A Bach Triple Concerto

I'm trying not to talk about musical things my readers are not familiar with, so: what's a Concerto, again? It is a piece of orchestra music, featuring a solo instrument; in other words, that instrument is given a very prominent part in the piece.  (These days, piano concertos are some of the most common, but in the time of Bach, for instance, concertos were written for all sorts of solo instruments.  The one I'm going to write about is a triple concerto.  The instruments are flute, violin, and oboe.

Now remember, Bach died in 1750, which is centuries ago, so a lot of what we know about him has to be painstakingly dug up, and we only know about this flute / violin / oboe concerto from indirect evidence, but the evidence is very strong.

Around about 1735, Bach applied to work at St. Thomas's School in Leipzig.  The job involved teaching, and training the choir, and providing music for church services.  Being an energetic guy, he also undertook to provide live music at a certain Zimmermann's Coffee Housein Leipzig.  Now, at his earlier job, Bach had written numerous orchestral pieces to be performed by the modest orchestra of the Duke he had worked for.  About half the music from that time never came down to us, but we have catalogs, which tell us what sorts of pieces he had written.  In Leipzig, Bach's three oldest boys were around 20, and he (and they, probably) wanted to display what they could do, and they being skilled harpsichord players, Bach rewrote some of his older multi- instrument concertos for various numbers of harpsichords.

There is also a concerto for three violins, which is well known.  It was evidently the work that was the origin of the three harpsichord concerto!  In fact, Bach was well known for borrowing his own music, and cannibalizing it to write more music for different instruments.  Most interestingly, musicologists (sort of musical detectives) studied the triple  harpsichord concerto, and the triple violin concerto side by side, and, as you can imagine, learned a ton about how Bach went about converting one type of concerto into the other!  If modern-day composers were to go about doing this, they would possibly do it differently, but musicians have been insanely fascinated with Bach's methodology for a long time, so this process of comparing concertos was fascinating. 

But, listen to this.  They studied the violin triple concerto, and decided that that was also a conversion from an as-yet-unknown earlier concerto, for different instruments.  So, working backwards, they reconstructed this triple concerto for flute, violin and oboe. 

Approximating with Polynomials

I recently saw a title of a video about how to find the square root of 2000.  Having taught the math background for solving problems like this for our computer, and actuarial students, I was happy to try this problem, without watching the video.  The easiest thing in the world is to type in 2000 into a calculator, and then press the Square Root key, and we would get the square root in one shot.  But that would be no fun to us math people; we would prefer to have some more meaty mathematics to sink our teeth into!

Finding square roots directly is a skill that is slowly vanishing.  It isn't something that we teach youngsters in school, to do with paper and pencil; over the years, math teachers have never been coached with this method in their school years either, so they don't even know that there is a direct method.  Everyone relies on calculators to do it for them; in fact there's hardly any reason to actually find square roots anymore in this brave new world.  Approximations, though, could still be useful, especially polynomial approximations.

[I don't really know why I put this post in this blog!  The topic of 'Approximation with sines and cosines' might have made a little sense, because of the harmonic series, and so on ... Some of my best buddies are dead; they might be messing with my head ... Anyway, it's probably time to move it 'next door', into I Could Be Wrong, But ...]

My Band Debut!

I thought I had told you (my readers) this, but I mayn't have: I have taken up a new instrument!

My wife saw an announcement that the local New Horizons affiliate was ready to sign up new members, and urged me to go and see.  What is New Horizons?  It's a countrywide (and maybe international, to some extent) organization that has brass bands in many localities, that encourage retirees to take up playing a band instrument.  In our area, it's sort of associated with a large music store, which provides space for rehearsals, rental instruments, administrative support, and so on.

So, I attended one of their rehearsals, and when it was over, I talked to the band director, and I said I wanted to join. 

"What would you be interested in playing?" they wanted to know, and I said, 'Anything; but I would really like to play a bass instrument!'

They said: well, we have found that it works better if the new member chooses their own instrument.  In spite of all that, I was strongly encouraged to learn to play a baritone horn.  These things are also called just baritone. It is a brass band instrument (not an orchestral instrument), and is pitched roughly an octave higher than a Tuba.

 

They meet for rehearsals every Tuesday and Thursday; and I would get a half-hour lesson each Thursday, after which I'd sit in with the band rehearsal, though all I could do at first was play the B Flat in the bass stave.  So I gazed intently at the scores they were playing from, and pounced on any upcoming B Flats, and played them.  (New members who couldn't read music would have to be taught that skill too.)

That was in early October.  We were rehearsing some standard marches, some carols, some Christmassy songs (Rudolph the red-nosed reindeer, Jingle Bells, etc.) and a few items that the locals liked, e.g. some Penn State marches, etc.

Finally, today, we got all dressed up, and went out to play at a state hospital!  (In Pennsylvania, state hospitals are mental institutions, but they're not called that, to save the feelings of the inmates.)

It went off OK.  I couldn't play everything I should have played, but I figured it was better to skip the notes I couldn't get than play wrong notes.  Every rehearsal I seem to be playing more notes than before; there are some chromatic sequences, like F, E, E Flat, which I can play now, as long as it's not too fast. 

The Baritone is keyed like a trumpet.  There are three pistons; the first one drops the note by a whole tone.  The second one drops the note by a semitone. The third one drops the note by three semitones—a minor third.  So the B Flat scale goes like this:

• B Flat: just blow. 
• C: pistons 1 and 3 (and blow).
• D: pistons 1 and 2 (and blow).
• E Flat: piston 1 (and blow).
• F: just blow, a little harder. 
• G: pistons 1 and 2, blow harder. 
• A: piston 2, blow very hard.
• B Flat just below middle C: just blow, quite hard. 

You must have guessed that, when I wrote 'blow harder,' there must be more to it than that!  There is; you have to tighten your lips, and blow harder.  But, as with almost all wind instruments, blowing a little harder does give you a new note. 

Without any pistons, you get a B Flat, then an F, then octave B Flat, then you get the entire so-called harmonic series of B Flat.

Using pistons 1 and 3, you actually get the harmonic series of F, which happens to contain C.

Using piston 2, you get the harmonic series of A (which happens also to contain E).

Using piston 1, you get the harmonic series of A Flat, which contains E Flat.

Knowing all this is well and good, but since the fingering of consecutive notes isn't simple—as it would have been on a recorder, for instance—you just have to memorize the way each note is played.  But when a note sounds perfectly, it sounds like it's being played on a horn; in other words:  beautiful. 

Archie