Tchaikovsky

I had always regarded Tchaikovsky as a good composer in his own way, but not to be compared with Mozart, and Schubert, and the composers I considered 'The Greats'.

Now, you all know about the band I play in.  I had to learn an instrument from scratch, and attend rehearsals and all that sort of thing, and presently I was learning all about about music from the inside. 

One piece we're playing is a number from The Nutcracker ballet suite, and I'm learning what an amazing composer Tchaik was.  Now, because ours is a very humble band,  in many ways, the music we play is far removed from the Nutcracker music played by a concert Orchestra.  The arrangement itself is ingenious; it contains all the melodic lines that would catch the ear, and leave out as much as possible, so that we can play it with the few players we have—around 14 of us.  Even with that stripped-down version, the music is brilliant!

It was quite some time until I began to pay attention; I was preoccupied with fingering, and just getting the notes.  But one day,  I noticed: wow,  this is amazing writing!

The man was not universally admired in his lifetime, which was tragic.  I'm not familiar with his life story, but I'm going to read up on it when I can.  If you didn't know, Tchaikovsky wrote several symphonies as well, at least some of which are considered masterpieces. 

Archie

Small Ensembles

Let's start from 19th Century, and work backward. 

The most common sort of small ensemble is probably the string quartet.  It consists of two violins, [lowest note: G below Middle C], a viola,  [lowest note: one octave below Middle C], and a Cello, [lowest note: two octaves below Middle C].

The string quartet has the interesting property that the four instruments sound almost just like each other; in fact, they're essentially four sizes of violins, with the larger ones sounding lower.  We call this character homogeneity; they blend together perfectly. 

Another group for which a lot of music is written is a wind quintet.  Music for a wind quintet sounds beautiful and balanced, but the balance doesn't come from the nature of the instruments.  A wind quintet consists of (typically a flute, an oboe, [lowest note Middle C in both cases], a clarinet, [lowest note B Flat, an octave and one more whole note below Middle C], a bassoon [lowest note: E Flat, a little less than two octaves below M. C.], and a French Horn, [wait, I have to look this up ... Lowest Note: Two octaves below M.C.].

The presence of the horn in the wind quintet is often a surprise for anyone learning about them for the first time.  I don't know the history of the situation, but I imagine that someone must have tried it, and it must have sounded satisfactory. 

Obviously, the Wind Quintet does not sound homogeneous by design, but they do sound wonderful.  There are certainly other combinations, for instance lots of combinations with pianos: the piano quintet, consisting of a piano and a string quartet; the piano trio, consisting of a piano, and violin, and a cello.

There are also many different Quintets, consisting of a String quartet, and one instrument not from the quartet, e.g. a Clarinet Quintet (string quartet + clarinet).

In earlier times—say before the 17th Century—small ensemble were assumed to consist instruments of the same family; for instance a recorder consort: which would consist of several recorders all of the same style.  There are bass recorders, tenor recorders, alto recorders, soprano recorders, and sopranino recorders.  Often they were sold in a matched set, in a special case with a place for each recorder. 

There were also what was known as a school of viols, consisting of viols of grades sizes, from a treble viol, down to a bass viol.

Recorder ensembles and Viol ensembles had extremely homogeneous sounds.  In early music, I suppose pieces written for them were monophonic; that moving from chord to chord, without the complexity of Baroque Music. 

Contorts with different sorts of instruments were called 'broken consorts'.  If a consort consisted all ofthe same type of instrument, they were called 'whole', or 'closed' consorts—at least, according to Wikipedia.

I'm sure that in earlier posts I have linked to examples of many kinds of small ensemble, but I could be wrong.  Someday, I hope to link to pieces for small ensembles on YouTube, and that would complete this post. 

Archie

Nutcracker Suite Item #2: March of the Toy Soldiers

As some of you might recall, I took up the Euphonium (actually just a Baritone, but Euphonium sounds so much more euphonious), and joined a special band for seniors.  It's an organization called New Horizons, which establishes these little bands in many towns, and teach an instrument for anyone who wants to join, and they play at nursing homes, and similar places, as a treat for the residents, and a treat for the players too. 

One of the pieces we're playing this season (Fall/Winter 2024) is the March from Tchaikowsky's Nutcracker.  The Ephonium is a tenor instrument.  Sometimes it plays an inner part—often an interesting one, a so-called counter-melody, which are so common in Souza marches.  Other times, we double the bass line (played by the Tubas).  I love it when we do that, because I love playing bass anyway. 

In the Nutcracker March, there are interesting passages, which you will recognize at once if you hear the March, e.g. via YouTube.  I really ought to insert here the music of a sample passage, but it isn't as easy to do using my phone as it used to be when I posted these things using my computer!

March of the Toy Soldiers [Tchaikowsky]

J.S.Bach, Benjamin Franklin, Near Contemporaries

JS Bach was born in 1685; Ben Franklin in 1706.  Franklin was younger by 21 years,  maybe more or less depending on the actual dates. 

Bach died in 1750, while Franklin died in 1790, 40 years later.  Franklin lived a lot longer, and a few years moor recently than Bach, but to me it's useful to think of them together, as I imagine their costumes, which were very similar, except that Franklin never wore a wig. 

Franklin is often described as a 'polymath', which is an old word that means 'a person with very diverse interests, skills and talents, what is also described as a Renaissance man.  About Bach, we don't really know; we do know he was interested in music, and theology, but apart from those subjects, we don't know much about him. 

We are told that he was interested in the design of organs; he was an excellent organist, and was hired as a consultant for at least one church that was having a new organ built. 

Music, at that time, was a broad area of interest; there was composition, in several different forms; Bach was a master of many of these, and the Oratorio form extended into the area of drama.  Bach could play almost any keyboard instrument, but also strings instruments: violin, viola, and very probably cello and double bass.  He knew the theory of oboes and bassoons, and probably trumpets and horns, and recorders.  Because of this wide range of expertise expected from a court musicians, there was very little time for one to explore other interests.  We know Bach had s limited interest in local politics, because it impinged on his management of a small court orchestra that was expected of him. 

Franklin was interested in writing, publishing, politics and political philosophy, he was an ambassador, he was involved in the independence movement, he was interested in science, and a host of other things.  I can't even imagine the two men meeting, or even whether they would have had a common language of discourse.  I can imagine that Franklin spoke French, having been the Ambassador to France.  We are not told whether Bach spoke any language other than Deutch, and read a little Latin.  And also perhaps a bit of Italian, because by Mozart's time many musicians could understand a little Italian.

Mozart, who was born two years after Bach died, could speak several languages fluently, certainly Italian.  Mozart's entire life was within Franklin's lifetime. 

Archie

Schubert

You might not know that (as far as I know, which is not a lot) both 'Schubert' and 'Schumann' mean 'Cobbler,' in German. It makes very little sense for me to bring that up, because very few of you younger people have had any experience with cobblers at all!

A few years ago, there was a hole in the sole of my shoe.  It was a pair of Clarks—or another make, equally good—and just on Market Street, a block and a half from my apartment, was a shoe repairman, or to call him by the traditional name of his profession, a cobbler.  To make a long story short, he said—from his point of view—the shoe was good enough to repair.  (A cheap pair would be thrown out and replaced, you see.)  It cost about $40, which I cheerfully paid.  A new pair would have been outside my budget.

By the time Schubert was born, the literal meaning of his family name would have had nothing to do with the occupation of the family, so the little anecdote is quite irrelevant.

Schubert composed lots of fabulous music, but the best known work is probably the famous  Unfinished Symphony, or Symphony no. 8 in B minor. 

The first item on my agenda is to get you listening to this symphony!  Schubert wrote lovely, melodic sonatas and songs, and piano pieces.  I'm ashamed to say that I'm not familiar at all with them!  But my parents—mostly my Dad—would put on the Unfinished, when I was in elementary school, and the tunes stuck with me. In fact, one time he participated in producing a play, about Elijah and the priests of Baal, and they used the Unfinished as incidental music.  Furthermore, our family music box was an old HMV phonograph, and the records were what are called '78s' these days; and only held about 10 minutes of music!  So Dad did a lot of changing discs.  (These were platters made of Bakelite, a very early kind of plastic.  Very soon, once LPs were invented, they (the LPs) were made out of Vinyl.)

Now, I don't know a lot about what was going on with Schubert while he was writing this Symphony; those sorts of details help many people to relate to a piece.  I'm just going to describe my own reactions to the first movement. 

It begins with the main theme played quietly—and ominously—deep in the bass.  Then some woodwinds (flutes, oboes, clarinets) enter, and things seem to be going swimmingly, until it's all Interrupted by some loud, full orchestra chords.

Don't get me wrong; the alternation of quiet passages and the loud chords is very musical; I can't describe it better than that.  In some works, it almost seems as if the loud interruptions are there solely for their shock value.  I don't think this is true ĥere.  It's almost as if Schubert had to have these loud punctuations exactly where he put them.  There's a lot of drama in the movement.  Maybe someone was teasing him about not being able to compose a dramatic Symphony!  Well, he certainly showed them.  The music sounds almost angry at times, and really serene at other times.  The serene parts are just fabulously lovely; perhaps they would not be as lovely if not for the contrast with the loud and noisy parts.  Stormy is the one word that describes this movement.  It ends with three huge crashing, angry, almost despairing chords. 

The second movement opens as though it was the sun rising after a huge thunderstorm.  (You can easily see why my dad and his friends chose this Symphony for their play!  For those not in the know, there was a weather competition, where stormy weather was involved.)  I'm going to stop there; you don't need Cliff Notes for this second movement.  This might not be good news, but: there are only two movements.  Most symphonies have four movements, this is why this work was nicknamed The Unfinished.  Lots of people agree, though, that it's perfectly fine the way it is.  So listen to it on your own, and take ownership of this wonderful, tuneful Symphony.

Maurice Ravel: Couperin Suite for Piano

Marice Ravel is one of my favorite composers.  I'm not so crazy about his works as to love every one of them.  (Bach is a favorite, too, but I don't love every piece by him, either; the same with Mozart, Haydn, Beethoven, Mendelssohn, Brahms, Debussy, Wagner, and so on.  But with Ravel, I've liked everything from him I've heard so far.)

One of the earliest pieces of Ŕavel's that I learned to like was Pour le tombeau de Couperin, a collection of orchestral pieces, in celebration of the French composer Francois Couperin.  I have heard hardly any music by this older composer, but evidently Ravel admired him. 

The Tombeau that Ravel wrote, though, was fabulous.  In contrast to the music of Bach and Wagner that I liked as a teenager, that was filled with the exalted German harmony that was easy to love, Ravel's music was light, and full of fairy filigree!  You could imagine tiny fairy people dancing, skipping to this music. 

I then learned that the few orchestral pieces in the orchestral  Tombeau were an arrangement of an earlier piano work by Ravel, and that early version had more movements. 

That did make sense, because Couperin was a composer of keyboard works, harpsichord, and maybe piano.  I recently heard this piano (original) version, and I fell in love all over again. 

I urge my readers to listen to this work for themselves; skip over the movements that aren't to your liking.  There's nothing that says you have to like every movement of a multi-movement work.  Here's a link to the piece I was listening to:

Ravel: Le Tombeau de Couperin

Mendelssohn's Octet for Strings

I featured the Scherzo from this work in the radio show Archie's Archives.  This afternoon, though I got a desire to hear the whole thing—four movements—in its entirety.  Somehow I had a CD of it in our car, so we could listen to it on long journeys.  I must have listened to this CD, because I was familiar with both the first movement and the third movement (the Scherzo, which is especially famous).

Mendelssohn is a composer whom I especially like; very possibly because of he having written this very Octet.  Musicologists note that octet that had been written by other composers, before this one, were actually two quartets, seated across from one another, playing antiphonally.  (I'll explain that another time.)  Most importantly, Mendelssohn is said to have instructed that this octet was to be played not antiphonally, but as if all the players constituted a tiny orchestra.

Mendelssohn wrote a lot of chamber music,  that is, Trios, Quartets, Quintets, Duets, etc.  Every weekend, they had a concert night in the Mendelssohn household, which is a huge incentive for the young folk to compose their own music to be performed at these musical evenings.  (The Octet was composed when Mendelssohn was 18.)  Felix and his sister, Fanny, were both accomplished instrumentalists.  In fact, Fanny was also a composer.  Felix's string quartets are among the best known string quartets we have, together with this of Haydn, Mozart, Beethoven and Schubert.  (Shortly after Haydn's time, lots of composers began writing String quartets.  The reason being that any group of friends, two of whom could play violin, and one play the viola, and one play the cello, could form a string quartet, and frequently did.  All these amateur String quartets were on the lookout for music to play, and anyone who composed a string quartet was reasonably sure of getting it performed fairly promptly.  It's no fun writing a String quartet if nobody plays it, I can tell you.)

One of the important aspects of a String quartet is: counterpoint.  This is a hard property of a piece to describe, but it makes a piece so much more interesting to listen to!  And Mendelssohn was a master of introducing just enough counterpoint to make his music interesting. 

[Bach, writing music some decades before, was a master of counterpoint.  Audiences of the late 1700s found so much counterpoint difficult to tolerate, and Mendelssohn found just the right degree of counterpoint that was pleasing to audiences of his time, and even our time.]

In the recording I own, the First Movement was the longest, about 15 minutes long; each of the others were about 6 minutes long.

Magic Moments

There was a tune that had been stuck in my head, for close to 50 years!!!  I can almost remember the year, roughly, when I heard the tune; it was around the time the Disney movie The Lady and the Tramp arrived in theatre's in our town (the City of Colombo, in the land of the Brave, and the home of the Coconuts).  This is going to be s confusing story-- not least because of the coconuts, I suppose-- but try to follow.  While waiting for The Lady and the Tramp, I think I heard an instrumental version of Mac The Knife.  I somehow learned the name of that tune, but the two tunes were somehow connected in my memory, and I learned a lot about Mack the Knife, but absolutely nothing about the other tune!

I had got to the point where I was considering writing down this unknown tune from memory, making an mp3 out of it, and putting it up on fB, and asking if anyone knew the name of the tune!  That brings us to today, when, our of the clear blue sky, a video of the song comes over my fB feed!!!

How did fB know that I was interested in this tune?  Maybe I was humming the tune to myself, and some AI program heard it!

Anyway, the song is called "Magic Moments," and is sung by Perry Como.  Perhaps it's just as well I didn't go through with putting the tune up on fB; I had gotten some little details wrong in how I remembered it. 

Well, that's my post for today!

Archie

Santana covers a Beatles Classic

What came across my fB feed but a video of Santana's cover of the Beatles classic "While my guitar ..."

What's sad about this version is that the song is sardonic in its very intention ["I look at the floor, and I see it needs sweeping ..."]  It's not a lovesong, by any stretch of the imagination!

In the original, sung by George Harrison, the guitar solo, where the 'weeping' happens, still makes sense, though it isn't George playing it; it's Eric Clapton.  In Santana's cover, he has a woman singing the words, and there is a feeling of humor in it that may or may not be intentional!  

This song---and this is not why made the remark about Santana's cover---is considered important above and beyond its intrinsic significance as advancing the Beatles'style.  Some rock musicologists claim that it is the birth of Heavy Metal.  I don't really know what heavy metal is; of course I know, in a vague way, what it's considered to be, but in a question about the birth of something, you have to know precisely what the thing is.  That extended guitar solo might or might not be the mother of the sub-genre of Heavy Metal, but it is an interesting thought.

Well, to quote the immortal words of Forrest Gump: That's all I have to say about that.

Queen

[This was first posted on "I Could Be Wrong'.]

I found myself calling out:  'I see a little silhouetto of a dog!'  And I added, Scaramouche, Scaramouche ...

Can you believe how much Queen has impacted our generation—and those immediately following? 

When our daughter and her OM team had gone into regional competition—usually at Berwick SD—they usually had "Another one Bites the Dust" playing over the speakers (and, of course "We will rock you").

A friend of mine, from our choir days (Messiah,  Nelson Mass, Christmas Carols) brought 'A Night At the Opera', and we (and Umanga) thoroughly enjoyed "I like to ride my bicycle" and other jewels!

And last, but certainly not least, there was 'Somebody to Love', and let's not forget the version with George Michael!

They were the Champions. ... Maybe I can talk our Band "The Encores" into playing a Queen song.

The Recorder in the Music of Bach

There was a time when I thought that all the flutes in Bach pieces were, in fact, recorders.  (I mean the so-called blockflute, that has a built-in whistle mouthpiece, see pictures below).  Later, I discovered that even the usual transverse flutes (called Flauto traverso in Italian) had the tone I was associating with recorders. 

This is one of the Brandenburg Concertos, written by Bach as a gift for the Margrave of Brandenburg, as a sort of calling-card.  (He was hoping for a position at that court, or at least a commission for a work.)  It is a concerto for multiple instruments (a concerto grosso) in this case for three recorders, a solo violin, and a harpsichord, and strings.  The recorders are prominent in the whole work, and create a truly magical fairy-like, or heavenly effect.  All through my teen years, this was one of my favorite pieces, and if you're not careful, it might get adopted by your kids, too.

https://youtu.be/Ra29AHsZQSQ?si=CvzIggOzk-jWxbN_

The Meaning of Music

The title to this post is ambiguous.   So much so that its intended meaning might not strike the reader at all.  What I mean is that certain music phrases have been used, for centuries, to convey certain musical feelings and moods; so much is obvious.  But we expect that they convey different feelings to different people.  No!  From hearing the same phrases used with the same meaning (by different composers) so often, music lovers can begin to understand a conventional meaning to these phrases, which the composer could (I'm not saying they consciously do, but they could choose to do so) use them to underline particular feelings!

On my own, I had begun to think this way as a teenager.  But then, I came across a book by Deryck Cooke, a somewhat specialized British author and musicologist—now dead—called The Language of Music, in which he tried to prove this very thesis: that certain musical phrases can be used intentionally to convey specific emotions. 

Cooke is best known for his thematic analysis of Richard Wagner's Ring of the Nibelungs.  This is a cycle of four operas, based on an epic poem, and—I believe—certain germanic myths and legends.  These matters could take an interested music lover a lifetime to get to the bottom of, but the basic idea is that Wagner deliberately used musical melodic fragments—called Leimotifs—to convey the dramatic logic, the cause and effect, of the thoughts and actions of the protagonists of the opera.

Soon after I had learned about Deryck Cooke, I stumbled on a two-CD album, with copious accompanying notes and musical illustrations—today easily available in almost any public library; certainly in our own—in which he sets out his analysis of the Leitmotifs of Wagner's Ring Cycle, and I for one think his analysis is exactly on the money.  It is a huge edifice; and that's what the opera cycle needed, lasting close to fifteen hours, total, to hold it together.

I'm not going into the Wagner operas today.  But the old hymns of Easter illustrate one of the family of musical phrases that are most obvious, in those that I recognized as a youth: triumph, and joy!

Those two words, more than any others, encapsulate what Believers feel at Easter.  (In the interest of full disclosure, I'm an atheist, but anyway ...)  Actually, there are two emotions I want to talk about: the feeling of triumph; and the feeling of completion.

The rising scale.  In the scale of C, the notes C, D, E, F, G, in sequence, convey a feeling of assertion, a feeling of having something to say.  Even just the rising triad, C, E, G, which sounds like the beginning of a fanfare, sounds like a challenge, or even a defiant challenge.  And there is a feeling of uncompleted business.  (Note that, almost necessarily, the meanings I'm trying to convey are vague.  There is no exact correspondence between musical meanings, and literary meaning.  The phrase can be abbreviated to just a rising fifth: C-G, and still convey that feeling of a challenge, or just a question: What?!

The second phrase I want to describe is the descending scale: C' B A G F E D C.  As Deryck Cooke describes it, this musical phrase conveys a feeling of coming home, of closure.  The two half- phrases C' B A G, and F E D C convey parts of this idea of conclusion. 

In a lot of Easter music, these two phrases are combined, to convey a challenge, triumph, satisfaction, the conclusion of an argument.  The easiest examples are, of course, Easter hymns. 

One of the oldest, and most famous Easter hymns is: The strife is o'er, the battle won.  The tune by Palestrina sorry  Melchior Vulpius, I believe, incorporates both the challenge tune, and the satisfaction tune. 

There is another hymn, not as ancient, nor as well known as the Palestrina: This joyful Easter tide, often used as an anthem for Easter.  This tune, too, incorporates the two phrases, for a challenge, and for a successful conclusion.  If I can, I will color-code the examples. 

Here is the music of The Strife is O'er, the tune of Melchior Vulpius.  Again, the tune dates from around 1611:

The tune for the first two measures has the descending phrase, which I described as conclusive, satisfaction.  The next phrase or two, in the example, raise the challenges; the ending descending scale repeats the satisfactory conclusion.  In fact, the entire tune is replete with satisfaction, confidence, and, I suppose, celebration.
 

Here is a reconstruction of This Joyful Eastertide, which is apparently derived from a Dutch tune of the 17th century, harmonized by the well-known arranger of sacred music, Charles Wood (but here by me).

The first complete measure has the ascending tune of assertion and challenge.

The last three complete measures have the complete descending scale of F major!  As a treble, I loved to sing this line, and I'm sure, so does anyone singing this part.

Conclusions

Both these examples are from the 17th century, and that's not a coincidence; that was the era of protestant congregational singing, and that doubtless had a lot to do with establishing the emotional content of musical phrases.  Some would argue that this entire phenomenon flows from hymnody.

Arch

'Bist du bei mir'

Anna Magdalena's Notebook

 Johann Sebastian Bach's second wife—to whom he was married at the time he died—was Anna Magdalena, a woman much loved by many generations of music-lovers, and certainly Bach-lovers.  Anna Magdalena maintained an album, in which she copied many short pieces by her husband, and many other pieces that took her fancy.

Among these is a remarkable aria: Bist du bei Mir, which was, identified last century, to have been written by Heinrich Gottfried Stölzel, a talented contemporary of Bach's.  (In fact, a biographer of Stölzel is said to have declared that Bach and Stölzel were equally talented.  However, Stölzel did not have nearly as great an impact on music as did Bach.)

I've joined the New Horizons band for seniors in our hometown, and this spring, we're performing Bist du bei mir, arranged for band.  When I was 17 or so, a friend of my parents was anxious to teach me violin.  So I was given the loan of a violin, and asked to practice this very piece.  At that time, I had never heard it before, and thought it a fussy little tune; I had been told it was by Bach himself, and I told myself that it couldn't possibly be by Bach, whom I revered.  Soon my violin teacher gave up on me, saying that my intonation was too 'piano-like', by which she meant that my ear wasn't good enough to tune my fifths according to the just intonation that string players use, but that I was playing 'piano fifths', that were just a tiny bit out of tune to the ears of violinists.  (Hardly anyone today can tell the difference, unless they're temperament experts, which I certainly am not.)

The Stölzel aria, I have come to recognize for half a century, is just a gem.  Early in the aria, there is a chord that I described in the post about Harmonica Harmony, the dominant ninth but without the root.  There are numerous features in the song that provide 'hooks' for anyone wanting to hear it, but no hooks are necessary; it is a brilliant tune, evidently recognized by Anna Magdalena Bach, who was an extremely musical person.

Bear in mind that the tune is, basically, an aria, that is, a song.  Most of the recordings of it on YouTube emphasize the soprano line.  But to me, the counterpoint is wonderful.  Without being obtrusive, the parts caress the melody, giving the accompaniment a lot of character.  In orchestral arrangements, the counterpoint is usually smothered, but here is one, FWIW.

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.

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 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