don't worry about that.

I know it sounds very confusing, but it really isnt that bad. Take a look at the structure of this fugue. You can see from the picture that this Fugue is written for 3 voices (three notes on a keyboard, not actual voices) and the Subject is introduced a total of 9 times (The Pink Boxes).


Lets look at that first section on the actual score

(*Oops there is a typo, the Answer is down a 4th from the original, not a 5th)

The sections circled in green are the subject. Originally played starting on C in the upper voice, then introduced on F in the middle voice, and then finally C again in the lower voice. I decided to color code each voice (1 = Blue, 2 = Red, 3 = Orange). This will help clarify exactly what is going on as I rearrange/swap voices.

Also, each place the subject enters in the score I have placed a rehersal mark (The big A,B,C,D... lettters in the score) to make it easier to see what is going on.
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The overall goal of a Fugue is to give a thorough exposition of the melodic possibilities of the subject. I find fugues especially fascinating because of the difficulty that is inherent in writing one musical idea to be used in all the voices. It needs to be both melodically engaging and harmonically well defined. It needs to be used at the tonic and at the dominant so there are strict rules on the types of interval leaps that can be employed. Its rhythm needs to start out simple enough to be embelished in an interesting way during the other parts of the fuge. WHAT A HASSLE! Bach is the master.

After the theme has been introduced in each voice the next section of the Fugue begins, the first Episode. This is where the material is developed and jostled around in fun ways. After that comes the Middle Entries (When the subject comes back in the middle), then followed by more episodes. This cycle of entries and episodes continues until the composer gets tired of pulling out his hair trying to make it work. It is like the most frustrating logic/jugsaw puzzle you have ever seen putting a fugue together. Since the lines chase each other around across all the voices its like a pair of handcuffs on what you can and can't do. And all the pieces need to be written so that they can be inverted and still sound good.

I wanted to try to share my appreciation for Bach's talent by ripping this piece apart and rearranging it in different ways. Because surprisingly, as impossible as it may sound, you can jumble up all the parts and it still sounds good. Its hard enough to write good music, but good music that can be played upsidown or inside out? No Way. For Bach only. (TANGENT!: In fact Bach's compositional precision and consistency is so impressive that you can actually use Calculus to create integrals of the lines and harmonic movement of many of his pieces)

Now might be a good time to give it a listen. Lets check out Listening Example #1 (For those interested, the scores for all examples are available in the image section at the end)

Example #1



Sounds Pretty Good Huh? Well, maby you don't think so, ...But I like it!

Once I got this bad boy into my computer I decided that I would slowly start rearranging it til we ended up with something totally different.

The first thing that I thought I would do is to flip voices one and three (Blue/Orange). This reverses the order of entry for the voices in the exposition and essentially turns the melody line into the bass line, and vice versa. The inner voice remains unchanged. The results are in Listening Example #2. Isn't it amazing that it all works so well when you change what is on top and what is on bottom?!? The subject now initially enters in the lower voice.

Example #2


Still sounds good!
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For the next level of take apart I decided to divide the piece into sections based on the subject entries. Then I utilized chance operations (Thanks John Cage!) to randomly determine the ordering of the voices through each section.
I took out three playing cards and chose them at random for each section.



The results I got on my chance operations were as follows:



This is where the whole exercise got a bit more artistic. Using the random ordering I went in and started moving around the voices. I used my own discretion about which octave to place the parts in and on which beat to exchange the voices to preserve the subject entry and clearly as possible. I tried to remain as close as seemed reasonable to the total range of the original piece and the spacing between the original voice positions. It worked out very fluidly, as can be expected, since i retained the integrity of the original section lengths.
Check it out in Listening Example #3.

Example #3


Fun Fun Fun! "It's can't be that hard to write music that you can play in any voice?!?" Um....Sure.
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I was very pleased with the results from my chance operations so I decided to extend the technique further. For the next layer of deconstruction I decided to use the same methods, but I employed randomization to each individual meassure.


Piecing the meassures together got a little bit harder. There was lots of harmonic stagnation that resulted. I used my own judgement as to whether or not the voices should be mostly ascending or descending, I tried to avoid consective large leaps in the same direction and voice crossing to remain idiomatically consistent with the original.

This resulted in Listening Example #4. Certainly it continues to get more distant from the harmonies of the original, but it maintains its integrity well under the circumstances.

Example #4


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I thought I wanted to do one more after this, I was dabbling with the idea of a remix by adding some sampled beats, or cutting up all of the meassures and placing them completely at random. But honestly I shyed away from these ideas because I estimated they would take way too long. Instead I thought that one more chance operation could thoroughly break this piece into unrecognizable parts. Starting with the score for Example #4 I decided to flip a coin for each meassure in each voice. If it came up heads I left it alone, if it came up tails I reversed the order of all the notes in the meassure (this is called Retrograde).

In order to show the meassures that underwent a retrograde transformation I used similar colors. Blue -> Green, Red -> Pink, Orange -> Yellow

After a couple hundred coin flips I ended up with Listening Example #5. Finally the original subject is nearly unrecognizable, this sounds almost like a totally new piece. The random switching introduces a couple new rhythms into the piece that give it a very different feeling. Especially the switching of phrases consisting of one eighth followed by two sixteenths. This rhythm feels much more rushed and unsettling. It changes the character greatly. This still has obvious stylistic nods to music of Bach's time, but this clearly would/could not have been written in that time. (Only Satan would make you write music like this in the late 17th century, and that could be dangerous buisness!!)

Example #5

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I had a blast doing this! I hope you have enjoyed. I think there will be more Classical music Frankenstein-ery in my future, just for fun.

Besides when else am I gonna use my powdered wig?

"I Got Duckets In The Bank, Whatchu Think About That!?" - Bach