Catapulting into Classical

A headlong leap into music, history, and composing

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Molecular Bach

Portrait of Bach inside the ring of a caffeine molecule

In my last post, I gave you a quick glance at a problem I was having with a Bach piece–a furry problem.

After the cat stopped “helping” me* with Bach’s Invention No. 1, I decided to examine the work in closer (and less fuzzy) detail.  I decided to go molecular.

Let’s look at some of the printed music.

If you’re very good at reading music, you can see which notes sound with which other ones, and how they interact with each other.  You can see patterns in the music.

But for some reason I was having a hard time.  And I suspected that closer inspection would yield more information that I was picking up trying to play it as written.  So I decided to take an extreme close-up approach.

I took each measure, and expanded it to an entire line of music paper.  I then broke up each line into sixteen segments, to accommodate the sixteenth notes in the music.  Each little segment contained a single note (except where there are ornaments, like trills and mordents).  Then I transcribed the invention (thankfully, it’s only 22 measures).

When you get down to that molecular level, and you’re transcribing each note, patterns appear much more clearly.  It feels a little like examining a picture at the pixel level (and kind of looks like it), but it reveals so much.  It turns out that nearly every measure of the invention, in both the bass and treble clefs, uses one of three patterns: (1) four or more notes in an ascending or descending scale (blue); (2) movement by thirds in a scale-like way, up or down (for example, C-E-D-F, two steps forward, one step back, repeat; red); (3) eighth notes in intervals greater than a third (green).  And the patterns repeat, over and over.  First, he goes up (1), then down (2); or down (1) and then up (2).  The simplicity of the movement was shocking.  When you think Bach, you think complicated.  You think of this flurry of intricate notes.  You don’t think of individual snowflakes.

But no.  It goes up as a scale; it goes down by thirds.  Again. And again.  Look, and enjoy the many smiley faces formed by linking the segments to indicate eighth notes.

Bach's Invention 1 with patterns indicated

Now, Bach might be looking down at me and saying, “Well of course it’s simple.  I wrote it for my son Wilhelm Friedemann to learn how to play.  And it’s only a a two-part invention, not three, or a four-part fugue.”

But that’s the genius of Bach.  With the utmost simplicity, he builds beauty.  He takes bricks and makes cathedrals.  He does the same kind of thing in the Magnificat, in Omnes Generationes, making the simple spectacular.  Bach’s music can be enjoyed without understanding the details involved in the composition, but once you see the patterns, once you can say, “I see what you did there”, you can appreciate it even more.

Here is Invention No. 1.

Here is Invention No 1 played by five different pianists:  Walter Gieseking, Rosalyn Tureck, James Friskin, Tatiana Nikolayeva, and Glenn Gould.


*the cat is also very helpful with conference calls and intricate computer machinations.  Thankfully, she is not as helpful as Borodin’s cats.


  1. Here’s the sheet music:

Image attribution:  Caffeine molecule by Mstroeck at the English language Wikipedia [GFDL ( or CC-BY-SA-3.0 (], via Wikimedia Commons,

Bach portrait by Elias Gottlob Haussmann [Public domain], via Wikimedia Commons,

Seems appropriate to use the caffeine molecule for the guy who wrote the Coffee Cantata.



Haiku Wednesday: Bach’s Ukulele-Piano Duet

Bach in Hawaiian shirt photobombs picture of the Thomaskirche in Leipzig

Bach photobombs tourist’s picture of the Thomaskirche in Leipzig

What would Bach do if
He had a ukulele?
I picture the scene:

We see him scowling,
As he does in his portraits,
Unwrapping a box.

Carefully, he lifts
The lid, and peering inside,
Smiles, then roars, laughing.

The kids all gather
As he gleefully extracts
His new tiny lute.

And, of course, he then
Plays it instantly and well,
Playing his own tune.

A kid brings a bow
As he sees what it can do,
Thinking what he’ll do.

And as the kids leave,
He sits at his desk. With quill
In hand, he begins…

A friend of mine got a ukulele for Christmas.  We were talking about the availability of music, and joking, said there were no ukulele and piano duets.

We were picturing a ukulele trying to contend with a concert grand, figuring that, short of amplifying the ukulele or alternating solos, it would be an exercise in futility.  A clavichord, maybe, they were known for being whisper soft.  But a piano?  It’s a classic(al) David and Goliath story.

Of course, I couldn’t leave it alone.

The easiest way to make it happen was to borrow from Bach.  So I borrowed the Minuet in G Major (BWV Anh. 114) from the Notebook for Anna Magdalena Bach.  As it turns out, it is now believed that Bach borrowed this little ditty from Christian Petzold.

Those of a certain age will remember hearing it popularized as the song “How Gentle is the Rain?” or “A Lover’s Concerto”.  I transposed it from G major to C major to make it easier for the ukulele to play.  Then, I tried to figure out how to integrate a piano without overwhelming the ukulele, while allowing them each to have their moments to shine.

No matter what, the pianist will need to use restraint (and the soft pedal).  A piano, even the subtlest piano, can easily overpower the ukulele.  But balance can be achieved, and it’s fun!

Here’s what it sounds like.  Warning: if you use the link rather than the player displayed on this page, you may hear unrelated music afterward.  Can’t prevent it (Soundcloud!).  Hit the pause button (at the bottom of the Soundcloud page).

Here’s what it looks like (below).  Click the image to magnify, or click the following link to view/download/print the Minuet for ukulele and piano as a PDF file.

Sheet music, Minuet for Ukulele and Piano page 1Minuet for ukulele and piano-2

If you’re a ukulele player (ukulelist?), give it a try and let me know how it turns out!


Image attribution: Photograph of Leipzig Thomaskirche by Tuxyso / Wikimedia Commons, via Wikimedia Commons,  Vintage Hawaiian shirt by Omaopio (Own work) [Public domain], via Wikimedia Commons, Portrait of Bach by Elias Gottlob Haussmann [Public domain], via Wikimedia Commons,


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.

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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.”


Catapulting with a Saxophone

flying stick figure playing a saxophone

Sometimes you have to just do things, not knowing for sure where you’ll end up.* Never blogged?  Never fear!  Never wrote music? Go ahead and try! Never played an instrument?  What’s stopping you?

So what happens when you combine that premise of Catapulting into Classical, the saxophone from Spring Cleaning, and Birdsong?

Surprisingly, not chaos…or not much anyway.  But let me explain.

I was faced with a dilemma with my composition Birdsong.  I heard it as a flute and piano duo.  But I don’t play flute.  I don’t own a flute. I had wanted to use the piece for an upcoming gathering of fellow piano students, but it would be too late to foist this on an unsuspecting flute-player. I tried turning it into a piano reduction, and wasn’t happy with the results.  As I was trying to find a solution, I cast my eyes on the saxophone.  Replaying the music in my head, I realized it would work.

It would, but would I?  I hadn’t touched it in…decades.

Time to catapult.

What little I knew, I remembered.

What little I knew needed some tweaking.

What I had learned, decades earlier, was what one might call empirical saxophone.  I had no access to a teacher.  So, I pressed keys, blew, and matched the sound with a note on a keyboard.

Concert pitch is when the note on a page matches the pitch that is played.   C means C.

Except it doesn’t when you’re playing an E-flat alto saxophone.  In alto sax music, when you see a C on the music staff, you’re really playing an E-flat.  The saxophone is a transposing instrument.  This system makes fingering consistent across entire families of instruments.

If you’re a human tenor, you are also a transposing instrument sometimes–if your music is written on a treble clef with a little 8 under it, you sing it an octave lower than it is written.

Of course, back then, it didn’t matter—I didn’t have access to alto sax music either, so I was playing the music I had around (music intended for a keyboard) or by ear.  So concert pitch worked.

But now it was time to learn things properly.

In this case, decades of neglect worked in my favor**, and, once I understood that a particular fingering yielded a pitch notated as Y not X***, it wasn’t too hard to learn the fingering for my piece, which was now written in the correct notation for the instrument.

Now, it’s just the small matter of technique (small meaning huge).  My first new empirical results were that the cat really doesn’t like all this tootle-ing****, and the vibrations continuously set off my doorbell, making it sound like a cast of thousands is beating a path to my doorstep on account of my saxophone playing.

At this point, not likely, unless they’re an angry mob with cotton stuffed in their ears carrying torches and pitchforks.

Nonetheless, I persevere.  I’m improving.  And it’s fun!

And that’s exactly the point.

Keep catapulting, my friends!


And now, Charlie Parker and Dizzy Gillespie show how it’s really done.


*Do not literally catapult with a saxophone.  And if you’re thinking of doing something, and one of the places you might end up is the hospital, please, DO NOT just do it.

**Instrument-learning kids: decades of neglect is a bad thing.  Don’t try this at home.

***Not literally Y and X; there is no Y and X in saxophone music.  It’s not that different.

****The cat wasn’t happy about George Crumb’s Black Angels either (audio here; startle warning).  I never saw her run that fast before.

Image attribution: Flying saxophone guy by C. Gallant, 2016.

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Haiku Wednesday: Microcomposing—15 Second Harp

Painting of angel with harp

Haiku, Quartweet, and now the
15 Second Harp

Harps look complicated.

And that is even before you find out there are seven pedals in the back to raise and lower the pitch of the notes.

Writing for the harp seems complicated.  How do you know it will work, that is, be playable, if you don’t play the harp yourself?

Harpist Olivia Jageurs has come up with a solution.

Jageurs has set up a website called  She also posed a challenge:  she would create a video of any notated harp music that anyone composed and submitted, and post the video the next day.  However, the music can only be 15 seconds long (Instagram limit).

This is brilliant!  You can see the submissions on the website, Instagram, Facebook, and Twitter.  Jageurs comments on the submissions, explaining what works well, which components might cause difficulties, and why.

It has been so successful, she has had to limit the number of recordings that would be produced per day, but all submissions in the queue will be recorded.

Add this to the quartweet (the 140-note string quartet) as an achievable and accessible way to encourage composing.

Ready to try but need to know how a harp works?  Jageurs has also posted brief videos on the range of the harp, how the pedals work, and how chords and glissandi are played.  Useful articles on composing for the harp may also be found here, here, and here.

If you submit a harp composition, let us know!  I’m sure everyone would love to hear it.