Prof: Let us begin then
with the subject of today,
which is the fugue.
 
Every educated person should
know what a fugue is.
Why?
 
Because it's an intellectual
model, an intellectual paradigm
that surfaces in a number of
disciplines--for example,
in poetry, oddly.
 
If you've ever peeked at
Thomas--T.S. Eliot's "The
Four Quartets,"
the structure of the fugue is
referenced there frequently.
 
We could go to literature--a
novel written about the same
time, Aldous Huxley's Point
Counter Point.
It's framed in the shape of a
fugue.
We could go to geology.
 
Geologists occasionally will
say, "This particular
crystal has a fugue-like
structure to it."
Turning to painting,
there are painters of the
twentieth century.
 
I can name at least three,
Franz Kupka,
Henry Valensi,
and Josef Albers,
who used to be the dean of our
own Yale School of Art and
Architecture.
 
They all painted fugues and we
will be looking at Alber's
fugue--
which actually happens to be in
your textbook--
when we come to section this
week, so be sure to bring your
textbooks to section this week
'cause we'll--
we will be using them.
I'm interested in the fugue
also because of this book,
Douglas Hofstadter's Godel,
Escher, Bach.
Oh, my. That's heavy.
 
My--mine--I didn't bring in my
copy.
This is the Bass copy that
Lynda was kind enough to pull
over.
 
Mine is a paperback.
 
It's not this heavy,
but in a way this is
indicative, because it's heavy
reading.
Anybody ever peeked at this
book and any other--good.
Is it Adam?
 
Student: Yeah.
 
Prof: Yeah.
 
Adam, what course did you read
this in?
Student: It was
recommended by a friend.
Prof: Recommended by a
friend.
I can follow about the first
twenty-five or thirty pages or
so.
 
Then when it gets to the math
it really gets over my head,
but what it is is an attempt to
use the fugue as a way of
bringing a common mode of
understanding to the visual
arts,
to mathematics and to music.
The musician that is
foregrounded here,
of course, is J.S. Bach,
the master of the fugue.
So we want to know about how
fugues operate,
so let's take a look at the
specifics here.
The term "fugue"
actually comes from an old
Latin word,
"fuga,"
which means "flight"
or "to fly,"
so in a fugue what you get is
one voice going ahead,
leading ahead,
and another voice following it.
Now I just used the term
"voice"
there.
 
Fugues can be written for
actual voices sounding voices or
they can be written for
instruments such as the violin
or the cello--individual lines.
 
They can even be written for
instruments that can play
several lines or several parts
at once.
The piano can do that.
 
The organ can do that.
 
Even the guitar and
occasionally the violin will be
asked to do that.
 
Fugues have been written for as
few as two voices.
Yes, you could have a two-voice
fugue--
up to as many as thirty-two
voices--
and they can be,
as mentioned,
written for--
and they are best,
perhaps, performed on--
these keyboard instruments that
have the capacity to play many
lines,
many parts, many voices at once.
 
The greatest collection of
fugues,
that you may have bumped into,
heard about or at least heard
the term,
is this collection of preludes
and fugues by J.S. Bach called
"The Well-Tempered
Clavier."
 
First of all, what's a prelude?
 
It's just a warm-up piece,
>
to just sort of get relaxed.
 
You get to see your fingers,
get a feel of the keyboard or
the--
of the lute or whatever it
might happen to may be--
a prelude, a pre play,
a warm-up, and then we go on to
the meat of the issue,
which is the fugue.
 
Now why is this called
"The Well-Tempered
Clavier"?
 
Anybody know?
 
Anybody have--that's an odd
term.
"Clavier"
just means
"keyboard,"
the well-tuned
"keyboard."
 
Thoughts there?
 
Well, what was going on in
Bach's day is that they didn't
have a keyboard that--
>
they didn't have a tuning
system in which all of the
pitches were exactly a half step
apart.
Some were slightly
>
closer together,
and then others farther apart.
And the key of >
C actually had a slightly
different sound than the key of
D, >
 
and it's only in the eighteenth
and nineteenth century that we
gradually shifted from an
unequal keyboard to an equally
tuned keyboard.
 
So Bach is kind of part of this
transition to the equal-tuned
keyboard.
 
He was getting close to the
equal temperament of the modern
keyboard and that's why he
called it the well-tuned
keyboard,
and it--by tuning it this way,
it allows you to modulate to
all keys,
and that's what he did in this
collection.
He wrote a--two books,
one in seventeen- about 1722,
when he was in Cöthen and
another about 1742,
when he was in Leipzig.
 
And in each of these books we
have a total of twenty-four
preludes and fugues:
one, the prelude and fugue in C
major, >
one prelude and fugue in C
minor, <<plays
piano>>
 
one prelude and fugue in
C-sharp major,
>
 
and one prelude and fugue in
C-sharp minor <<plays
piano>>
 
and so on it goes,
all the way up the keyboard in
that fashion--two books of
those.
And this is kind of standard
fodder for those that want to
become professional musicians.
 
Okay.
 
So that's what that is about,
"The Well-Tempered
Clavier."
 
We've been referencing Bach
here and nobody,
of course, wrote better fugues
than J.S. Bach.
Some continued.
 
Some continued to write fugues.
 
Mozart wrote some fugues,
Haydn wrote some fugues,
Beethoven wrote some fugues and
so on,
and even into the twentieth
century we have a few composers:
Paul Hindemith,
used to teach at Yale,
Dmitri Shostakovich.
 
They wrote fugues,
but generally speaking the
fugue has its heyday in the
Baroque period,
roughly sixteen hundred to
seventeen fifty,
the heyday of Bach and Handel.
 
How do fugues work?
 
Well, they start out--as
mentioned--with one voice
leading forward and then another
voice imitates that voice
exactly.
 
Now if that following
voice--here's a question.
If that following voice
imitated the leader exactly from
beginning to end,
what would we have?
Hm?
 
Student: A round.
 
Prof: A round.
 
Okay.
 
Good.
 
That's what we would have,
a round.
Or we could call--use the
fancier music word,
a "canon."
 
Canon, round--the same thing,
one voice imitating the other
exactly from beginning to end.
 
But in a fugue what happens is
after the main idea--
which we'll be calling the
"subject"--
the main idea is stated,
then the parts go their
independent ways generating
counterpoint,
but they're not exact;
they're not precise
duplications of the rhythms and
the pitches of the leaders.
So what we could do would be to
visualize this in a sort of
crude way up here.
 
We have a leader and then a
follower.
And the follower duplicates the
main idea, which we're going to
call the subject,
for a period of time,
but then it kind of breaks off.
 
So voices will come in and
duplicate a certain amount of
material and then break off and
go their own way.
So that's a good way of
thinking of the beginning of a
fugue, which we will call the
"exposition."
I'll come back to that point in
a moment.
Notice here I've put a
little--silly little tree up
here.
 
We could say that we have the
genus polyphony here and we've
got monophonic texture,
homophonic texture and
polyphonic texture.
 
So within polyphonic texture we
have non-imitative texture and
then a stream of imitative
polyphony and then two forms of
imitative polyphony,
rather strict--exactly
strict--imitative polyphony,
the canon, and less strict
imitative polyphony--
the fugue.
Okay?
 
Questions about that so far?
 
All right.
 
Let's go back to the beginning
of the fugue.
We have this opening melody,
the distinctive part of it,
which we're going to call the
subject.
That's just what we call the
melody in a fugue,
the subject.
 
And the way this works is in a
fugue each of the voices in turn
will come in with that subject.
 
One will start out,
then another will come in,
then another will come in.
 
After all of the voices are in,
we're at the end of what we
call the exposition of the
fugue.
Now we have had the term
"exposition"
before and where was that?
 
Student:
>
Prof: Over there,
Elizabeth.
I hear you.
 
Student: --sonata form?
 
Prof: Yeah,
sonata form,
sonata-allegro form,
so we--and what do we mean by
"exposition"
there?
Well, it's a chance where you
present all of the--all the
themes, and we talked about
first theme and then second
theme and closing theme.
 
Well, here in a fugue we have
just one theme but everybody's
going to get a chance to present
it,
and after everyone has a chance
to present it--
every voice has a chance to
present it--
then we're finished with the
exposition;
all the voices have exposed the
theme in their range.
After that we go to what's
called the "episode"
of a fugue.
 
What happens in an episode?
 
Well, usually it modulates key
and the vehicle through
composers frequently modulate is
melodic sequence,
either up or down.
 
You can kind of move around by
using sequence.
You can get to different places
by using sequence.
So it tends to be contrapuntal
because it's using little
motives from the theme.
 
It modulates,
moves around a lot,
goes to different keys,
sounds a bit unsettled.
If you were to think back on
sonata-allegro form and try to
find an analog for
sonata-allegro form in the fugue
episode, what would it be?
 
What is the episode of the
fugue like in sonata-allegro
form?
 
Roger.
 
Student: The development?
 
Prof: Exactly--the
development section.
So these episodes in a fugue
are sort of mini development
sections,
so visualize if you will--we've
started out here with the
exposition,
in which all voices present the
subject.
Then you have this kind of free
period in which the motive out
of the subject is played with,
developed, moved around,
different pitches.
 
Then the subject will come back
in a new key because we've
modulated in the episode,
subject in just one voice,
new key,
then another episode in which
there's modulation,
more counterpoint,
more movement;
another statement of the
subject in a new key;
another episode;
another statement of the
subject, and on it goes until--
oh, we run out of energy
usually about--
after four or five minutes or
so, at which point the composer
will bring the subject back--
maybe in the bass or in the
soprano in a very prominent
range in the tonic key--
and we have the sense,
"oh,
this is a very solid moment;
yes, this fugue is ending."
And maybe they'll throw upon
one or--throw one or two chords
on the end but that's it.
 
So it's a complex form,
but maybe not quite as complex
as sonata-allegro form.
 
What's a definition then?
 
If you're taking notes there,
what's a definition of a fugue?
Well, I wrote a definition of a
fugue and I will read the
definition out of the textbook.
 
Students don't like this,
I've found, if you read out of
a textbook.
 
But I ought to be able to do
this since I wrote the textbook.
Okay?
 
So I'm going to read a good
definition of a fugue here.
Definition of the fugue:
A composition for two,
three or four parts played or
sung by voices or instruments
which begins with a presentation
of a subject in imitation in
each part.
 
The episode--excuse me.
 
The exposition continues with
modulating passages of free
counterpoint--
the episodes--and further
appearances of the subject,
and ends with a strong
affirmation of the tonic key.
 
Well, you can't write all that
down, but if you want to just
put in your notes:
For definition of fugue,
see page 144 of the text.
 
Fortunately,
as I say, it's easier to hear
and look at fugues than it is to
define them.
All right.
 
Now today we're going to do
something different.
It's the only day in our course
where we're actually going to
look at music.
 
Okay?
 
We've handed out music for
you--an entire piece,
an entire fugue by J.S. Bach
here, and ideally,
I guess, we'd be in a seminar
format and we'd all be standing
around the piano here.
 
So my first question for you is
for how many voices is this
fugue written?
 
Look at just the first page and
look vertically and see what's
the maximum number of pitches
you have sounding simultaneously
at any one moment.
 
Caroline, is it?
 
Student: Three?
 
Prof: Three. Okay?
 
Yeah, we have three.
 
If you look through,
there are--sometimes at the
very beginning there's just one
voice and then there are two
voices and then the three
voices,
three lines.
 
But it never gets to be more
than three lines.
So we have our exposition here
and it consists of three
statements of the subject.
 
We're going to call these three
voices, or lines,
the alto, >
the soprano,
>
and the bass,
>
which comes in in bar seven
there.
So here's a little bit of the
beginning of this.
>
 
Okay.
 
So that's our exposition,
because each of the voices,
alto, soprano and bass,
has come in and presented the
subject.
 
Now we have bars nine and ten
here.
>
 
What's that if I just go
>?
Jerry, what's that?
 
Student:
>
Prof: It's a melodic
sequence, and which direction is
it going?
 
Up or down?
 
Well, that's maybe harder than
you think.
>
 
Generally going down,
not because the line is going
down, but we're starting
>
each time on a successively
lower pitch, and this sequence
takes us >.
So we've started in this kind
of tonality <<plays
piano>>
 
which is minor,
but now by the time we've
gotten to bar ten and eleven
particularly <<plays
piano>>
 
he's modulated.
 
So that's what our little
episode was in bars nine and ten
there.
 
It allowed us to move from a
minor key to a major key.
And now the subject comes back
in and, as you can see,
what voice is it in there?
 
What voice is the subject in
bar eleven?
Pretty straightforward.
 
Somebody yell it out.
 
Student: Soprano.
 
Prof: Soprano.
 
Okay, so here--heads up on the
soprano.
>
 
So there we are,
a nice statement of the theme
in the major in the soprano.
 
>
 
What happened in that little
episode?
We were here >
and now we're here,
>
modulated again to minor,
and there in bar fifteen,
where is the subject?
 
>
 
Which bar?
 
Chris.
 
Student: Alto?
 
Prof: Alto part.
 
Good.
 
Thanks.
 
So there it is in the alto part.
 
That's an interesting moment
there because we've got a
three-voice fugue,
and how many hands does the
performer have?
 
Obviously two,
so at some moments these hands
are going to have to share a
subject, and that's what happens
in that voice.
 
When you play this--take a look
there, the very last measure of
that page.
 
It must be fifteen.
 
>
 
It starts out--my left hand is
playing here <<plays
piano>>
 
and then the left hand has to
go down and pick up the
counterpoint in the bass and the
right hand takes over that
subject,
>
but it's the job of the pianist
there who--
or the keyboardist,
whoever is playing it--
to really lean on the inside of
your hand there because when
you'd normally play these
instruments,
there's a tendency--and I'm
sure Santana,
who is a far better keyboardist
than I,
will confirm this--there's a
tendency to roll to either side.
It's easier to play bass and
soprano.
What's hard to do is to get
those inner voices so the
keyboard player has to
>
and then >
so you can really hear that.
 
If you didn't hear it,
then that wasn't a good
performance.
 
All right.
 
Now that takes us across the
page there.
We're now back in >
a minor key.
 
This is bar sixteen and
seventeen, and in bars
seventeen, eighteen,
nineteen, the beginning of
twenty, we have an interesting
moment.
It's called invertible
counterpoint.
What do we mean by that?
 
Well, he has a motive
>
and we're going to call that
motive A, and he has another
motive, motive B.
 
>
 
So there is B in the alto,
A in the bass,
and together they sound sort of
like this.
>
 
Okay? Cool.
 
Now the next three bars.
 
What happens?
 
Well, he takes B >
and so he takes B and puts that
below A.
He's switching the positions
here.
A is now >.
Both of these motives are
coming up in rising sequence.
So let's go back to the
beginning of seventeen there and
we'll listen to the switch.
 
>
 
All right.
 
So that goes by very quickly.
 
Right?
 
How long do you think it took
Bach to figure that out?
I don't know.
 
He's a very good
contrapuntalist,
maybe "boom,"
like that.
I'd have to sit there--Santana,
how long would it take you to
figure out some invertible
counterpoint that you could
think of one melody,
think up another melody that
would be a harmony against it,
but yet you could flip the two
and it would still sound pretty
darn good?
It'd take a long time to kind
of work that out.
So that's what's kind of neat
about fugue.
There's all these intricacies
embedded in them that almost
sail by the general listener
unless we happen to have the
music right in front of us and
can dwell on them.
All right.
 
So that takes us over now to
bar twenty, where we are here
back, I guess,
>
in our tonic key of C minor,
and the theme is up in the
soprano >
and then one final statement in
the soprano <<plays
piano>>
 
--a couple of interesting
points there.
When we concluded this piece we
had this sound <<plays
piano>>.
 
What's a little bit surprising
about that?
We're ending a piece that's
called the Fugue Number Two in C
Minor.
 
We are ending here with
>.
Does that sound like a minor
chord again?
No, no. A major chord.
 
All right. So he's changed it.
 
This is a standard
gamut--gambit from the late
sixteenth right through the
eighteenth century-- last chord.
They didn't like to end pieces
in minor.
Maybe it was too depressing or
whatever.
>
 
Oh, don't want to do that,
so >
>
 
with the major third up there
above.
That's called the Picardy
third, maybe from the Old French
word picart,
which means sort of sharp or
pointed.
 
So we have a pointed ending
there.
We have a major ending.
 
Here's another issue when
we're--since we're on the topic
of points and that's called a
pedal point.
What was J.S. Bach known as
in his day?
Was he known as a great
composer?
What was he known as?
 
How did he earn--basically,
how did he earn his living?
Student: He played--
Prof: He played
the--you're getting warm.
 
Yeah?
 
Student: Is it organ?
 
Prof: He played the
organ.
He was the great organ virtuoso
of his day, and I think at the
end of this particular fugue
here, it's interesting.
He just has this line sit there.
 
>
 
Okay.
 
On the organ that would just be
fine and dandy because you'd put
your foot down there on that low
C >
>
 
and that tonic note would
continue to hold,
but if you were writing this
for the clavichord or the
harpsichord or the piano,
what happens to that sound once
you hit it?
 
It dies away.
 
I think in the end of this
piece here Bach had the sound of
the organ .
 
He didn't really--he wasn't
thinking "gee,
if this is really for a
harpsichord or something,
I'd better write this like
this-- <<plays
piano>>
 
so we get a nice,
strong tonic sound at the
end."
 
He may have had the sound of
the organ there in his ear,
but perhaps the important point
here is this idea of a pedal
point 'cause we've actually even
talked about that before in the
Johannes Brahms Variations on
a Theme of Haydn that was
performed Saturday night.
 
Pedal point is what?
 
Anybody who can define pedal
point for us?
Hm?
 
Well, what goes on?
 
It's pretty simple.
 
Roger.
 
Student: The bass holds
a note >
Prof: Yeah.
 
The bass holds a note and
basically you're just kind of
running over top of one,
possibly two harmonies up above
it, but it all sounds consonant.
 
So just be sure of the idea of
one note usually in the bass
just holding,
holding, holding for a long
period of time.
 
 
 
Okay.
 
Any questions about that fugue
by J.S. Bach?
Anybody want to ask anything
about that?
 
 
Marcus, that works for you?
 
Ugonna, okay?
 
Thaddeus, no questions?
 
Frederick.
 
Student: At the very end
that's a total of what?
Four notes being played at once?
 
Prof: Oh,
okay.
Good.
 
Yeah.
 
Thanks for bringing that out.
 
There at the end we could even
have--
you're right--four,
maybe even five notes played at
once,
so this idea that you--once you
have three parts you can only
have three parts or once you
have five-voice fugue,
you can have no more than five
voices--
breaks down at the very end.
Why would you imagine a
composer would want to do that,
Frederick?
 
Student:
>
pieces at one time.
 
Prof: Well,
no, it's not that hard because
you--
once you get used to the idea
of a C major triad,
you--a musician would look at
that end and say,
"I've just got a C major
triad.
 
I'm going to just bang down on
it."
So that's not hard technically
or intellectually,
but why would a--the--you
raised a very interesting point
here.
 
Why would a composer want to
add more notes at the end?
I think it's a pretty
straightforward idea.
David? Michael, yeah.
 
Student: They make it
louder.
Prof: Yeah,
just make it louder,
make it more sonorous,
a big bang ending sort of
thing, yeah,
to tell the listener once again
that this is something special
and we're probably at the end.
All right.
 
So let's listen to just a bit
of this.
We had one version of this.
 
Let's listen to a contemporary
jazz ensemble playing.
It starts out with a kind of
guitar synthesizer with a piano
here and then we'll see what the
other instruments are.
Here's a jazz rendition of the
same fugue by Bach.
>
 
What instrument is playing this
bass line?
>
 
Okay.
 
Here we are in bar thirteen,
>
fifteen, subject in the inner
voice.
>
 
Here's our invertible
counterpoint,
>
 
switch, >
subject soprano,
>
now just modulating from one
key to the next here.
>
 
And here they actually do
repeat that tonic note,
>.
 
Okay.
 
>
 
And then what they do is go off
and improvise on that.
But it's interesting,
the similarity between jazz
style and Baroque music.
 
Why is that the case?
 
Well, Baroque music has a lot
of driving rhythm in it,
kind of regular rhythm in it,
and jazz has a kind of regular,
pulsating rhythm in it too.
 
I asked you what instrument was
playing the bass line there and
Daniel, you started going like
this so what were you doing?
Student:
>
Prof: The double bass of
the--but is it bowed?
No.
 
It's a plucked,
a pizzicato double bass,
but that's a standard
instrument in a jazz quartet,
jazz ensemble.
 
But it's a very strong bass and
Baroque music also has a very
strong bass, so lots of
similarities between
contemporary jazz and baroque
music.
And sometimes these jazz
ensembles like to get to this
Baroque music and resurrect them
in modern idiom.
All right.
 
So normally a fugue is a
freestanding piece or you could
have an entire movement written
as a fugue.
Haydn--the last movement of the
Haydn quartets will sometimes do
that,
a Beethoven piano sonata might
do that,
but usually they're
freestanding pieces.
 
Occasionally,
you run into a fugue that's
embedded inside another
movement.
You might have a movement in
sonata-allegro form and you get
to a particular section,
let's say the development
section, and the composer says,
"Well, I want to write a
fugue here as my
development."
When that happens we call it a
fugato, so a fugato is a fugue
placed inside another form.
 
So we're going to listen to an
example of this from the
romantic period in which we have
the young composer Georges
Bizet.
 
He was exactly your age when he
wrote this.
He was nineteen years old.
 
Georges Bizet wrote this
symphony.
There's a lovely romantic
string sound,
sort of break-your-heart string
sound, and then we have a segue.
We have kind of a romantic
transition here as he changes
mood and then a fugue will break
out and it will start in the
bottom voice so I'll tell you
that much.
And my question to you or my
challenge to you is this:
What's the order?
 
Let's say--and I'll tell you
this.
We've got a four-voice fugue
that's going to start here.
Can you track the order in
which the voices enter?
You know we've got the four.
 
You've got the bass,
tenor, soprano,
alto--or bass,
tenor, alto,
soprano, or soprano,
alto, tenor,
bass.
 
They can come in any one of
four different--
well, probably more than four
permutations but the order might
be alto,
bass, soprano,
tenor or it might be bass,
alto, tenor,
soprano or soprano,
alto, tenor and bass.
We don't know,
and that's your challenge here
to see if you can track the
subject.
Here we go.
 
>
 
Start.
 
>
 
Okay.
 
We're going to stop it there
just for a minute.
We're going to pause there.
 
That's the--all four voices are
in there.
Could anybody on just one
hearing tell me what the order
was?
 
 
 
Okay.
 
Let me--somebody different
here.
Robert, I haven't called on you
this morning.
Student:
>
Prof: Okay.
 
It started with bass
>
or maybe even an octave lower.
 
>
 
Okay. Then where did he go?
 
Student: Alto.
 
Prof: Yeah,
it actually went to the alto
>
 
and there--and then where?
 
Tenor >
and then finally--yeah,
>
way up high in the first
violins.
>
 
And now we're going to get
a--an episode in which he's
going to play with just a
motive, and then the subject
will come back.
 
So here are two questions for
you.
In which voice is the subject
coming back and what's happened
to the subject when it comes
back?
It's changed in one way.
 
>
 
Okay. Let's stop it there.
 
Any takers on that?
 
And if we were doing a quiz on
this, we'd give you three or
four playings of that.
 
Which voice did it come back in?
 
>
 
Thaddeus.
 
Student:
>
Prof: Not bad.
 
We would take that because it's
kind of high--I'm playing it in
kind of tenor range here.
 
I think it was more cellos and
we'd probably--
with bassoons--and we'd
probably call that bass,
a bass part,
but fair enough,
tenor,
and what happened to it?
>
 
Roger.
 
Minor.
 
>
 
So he modulated to a different
key and then gave you the
subject in a minor key,
and that's kind of the way
these fugues operate,
give you an exposition episode
in which you change key,
bring back the subject in a
different key.
 
All right.
 
So we've now had a fugue from
the nineteenth century,
although we would call it a
fugato because it's embedded in
this lovely,
lovely sonata-allegro movement.
Let's turn to a fugue from the
twentieth century,
and for this we go to Leonard
Bernstein and you can see the
playlist up on the board.
 
New Haven used to be a favorite
try-out city for Broadway
musicals.
 
Indeed there was a musical
entitled--it never went
anywhere.
 
It was entitled We Bombed in
New Haven,
meaning that the try-out
>
of the particular musical was
not a success,
and where would they try out in
New Haven?
What was the great theater for
this?
Hm?
 
Student: The repertory
theater?
Prof: The Yale Rep
Theatre?
Any other takers?
 
The Shubert Theater.
 
Yeah, actually in that period
the Yale Rep was actually a
functioning house of worship.
 
It was a church at that
--what's now the Yale Rep.
So is it the Shubert Theater,
which has been here for a long,
long time?
 
So Leonard Bernstein came in
here with a show in 1952 called
Wonderful Town and he
tried it out there,
and generally speaking it was a
success and he took it down the
train tracks there to Broadway.
 
But he took some music out of
it, some music that he thought
actually was a little bit too
complicated for the choreography
that he wanted to work into it--
later took that material and
worked it in to a freestanding
piece called "Prelude,
Fugue, and Jazz Riff."
 
So we're going to look at now
just the fugue portion of it
because it's a very interesting
kind of fugue.
It's a very complex fugue.
 
So we're going to start out
here and I'm going to break
this.
 
We'll listen,
we'll stop, we'll listen and
stop so that we can focus on
particular passages.
So as we start to listen,
see how many voices there are
in Leonard Bernstein's fugue.
 
Have a general sense of what
the range is:
soprano, alto,
bass.
What else do we need?
 
Oh, yeah.
 
What instruments are playing
here?
>
 
Okay.
 
So that's the exposition and a
little bit of the development
there so what instruments?
 
Hm? Ducks?
 
Student: Saxophones?
 
Prof: Yeah, saxophones.
 
Yeah.
 
Okay.
 
Kneeland said saxophones and
he's right.
Yeah, so saxophones there.
 
So we've got--and then
how--roughly how many did you
hear?
 
Two, three, four?
 
Yeah, maybe four,
maybe four different
saxophones, sort of alto sax,
maybe baritone sax in there.
And there was one--and so we
are playing this out and it's a
rather syncopated fugue,
sort of >.
Let's listen to it again.
 
No, we don't have time to do
that but here's one thing that
happened, >
that kind of sound,
>.
Then after one episode one of
the saxes brought back that
subject.
 
>
 
What's it doing there?
 
>
 
What is that?
 
What's the relationship there?
 
Student: Is it inverting
it?
Prof: Yeah,
it's just inverting it.
It is taking the intervals and
flipping them and that's what
composers love to do with
fugues,
and I'll be talking about
interchangeable parts,
reciprocal relationships with
the mathematical quality of
fugues.
 
And so that's what's happening
here.
We have a moment of melodic
inversion.
And sometimes in fugues--and
Bach's did this in the musical
offering--
he can take his fugue subject
and run it backwards from
beginning to end so they like to
have these kind of mathematical
permutations of these intervals.
It's very cerebral stuff,
this fugue business.
So there we had just a moment
of Leonard Bernstein writing a
little bit of inversion.
 
Now what we're about to hear
next is something of a surprise
because we get a second fugue
subject.
And it's a different fugue
subject;
it is not syncopated.
 
It's rather lyrical,
>
>
 
something like that.
 
So it's nice and lyrical.
 
And let's listen to how he now
unfolds a second fugue subject.
So what we have here is called
a double-fugue.
He's got one exposition with
one fugue subject.
Now he's going to give us a
completely different exposition
with yet a second fugue subject,
>
and then number one comes back.
 
>
 
Okay.
 
We're going to pause it here
because he's now about to do
something rather interesting
that Bach used to do as well.
And Bernstein was a consummate
musician, had studied Bach,
had Bach coming out of his
ears, so he knew about this
particular trick.
 
It's called stretto.
 
You can design a fugue subject,
not only that it could go
upside down,
but in which the intervals
instead of coming in long
succession could be piled right
on top of one another.
 
So the way he sets this thing
up to begin with is this,
this, maybe this and then this,
but in the next section it's
going to go this,
this, this and this.
The intervals back up on each
other because they have been
arranged to be consonant at key
points and that's called
stretto,
Italian word stretto,
kind of tight--
tight entries here.
So here is fancy little bit of
counterpoint by Leonard
Bernstein that once again goes
by very quickly.
>
 
Do you hear it?
 
>
 
Now he's going to bring back
the two subjects together.
We have one and two together,
>
episode, >
syncopated episode,
>
one, >
two, >
and so on.
 
>
 
So it's a pretty nifty little
fugue there by Leonard Bernstein
with lots of intricate
counterpoint involved in it.
All right.
 
Let's end now with a fugue of
J.S. Bach and for that we're
going to turn to an organ fugue
that he wrote about 1710 when he
was a young man in Weimar.
 
Here is that fugue subject
>
and on and on and on it goes.
 
What's of interest about this
subject?
Well, two things.
 
First of all,
as I sing this
>
 
what is that?
 
>
 
It's an--
Student: Arpeggio.
Prof: Arpeggio.
 
Yes, it is, but it's an
arpeggio of what?
>
 
>
 
It's a triad,
just a minor triad.
>
 
One, five, three,
one, if I skip this note here.
>
 
As I come to every strong beat
in this theme,
every strong beat,
I have a member of the triad,
that same either G,
B-flat or D.
So these triads as we said
before are really the structure,
the backbone,
on which a composer like Bach
will place the flesh of a fugue
subject.
So it's very triadic and it
sounds pretty secure for that .
Now here's another thing that
this fugue subject does and many
other fugue subjects.
 
It starts with quarter notes,
>
quarter, quarter,
quarter, then next measure,
eighth, eighth,
eighth, eighth,
eighth,
eighth, and then we get in here
eighth,
eighth, eighth,
>.
 
It's gathering speed.
 
Of course, the beat isn't going
any faster.
The tempo is staying the same.
 
He's simply writing shorter
note values,
which has the psychological
impact,
as we've said several times,
of giving the sense of
movement,
gathering speed here.
It's like a train pulling out
of the station.
We want to get on this train.
 
This thing is really starting
to roll after five measures or
so.
 
So it's a pretty nifty fugue
subject here and we're going to
listen to this now,
and what I'd like to do is the
following.
 
We're going to listen to the
entire piece.
Think about--as the voices come
in, think about where they're
coming in.
 
Can you tell me what the
trajectory of the voices is in
the exposition?
 
And I'm going to turn out the
lights here because sometimes
it's good just to kind of go off
into your own world,
close your eyes,
but I would like you to do the
following thing.
 
Kind of lean back,
get comfortable,
close your eyes,
but every time you hear the
fugue subject-- >
and so on--every time you hear
that fugue subject raise your
hand so that I know you're
recognizing that it's the
subject.
 
Because listening to fugues,
it's basically one thing:
Differentiating between a
passage in which you've got a
statement of the subject and an
episode where there ain't no
statement of the subject.
 
Okay.
 
So this is a three minute and
twenty-second fugue and we're
going to listen to the whole
thing,
but do raise your hand when you
think that fugue subject is in
there.
 
>
 
So we've gone soprano,
alto, tenor and now bass.
>
 
Yeah, there it is.
 
It's in one of those inner
voices.
It's a little bit disguised but
it's in there.
>
 
Yep, >
inner voice.
 
>
 
Yep, way down in the bass.
 
>
 
A nice, long sequence here
>
>
 
Yep, all the way up on top in
the soprano.
>
 
Another episode,
descending sequence this time.
>
 
Rising sequences here,
>
falling sequences >
in the bass.
 
>
 
Okay, so that's a wonderful
fugue by J.S. Bach and we
could--we're going to talk more
about this in section,
this idea how you can run your
fugue parts this way or you
could order them this way.
 
You can think of these
constructs mathematically or you
can think of them musically,
but you're all working with the
same kind of material.
 
As you go out,
one final fugue by Glenn Gould
who is going to teach you how to
write a fugue as he sings a
fugue to you.
 
>
 
 
 
