Saturday, March 16, 2024

General Education

I just read, today, that the great Canadian pianist, Glenn Gould, did not complete high school. This is only the last in a series of stories about various—quite intelligent—historical figures who, for one reason or another, either struggled with, or gave up on, education.  Einstein is said to have struggled with simple mathematics.  Many important artists and musicians gave up school.  Actors have abandoned school, but have in some cases, gone back to school to try and complete their education. 

What are we to make of this?  Education is the imparting of certain skills from a knowledgeable person, to a (usually) younger person.  In modern times, the recipients are usually a group (a class), who are all taught together. 

I worry that this failure of the educational process could encourage young people in their belief that the education process is seriously flawed.  Well, we've all known that the educational process is flawed to some degree.  It does not take into account the great variation in the mental equipment of the members of a class; their different degrees of predisposition to learn; their psychological resistance to being taught; their emotional incompatibility with the instructor.  It's quite easy for a student to reject his or her teacher; "It's just not working out."

In case anyone thinks that all those future celebrities who bailed on school were incapable of completing school, I'd say that many of them had a firm grasp of most subjects in the curriculum; certainly Glenn Gould did, and probably Einstein.

What prevents modern schools from customizing the curriculum yet more than it is now, to match the preferences of the students (and parents) perfectly, is the cost.  In many ways, College accommodates this desire to have a more varied curriculum.

Thursday, March 14, 2024

Pi Day Once Again

Well, it's π day in the USA, and though we wish it's an international feast, it really isn't!

I, and I'm sure many other mathematicians, sneer at this celebration, but I'm thinking: who am I to spoil the fun of so many mathematician wannabes?  Let them eat π, to paraphrase Marie Antoinette!

A few bits of trivia about the fabled mathematical constant:

1.  Though it's commonly thought of as 3.14, one of the cardinal properties of the number is that it could not possibly be represented by a decimal number that stops.  Cannot be done.  However, you can represent it as accurately as you want, but it will never be exact.  It can't be written as any fraction, either.

2.  HOWEVER: Archimedes had discovered an excellent approximation to the number Pi, namely 22/7.  If you've got a circle of radius 10 inches, and if you want to know what its circumference is, we know that, in the abstract, it will be 10 inches × Pi × 2.  This will be perfectly accurate.  But since we cannot represent Pi exactly, we can only find this circumference approximately.  (This means not exactly, but closely—in fact as closely as desired.)  If you want an estimate to as close as 1/1000th of an inch, we need to use about 6 decimal places of the value of Pi.  (It's  been 10 years since I've done this sort of thing, so I might be off by a couple of decimal places!)  So basically, what approximate value of Pi you must use depends on how close you want your calculation to be.  You can easily Google Pi, and compare it with 22/7, and you'll find that they agree to more than 5 decimal places. 

3.  But guess what.  It was known by Eastern mathematicians (Indians, Persians, Egyptians, Chinese, etcetera) that 355/113 was even a better approximation to Pi!  The miracle of these two approximations to Pi is how close they come using such small numbers!  The next fraction that comes even closer, is a fraction of two enormous integers. Google sends us to a website that gives 100798/32085 ~ 3.14159264,correct to 8 decimal places. But see how huge the numbers in the fraction are?

Tuesday, February 27, 2024

Cadenzas

The word cadenza denotes a complicated thing.  At the end of a movement in a concerto—which is, as you know, an extended piece for a featured soloist and orchestra, usually in three movements—there often is a big chord, after which the orchestra players lay down their instruments, and the soloist plays an entire virtuoso passage, usually touching on the themes of the preceding movement.  This is a cadenza.  The exciting part, for me anyway, is how they smoothly flow into the last few chords of the movement, and end it.

In the old days of Vivaldi and guys, the cadenzas were improvised by the soloist.  More recently, the composer wrote out a cadenza for the soloist.  Modern soloists are eager to go back to the improvised cadenza!

Just the other day, I was listening to Joshua Bell playing the Mendelssohn violin concerto, (his only one).  But, JB played his own cadenza!  Oh, I missed Mendelssohn's own cadenza so much!!  It's a fun cadenza, but I guess musicians are bored with it; same old, same old, they think.  I first heard this piece when I was just about 14 or 15 years old, and got to know and love Mendelssohn's cadenza... oh man; that's really too bad.  I'll just go off and cry by myself, now...

Arch

Wednesday, February 14, 2024

Saint-Saens's 'Organ' Symphony

The local Symphony Orchestra gave a Valentine's Day concert (a day early), and the main program item was Camille Saint-Saens's so-called Organ Symphony.

We attended it with great expectation—mostly because the theater—unlike many music-halls does not have an Organ, and we were wondering how they would manage the organ part, and also because this piece was one of my wife's favorites. 

Well, it was fabulous.  There are so many 'earworms', bits of music in the work that keep nagging at you for days!  This is a wonderful piece for anyone to get into: very tuneful indeed!  The composer is not widely considered one of the 'greats', because the music is not very 'learned'; it is very accessible; more accessible even than Tchaikovsky, though—as I recently said about composers—you just can't rank them on any criterion. 

Arch

Thursday, January 18, 2024

Peter Schickele

I was just trying to explain to my cat—well, it's Katie's cat really—that Peter Schickele had died.  But she did not seem that concerned.  'But you're here,' she seemed to say, 'Pet me!'

Of course, Schickele has little to do with cats, but I report the facts as they take place.  My father knew Schickele's parents (who were also called Schickele) and the gentleman—Dr. Schickele—was a Ford Foundation exchange professor.  They valiantly tried to explain to us what it was that their son did, but they didn't have the background. 

Well, what he did was invent a fictitious son of the (real) composer,  Johann Sebastian Bach, called P. D. Q. Bach, and proceeded to 'discover' numerous works by this gentleman.  All the works were parodies of existing tunes by well-known composers, that were written by Schickele himself (the parodies, not the originals) and released a number of albums throughout the eighties and the nineties, that were extremely well received. 

In the nineties, and later, Schickele had a regular hour on NPR called Schickele Mix, in which he introduced his audience to a number of pieces, both classical and other, that fitted some theme that he was following. 

Schickele composed at least one wonderful opera (ascribed, as always, to PDQ Bach) called The Abduction of Figaro. 

Peter Schickele had provided those in the know with simply hours of hilarity.  His sense of humor was deliberately clumsy, as befitted an amanuensis of a non existent last child of a German composer of the 1700s.  What an amazing gift to us he was!


Friday, January 5, 2024

Do-Re-Mi

Back in 1965, we kids didn't know much about The Sound of Music, until a big fuss was made about the movie in the Sri Lsnkan newspapers. We didn’t even know about Julie Andrews at that time.  A wide screen was needed for Sound of Music, and we had to wait until theaters—cinemas, as we called them—were convinced of the necessity of the expanded screen, and refitted them. 

Then, of course, everyone saw the movie, which was a big hit, and the songs were being sung by kids everywhere.  Edelweiss was the big hit, and the Lonely Goatherd.  The Do-re-mi song trailed in popularity, and it did not strike me at that time why that was so.  In retrospect, at least one reason is clear: it is difficult to play by ear!

To my mind, that song is almost brilliantly well constructed; there are several sequences, as they're called; the fragments that start with 'Doh, a deer ...', then 'Re, a drop of golden sun ...' and 'Mi, a name ...' and 'Fa, ...' all have the same pattern; that's a sequence.  At 'Soh ...' a new pattern begins, that continues with 'La, a note to follow Soh,' and 'Ti, a drink with jam and bread...'

The song was so embedded in my consciousness that I didn't quite notice that some of those runs introduced accidentals (sharps and flats) that popped the song—which had started out in C major—first into the neighboring key of G major, and then into A minor!  The last line rather nonchalantly introduced a B Flat, not for harmonic reasons but just as a chromatic passing note.  You haven't lived until you've tried to play it on a baritone horn.

The little example I have shown is in the key of B Flat, which means that the accidentals that were introduced in the song are now an E Natural (which moves the tune into the key of F, temporarily,) followed by an F Sharp, which moves the tune into G Minor; and then an A Flat to get us out of G minor, and back home to B Flat.  A flat is not a note in the harmony, really; it is a chromatic note, just for fun.

Archie

Wednesday, December 27, 2023

Mozart's Piano Concerto in C minor, K 491

I think I have blogged about this piece before, but it needs to be done again!

The piece opens with the first theme played in unison (actually in octaves) by the whole orchestra, and then it bursts into an explosive flowering of a sort of bouquet of music.  (Alas, a few years ago I would have done justice to this description, but ...)

The first movement maintains this sense of seriousness throughout; the urgent statements of the piano and the orchestra are often underscored by the kettledrums.  (These are a set of tuned drums that can play melodies, but are actually sparingly used to emphasize the occasional bass note.)

The second movement starts with a very simple tune, almost like a nursery rhyme.  As the movement proceeds, we are treated to a sequence of lovely variations on that tune, that will probably stick in the memory of a first-time listener. 

The Finale (the last movement) is again a set of variations, on a much more studiedly serious theme, that has a characteristic pathetic cadence-like modulation (to D Flat, in this case) just before the end of the theme. 

It's easy to fall in love with this piece; we're told that this concerto was one of Beethoven's favorites, and in my humble opinion, Beethoven had excellent taste, most of the time. 

Earlier today, I was unexpectedly shown (the late) Claudio Arrau playing Mozart's Sonata in A minor, K. 310.  Well, it's been a Mozartian day, for sure.

Archie