PART 3: Video Intro

 

COUNTERPOINT:  The technique of combining two or more melodic lines in a single texture.

 

Sometimes people are a little intimidated by  the word counterpoint. But contrapuntal music is really a kick to listen to because it makes you split your attention several ways.  Imagine yourself seated at your computer writing a letter, while you're answering the phone, and studying for this class. I call this multitasking for the mind. If you can juggle all these things at the same time--and let's face it, we all do this--you’ll be able to follow Baroque counterpoint—and you'll enjoy it alot more!

Let's listen to some examples from the greatest master of counterpoint ever, Johann Sebastian Bach (1685-1750). Bach wrote a set of pieces called Two Part Inventions which are little contrapuntal exercises for keyboard. The two parts in the title refer to your two hands—each hand plays one independent part and each part sounds fine all by itself. Of course when you play them at the same time they sound even better together.

Here is the right hand of the d minor Invention.

Now listen to the left hand of the d minor Invention.

And here's what they sound like when they're put together—you can enjoy the totality of the parts at the same time as you listen to each individual one!

Let's take another example of a Two Part Invention, this one in C Major.  Here is the right hand of the C Major Invention.

Here goes the left hand of the C Major Invention.

Now try listening to the two parts together.

One interesting feature of this invention is the sequence.  When you sequence a passage you repeat it, but at a higher or lower level. Most commonly, a sequence in Baroque music goes through at least two transpositions of the original passage.  Here is just the sequence from the C Major Invention you heard above, but played in slow motion.

If you could listen to the above examples and keep track of each individual voice when they were put together with the rest, CONGRATULATIONS!  Now you're ready for the really heavy stuff!  FUGUE!

 

A  fugue is a piece in which one theme (or more) is used in imitative counterpoint among 3 or more voices.

Listening to a fugue is like attending a very cultivated dinner party. Let's say that you're seated at a beautifully set table, about to dine.  You can expect for the host to set the tone of the dinner conversation, something like, "Did you see the article about the President on the front page of today's newspaper?"  In the fugue this is the main theme being stated by the first voice, and it is called the subject. Then each guest-- each man and woman, high voiced and low voiced-- takes their turn answering with their opinion of the topic.  In fugue, the second entrance of the subject is actually called the answer.  After everyone has had a chance to join in the conversation, the topic of conversation might become slightly diverted or sidetracked momentarily-- in fugue this is called an episode.  An episode is not totally unrelated to the topic at hand-- it's usually made up of motifs from the subject or countersubject, and serves to bring all the voices together to cadence.  Once everyone has entered the conversation, established their "voice" in this manner, and cadenced, we have concluded the first section of the fugue, called the exposition.  Now, of course, when people discuss topics over dinner they don't always agree with each other, do they?  And so we have an analogous situation in fugue: after the subject has been stated, as the next voice enters, you might hear a counter-subject, which is a subject that runs counter to the subject.

As opposed to a Two-Part Invention, fugues can be for 3,4,5, or even 6 voices. Here's the subject only from Bach's G minor Fugue. Composers take great care in fashioning a great fugue theme to make it attention-grabbing, easily memorable, and distinctive so that it will stand out in the fugue texture-- just as a good conversationalist will take care to formulate their thoughts in the most attention-grabbing way also!  Listen also to the counter-subject for this fugue.

Here is the exposition of the G minor Fugue. Listen to the texture very carefully and count up how many voices you hear. When you finish listening to this fugue you can check your answer here. One little note about this excerpt: I played a bit beyond the end of the exposition (about one measure beyond), just so that you could hear a wonderful moment: right after the exposition Bach changes from the minor mode to major mode, making the piece suddenly sound brighter, losing its previous sullen quality.  See if you can notice the difference that this change of mode makes.  It takes place approximately 50 seconds into the example (you can watch the time-counter on the RealPlayer).  At that point, the main theme is transformed from minor into major, and the counter-subject is changed into major as well.

Try listening to the excerpt again and just listen to the top voice (the soprano part) all the way through. Then listen again and just follow the next lowest part. Go back and do the same for the other parts. The more you listen to the excerpt the more you'll hear in it.

Here's another example: the fugue from the Toccata in D Major, by Bach.  This three-voiced fugue is one of my favorites.

Here's another fugue to listen to, in C# Minor.  This one has a very slow-moving subject.  Such a fugue (with a slow-moving subject) is sometimes called a ricercar.  It is just a slight difference in lexicon, however, since a ricercar behaves the same way as a fugue.  If you listen to this fugue carefully you will hear five voices.

Now let me show you one of the most amazing pieces of music I know: The Musical Offering, by Bach. It is nothing short of miraculous and I know that once you've heard it—and especially after you've seen how it was constructed—you'll agree.

But first, there's a story behind the piece. In 1747, three years before he died, Bach was invited to visit his son, Carl Philip Emmanuel Bach, who was a harpsichordist in the employ of King Frederick the Great of Prussia.  The King was an amateur flutist himself, and had extremely cultivated and rather unusual taste in music.  I say "unusual" because at this time in Europe most people had already left the old Baroque style behind and gone on to listening to more "updated" music, such as rococo or a kind of pre-classical style music.  Music of the type that J.S. Bach was writing in 1747 was quite outdated.  Nonetheless, King Frederick had heard about C.P.E. Bach's father and his prodigious skills at counterpoint, so he invited J.S. to visit the court.

The story goes that J.S. travelled to the court and arrived in the evening tired and disheveled.  In those days every visitor had to "sign in" when they entered a major town such as Potsdam; the list of visitors was then forwarded to the King at the end of the day.  C.P.E. Bach tells the story that when the King read the list for the day and saw that J.S. had arrived in town he summoned him immediately to court.  Bach arrived in his travelling clothes, embarrassed and apologetic. None of that seemed to bother Frederick, however, who had him sit down at the keyboards without delay and start to improvise.

At some point Frederick presented Bach with a theme of his own invention-- and asked Bach to improvise a fugue upon it.  Mind you, under normal circumstances to improvise a fugue is well nigh impossible for any mortal.  Much less to improvise it before a King and an audience.  Much less to improvise on an unfamiliar theme.  Much less to improvise on a long, complicated, and rather recalcitrant theme such as the King devised.

But Bach was a maker of musical miracles.  Not only did he pull off the feat but, upon his return home to Leipzig, he composed an entire set of pieces based upon the "Royal Theme," and sent them off to the King with the title, A Musical Offering. Among the many features of A Musical Offering are a set of astounding canons that are based upon the most intellectual feats that a composer has ever constructed in music.

Here is the first canon.  It is notated on one single line of music. As you may know, one can certainly derive a canon from one single line of music ("Row, Row, Row Your Boat" is an example of that technique.) But what Bach does is thrilling: he takes one line of music and has one player read the line forwards and the other read the line backwards!  In this first canon the line is made up of the Royal Theme, but syncopated and later, varied!

Here is the second canon.  This has the Royal Theme in the bottom part (the harpsichord accompaniment) while the two violins above play in canon.

Here is the third canon.  This has the Royal Theme in the top voice while the lower line is made into a canon.  One note, however, about that lower line.  One person must read it forward while the other person reads it upside down!

Was Bach a mathematical genius?  The complexity of Bach's compositions--especially The Musical Offering--have prompted some people to speculate that he might have been a mathematical genius. The book, Godel, Escher, Bach plumbs this subject, making correlations between the mathematician, the artist, and the composer.

Does music have some sort of mysterious connection to mathematics? This is a large area of research now, with much evidence pointing to the positive benefits of musical study. Scientists are especially intrigued by the apparent connection of music and mathematics--kids who take music lessons were found to have higher math scores. There is also specific evidence that music affects the brain: professional musicians were found to have a larger 'corpus callosum' than non-musicians-- the 'corpus callosum' connects the left and right hemispheres of the brain.  Not being a scientist I can only speak anecdotally about these matters, but as a music teacher I have no doubts. Music lessons are definitely good for the brain. Musical training develops memory and concentration, as well as auditory, temporal, sequential, and rhythmic skills. It also teaches perserverance and sensitivity--all of which children use in school and throughout life.  There have been many, many articles written on this subject in magazines as well as scientific journals. One excellent article is from the July 24,2000 issue of Newsweek magazine.

 

There are many more intriguing canons with even more sophisticated "tricks" to them in The Musical Offering-- there is also a very beautiful Trio Sonata.  Definitely worth getting to know.

Finally, there is one last piece I'd like you to listen to and think about.  In the textbook, Kamien says that musical form is usually achieved through variation or contrast.  Listen to the following piece-- the first Prelude from Bach's Well Tempered Clavier and give some thought as to how form is achieved.  This piece is tricky in regard to form because variation and contrast are not particularly evident in it.  Here it is.

Now: after having listened to it, how do you answer the question of form? How was form achieved?  Did you hear any form?  The answers to these questions are subtle and may not be apparent until you listen repeatedly to the piece.  But give these points some thought: first, the phrase lengths are not all even.  Sometimes Bach groups four of the basic units together and sometimes he groups eight of them together. Sometimes he uses sequence to compare the sounds of certain groups. Toward the end he begins to build shape by making a line longer and longer and longer, building tension until the most beautiful harmonies begin to dispel that tension. This prelude is one of the most famous works in the musical repertoire so it pays to listen to it repeatedly.  See if you can begin to pick out a shape in it.  If you have any ideas you'd like to share about it, email me. I'd love to hear what you come up with.

West Indian Pepper Pot Stew-- a favorite dish served at City Tavern in Philadelphia in the 18th century. This dish is still served today at City Tavern in Philadelphia. I can attest to the great quality of this dish as I have made it myself and served it to friends at several 18th Century-themed parties we've hosted.  1 link Italian hot sausage 1/4 lb. corned beef 4 scallions 1 large onion 1 bay leaf 2 sprigs fresh thyme 1 small hot chili, seeded and minced, or hot red pepper flakes 1-1/2 tsp. allspice 1/2 tsp. black peppercorns 6 cups beef stock 2 cups shredded callaloo, spinach, mustard greens or other greens 1 medium carrot, peeled and diced 1/2 lb. yuca, peeled and diced (this is a root) 3/4 cup diced chayote or yellow squash salt to taste =========  1. Brown the sausage. Dice the corned beef and add to sausage and cook a few minutes. Add onion, scallions, bay leaf and thyme, and continue to cook until onion is tender. Stir in hot chili or pepper. 2. In mortar, grine allspice and peppercorns. Add to pot and add stock. Bring to simmer and add greens. Cook for 20 minutes.  3. Add carrot, yuca and squash and cook about 10 minutes more. Taste, adjusting s&p. Remove bay leaf and thyme before serving.

If you counted four voices you heard all the entrances. Now you can return to the Fugue.

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