Pi Day Once Again

 [Apologies, readers; this post belongs in the—mostly—nonmusical blog I could be Totally Wrong, but.]

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?

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

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

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!

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 Lankan 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

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

Bach with Trumpets and Drums!

Piccolo Trumpet

Valveless (Natural) Trumpet

Piccolo Trumpet

On Saturday the 9^th, Katie and I headed out to hear the Bach Choir.  (There's a Bach Choir in Britain, as well, but this is the local one, established in Bethlehem, PA, a million years ago.)  We had already got tickets, and I had dreamed of hearing this choir for close to 50 years, so Katie---always ready for an adventure---set out.  Knowing we were leaving Wilpo for a Big City, Bethlehem, the chances of finding Chinese food a little more authentic than at home was good, so we left home early.

Katie decided to take the road less traveled, and the GPS took us all over the place, sometimes instructing us to take sudden turns, to avoid congestion.  Finally, we were in Bethlehem!  But the Chinese restaurant we had wanted to go to had closed down, :( but we soon found another one, and had a wonderful lunch.

Presently we were at the First Presbyterian Church---why do they number these churches?  My aunt attended the First Methodist Church in Phoenix, and I had always wanted to get to the the other Methodist churches: the second, and the third, and so on.  For many of the Third Shall be First, and vice versa, and verse visa.

Both the Bach Magnificat and Cantata 63 (Christen, ätzet diesen Tag, BWV 63) feature high Bach trumpets, as well as interesting combinations of soloists.  Perhaps they had found two specialists in high trumpet (not something a typical trumpeter can be confident about) and decided to perform these two, which are appropriate for the season.

First of all, I just loved the contralto soloist (a mezzo-soprano, really) called Luthien Brackett, who despite having a quiet voice, did a fabulous job, and lent a lot of charm to the set of 5 soloists on the dais!  She alone would have been worth the price of admission---almost.

The orchestra---a small one---was beyond excellent.  The strings were lovely, but being about a 150 feet away, we couldn't hear well enough to give a critical appraisal.  But the tympani, the flutes, oboes, trumpet(s?) and bassoon, and the portative organ, were just fabulous.  This is the first time I have been in the same room as a portative organ, but I did not go up close, for fear that they'd think I wanted to smuggle it out of the church.

Another surprise was the Bach Trumpet.  Johann Sebastian Bach wrote amazingly florid but tasteful, lovely parts for high trumpet.  At the time of the first Bach revival of around the middle 1800's, the trumpeters available were baffled as to how to play these parts; they were so high, and so florid.  The first line of attack was to invent a new sort of trumpet, called a (high) Bach trumpet, that enabled some trumpeters to play these lines.  There are wonderful trumpet parts in the Brandenburg Concertos, a couple of the Orchestral Suites ('Ouvertures'), and some of the celebratory cantatas and choruses, such as those in the B minor Mass, and in the Christmas Oratorio.  Now, with the new Bach Trumpet, these trumpet parts could be played.

The Bach Trumpet unfortunately does not have the traditional appearance of a trumpet, but rather looks like something that MI5 dreamed up to crack enemy coded transmissions.  I wouldn't have known what it was, if I had been shown one, if not for the fact that Flip Herfort, my friend and teacher, had demonstrated one to me a week before.  In the 1970's straight trumpets that looked like heraldric trumpets began to be used---some of them with little holes on the side, instead of the valves on modern trumpets,  (To see one, find a video of the Christmas Oratorio, or the Weihnachts­oratorium, on YouTube; the video of John Elliot Gardiner and the English Bach Soloists will have three gentlemen playing straight trumpets), which makes them close to chromatic in the higher registers.

The first chorus of the Cantata had an interesting feature.  At the third line (or somewhere in the middle, anyway,) the harmony takes an abrupt left turn, and modulates to the relative minor.  In Bach's time, the congregations were probably accustomed to these harmonic jinks, but today, I'm sure Federal Safety Standards require a more sedate harmonic rhythm!  Bach has done this in other places; the opening chorus of BWV 147, for instance.  I don't think conductor Chris J. could have done much to ameliorate the violence of this modulation, but the congregation seemed to take it with great equanimity.

Well, to conclude, writing about music is always a bit of an iffy proposition; you have to hear what you're talking about.  It's a relatively easy operation to hunt down the two pieces on YouTube, and numerous video clips of Luthien Tinuviel singing.  Give yourself a treat!

Arch