Here’s a little break from all the coding/startup/development/business stuff we focus on so often at Dublin. For this post, it’s all about music. More specifically, it’s about J.S. Bach and fugues.

For those that aren’t familiar, a fugue is composition style developed in the Middle Ages/Renaissance/Baroque era revolving around counterpoint. Generally, these pieces have two or more voices and are built on two key components: a subject and an answer.

To make it easier to understand, here’s an example of a fugue (Fugue No. 2 in C Minor WTC Book 1) with each voice highlighted as well a link to a rendition by Glenn Gould, a pianist well known for his interpretations of Bach.

music

Now, I realize that not everyone can read music, so, if you can read music, follow along as you listen to the video and listen for the call and response pattern. If you can’t, pay particular attention to the single voice melody from the 0:00-0:05 of the video (this is the subject), and listen to how the other voices respond and react to that initial theme.

In this particular piece, there are three voices (the bass, the alto, and the soprano) which trade the subject. As you can imagine, to perform a fugue, you either need an instrument that can play many voices at the same time (the piano is a good example) or you need a group of instruments/voices, like a choir.

Now that you understand the complexity of a fugue. I’m going to show you my favorite one and explain why it’s so impressive.

Here’s a fugue from Suite No. 5 of the Bach Cello Suites (and a rendition of it by Mstislav Rostropovich):

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The first thing you might notice from the sheet music is how there is only voice at a time. But you just told me you need multiple voices! How can it be a fugue there’s only one voice?

Well, the simple answer is because Bach is a genius and managed to integrate four different voices into a single line fugue.

To provide some sort of analysis on how he fit four voices in a single line, I’ve provided some highlighting: blue is the alto subject, red is the soprano answer, green is the tenor subject, and yellow is the bass answer. By placing the subject and answer in different pitch ranges, Bach simulates voicing characteristic of a multi-line fugue with just one voice.

Pretty clever, Bach. Pretty freaking clever.

  • Walter

P.S. If you guys are interested, here’s my attempt at counterpoint