Catapulting into Classical

A headlong leap into music, history, and composing


Haiku Wednesday: The Great 48

View through a kaleidoscope

The Great 48
Await my attentive ears
And eyes: a wonder:

A stained glass window,
A kaleidoscope of notes
Gliding so smoothly.

Carefully crafted
Interlocking harmonies
Seamlessly progress

From key to key and,
Through light and shadow, we make
A splendid journey.

The Great 48 refers to Bach’s Well-Tempered Clavier, two books of preludes and fugues in all the major and minor keys.

As I continue to work on my own fugue, I gain better understanding (and greater appreciation) for the form.  My plan today is to listen to and read through some Bach fugues.  This is an endeavor that is certain to instill some humility.  It reminds me of the “we’re not worthy!” scene from the movie Wayne’s World.

You can see the first book of preludes and fugues performed by Kimiko Ishizaka at this link.  If you would like to follow a scrolling score, you may do so at this link.  If the fugue has four voices, each is presented on its own staff to make it easier to follow each voice.

The score may be downloaded here.

Here is a page with a wealth of information and references on the Well-Tempered Clavier.

And let’s not forget!

I find myself incapable of leaving without giving you a video of Glenn Gould playing Bach.  Here is Glenn Gould playing the Prelude in B-flat Minor from the Well-Tempered Clavier, Book 2.  Enjoy!


Image attribution:  Image through a kaleidoscope by Hide-sp, [CC-BY-SA-3.0 or CC BY-SA 2.5], via Wikimedia Commons,


Fugue Writing Fun

Today I’d like to share with you a delightful, if impractical, method of fugue writing.  First, here’s the back story.

So I wanted to write a fugue.  And right away, I found out something.

Fugue writing is hard.

First, you have to come up with a good theme, one that matches other music nicely.  Weird intervals will make that difficult.

On the other hand, it can’t be too chord-driven, or you’re likely to end up with pesky parallel fifths, errant intervals whose presence instantly brands you as a rookie.

Fast forward.  Ok, so once you have a subject, its “answer”, a countersubject, and maybe some nice filigree filler, you’re ready to start working with your nice, neat blocks of music.

Then I encountered another problem.

My software doesn’t make it easy to shift around blocks of music.  I was hoping to work that way because playback lets you know instantly when things are really wrong in your layering of lines of music, or when you’re on the right track, but maybe only need to tweak a few things.

And I feared if I wrote it by hand I’d soon be up to my ankles in eraser crumbs and/or vacuuming out the piano.  Or surrounded by tiny slips of paper arranged precariously and Tetris-like on a table, easily disturbed by a slight breeze or curious cat paw.

I was stuck.  How could I move around these blocks of music?

And then it hit me.  Blocks of music.

A fugue model built of LEGO® bricks!

If I put measures of music on the sides of bricks, I could easily shift them around—both horizontally (leaving room for filler) and vertically (getting the right juxtaposition of lines).  Bricks containing the measures of the subject or countersubject could be held together with long, thin bricks to form a single unit.

Now I was onto something.

And, having children, I have enough bricks to accommodate the orchestral score of a Mahler symphony.

I chose 4×2 bricks to accommodate four beats of music per measure; the notes can be lined up nicely on the studs.  I tailored the paper measure size to match the length of the brick, transcribed my music uniformly, scanned it, and made a zillion copies (including blank measures) to tape to the bricks.  Partial and pickup measures, difficult to maneuver in my software, are now (literally) a snap with smaller bricks.

Another advantage that I then recognized was that each voice could be designated by a different brick color, or you could color-code the subject and countersubject.

Snapped together, the notes were now easy to play with, durable, yet super easy to modify.  Like…well, you know.

My grand machination of a fugue (grand machination! to use car terms, I’m not aiming for a Ferrari, but I’d like something grander than a Yugo) is not ready, but to show the principle in action, here is a photo of the beginning of a fugue in Bach’s Magnificat (Sicut locutus est, the actual score and music at this link).  You can see from the photo why the slips of paper were not going to work out.

Sample of fugue writing using LEGO(R) bricks being inspected by a cat

I hope eventually to construct something that is not totally unlike a fugue.

And as long as I don’t step barefoot on measure 38, I think I’ll be ok.


Note: LEGO® is a trademark of the LEGO Group of companies which does not sponsor, authorize or endorse this site.

1 Comment

So You Want To Write a Fugue

P.D.Q.Bach music score with twisted staves.

I have been intrigued by fugues for a long time.  The one that most people have heard is from Bach’s Toccata and Fugue in D Minor, a Halloween staple and the opener in Disney’s original Fantasia movie.

But what is a fugue exactly?  It is a piece of music where different voices echo one another, but with a very specific formulation.  A voice means a melody line, which may be represented by a human voice, an instrument, or one of the melodies played simultaneously on a piano.

The opening passage, the theme of the piece, is called the subject.  For it to be an “official” fugue, the subject must be stated by each voice participating in the fugue.  Typically, the first restatement of the subject (in a different voice), called the answer, is an interval of a fifth higher.  The subject may be followed by a countersubject, a new passage that works well with the subject and will help in building the fugue.

The section where the subject, answer, and any countersubject are stated is called the exposition.  The way in which the voices play off one another is called counterpoint.  Typically, the key will change (sometimes multiple times), which keeps things interesting.

After the exposition, there is a development section.  The subject and countersubject may be restated, probably numerous times, but they don’t have to repeat themselves in the same way each time—otherwise it would be a round or canon (like “Row, row, row your boat”).  Changes will be made to reveal nuances in the musical passage (which sounds fancier than “to play around with it”), or to accommodate harmony in the interweaving of voices (so you don’t get unpleasant clashing of notes).

Finally, the whole fugue may wrap up with a coda or codetta that brings the fugue back to its initial key, but it’s not a necessary component.

Ok, so how do you do it?

Answer: not easily.

To start out, it helps to write a plain, vanilla passage for your subject (and countersubject), because once you start bouncing notes off one another, chaos will ensue if you pick weird intervals.

Chaos, like handing an 8-year-old an alarm clock and a screwdriver.  Bits will be left over; parts may disappear; things will not fit together right.  And it may never work.

That being said, it can be done, and done brilliantly.  Bach makes it look effortless.  His Well-Tempered Clavier presents preludes and fugues in every key, and his Art of Fugue is mind-boggling.  Here is a sample, Contrapunctus 11, with the themes indicated by different shapes.  Beethoven’s Grosse Fuge is a monument (although it was not initially well received).  Brahms caps off his Variations and Fugue on a Theme of G. F. Handel (Op.24) with a wonderful fugue (measure-by-measure analysis here).  And in the 20th century, Paul Hindemith used a fugue in the last movement of his third piano sonata and achieved a thoroughly modern sound.

The fugue is alive and well, though you probably won’t hear it on a top-40 radio station.  That being said, YouTube yields facetious fugues written on themes by Adele and Lady Gaga and more (the Nokia ringtone?!).

But the fugue that tickled me the most was this one by none other than Glenn Gould, titled So You Want To Write a Fugue.  The link is to a performance; you can find a performance with a visual presentation of the words and music here.

See the references for sites where you can find out more about the fugue.


Anatomy of a Fugue, a television program about the fugue and its history by Glenn Gould (really, a whole television program about the fugue)

Anatomy of a Fugue, a detailed written description unrelated to the television program above, from Northern Arizona University

How to Analyze a Fugue

Yale University lecture on the Fugue: Bach, Bizet, and Bernstein

What is a Fugue?

Composing a Fugue from Earlham College


Image attribution:  Schickele, Peter, The Definitive Biography of P.D.Q.Bach.  New York: Random House, 1976, p 149.  Original caption: “An unfinished keyboard piece employing invertible counterpoint.”