Music of the Christmas Season

All the music that floods the air during the season (especially the shopping season, gotta love it) brings out strong reactions from listeners, usually bad reactions. 

Let me start at the beginning. As a child, my earliest Christmas memories were the most common carols and hymns:
Adeste Fideles (“O come all ye faithful“, from a medieval Latin poem, evidently by a British monk during the Roman occupation);
Stille Nacht, hurriedly composed by Francis Grüber one night when the organ was out of commission, and they had to have carols accompanied by a guitar;
“Ding dong merrily on high”, played on our ancient His Master’s Voice gramophone (phonograph). [Note: “Ding dong merrily on high”appears to be sung to a French (dance) tune, Branslé Officiél.] 

There were also local carols, hardly ever heard outside a 100-mile radius of where I grew up. As I grew older, I found myself participating in actually singing these carols, and since my mother was the local musical impressario, I began to learn unusual carols, taken from the pre-eminent scholarly carol book of the time: The Oxford Book of Carols, edited by the venerable Martin Shaw. To this day, some of those carols remain relatively unknown, and as such the book remains an excellent source for ‘new’ carols. 

Eventually I got old enough to sing in the school choir, and I came under the influence of the celebrated carol festival of King’s College, Cambridge. This influence, felt throughout the Episcopal Church, had both good and bad consequences: the use of boy trebles and male altos, the use of the organ to accompany everything, the use of Victorian harmonies, and a strict metrization of the carols, and the canonical nine readings from the bible. The choir was moderately small, consisting of sixteen trebles, and about four each of the other parts. The director of the choir for many years had been Sir David Willcocks, and his personal influence over the Christmas Carol Industry has been enormous. 

The next, and final, step for me was to be given responsibility for an entire service of carols. I became interested in where the carols came from. They were medieval Christmas dances, for the most part, since Christmas had replaced the ancient midwinter festivals that kept up the spirits of the dwellers in northern climes during the dark, dismal days of December.  (Say that ten times real fast.) 

Romanticism has many aspects; two of these are exoticism and eroticism. Though in common parlance, the word romance is most often understood in its erotic sense (romance novels, etc), the exotic aspects of romanticism is almost as important (e.g. Orientalism, Science Fiction, Egyptology.) Thus, carols fascinate us especially if they are from ancient times (remoteness in time) and from far away (the East, South America), or unusual in some way (Latin rhythms, calypso) or accompanied by unusual instruments. (For instance, consider “Mary’s boy child,” made popular by Harry Belafonte, and Nina and Frederik.) So when people look for variety in Christmas music, they look at these alternatives, since the spirit of romanticism is complementary to the nostalgia of Christmas. 

This post has been influenced by my friend Ileana, who wrote to me deploring the fact that most stores and radio stations keep playing the same songs, until they sound too hacked to be tolerable. The ‘variety’ offerings in the CD market are very dull, and unavoidably so, since the variety offered is relative to the compiler, and, most of all, constrained by the necessity to be marketable.  This means that the contents of the CD must appeal to the widest possible audience, which in turn means that they must be dull, by definition. Dullness in taste is apparently a survival trait in the human species. (The individual who survives to propagate his/her genes is the one who has not been bored to death before he or she can do the propagation.) Wouldn’t it be lovely to have a Christmas collection that one could play through the season, through the quiet hours before midnight of Christmas Eve, to the first few carols of Christmas Day itself, and more lighthearted songs for later in the season? I would like to see a collection along these lines: 

(1) Traditional hymns tastefully performed: O little town of Bethlehem, O come all ye faithful, Brightest and best of the suns of the morning, etc. And let’s not forget Quem Pastores Laudavere. (A slightly more renaissance-sounding version is here.)
(2) Traditional French carols, e.g. Il est né le divin Enfant. Charpentier has immortalized several of these in his Midnight Mass for Christmas.
(3) Traditional German carols: Es ist ein Ros entsprungen (sung here by the choir of the same St Thomas’s Church School at which Bach worked when he was alive); Wie schön leuchtet der Morgenstern (the clip is of an elaborate setting by Bach, his opus No. 1, movement 1.); Vom Himmel hoch; as well as chorales made famous by Bach: In dulci jubilo, Break forth o beautious heavenly light; modern German and German-Swiss and German-Austrian carols, including Silent Night (Stille Nacht), and German versions of lovely Latin carols: O du fröhliche, o du selige; etc.
(4) Medieval English carols: Lully lulla, thou little tiny child; He came all so still; Lullay myn lyking; ...
(5) Medieval Basque, Catalonian, Spanish and Portuguese carols.
(6) Carols from the Middle East, and Eastern Europe: the Cuckoo Carol, the Zither Carol.
(7) Modern carols from other lands, tastefully selected. An example is Arirang, a carol created by Malcolm Sargent from a Korean Lullaby, and Ariva-rararo, a carol in a collection by D.T. Niles, from a Tamil lullaby. Cantique de Noel, by Adolphe Adam (sung by Joan Baez), (sung by Roberto Alagna).
(8) Modern English carols, e.g. The Little Road to Bethlehem (Michael Head), one of my favorites. Another lovely arrangement is by R. R. Terry, of Myn Lyking, with a string accompaniment by John Rutter.
(9) Last, but not least, Celtic carols, and carols of Ireland. Searching for an Irish carol, I stumbled upon the Cherry Tree Carol, which I had always thought of as English, but what do I know? 

If I do not see you before Christmas: a merry Christmas, a happy holiday season to all my readers, and any others who happen to stumble upon these pages! 

Arch, blissfully listening to Schlafe, mein Liebster

History, Literature and Music

All through school, I just could never get my head around History. It started out inauspiciously enough, with plain ol' history, which was the usual stuff about kings and tribes and war, and on a good day, pestilence. Then what should to my agonized eye appear but: The History of the Kings of Israel. (Israelly important to know this stuff?) This was when I first realized that there was History, and then History of this, and History of that. History of Fashion, History of the Theater, History of the Bible, History of Medicine, History of Methodism. It dawned on me that plain ol' History was merely the history of politics. 

When did I first become interested in History? It was not all at once; it happened obliquely. I was given a book of Letters of Composers, a fabulous book that everyone should not only read, but own. It started with the letters of the composers of earlier times (all in translations) and proceeded to the letters of Tchaikovsky, and he wrote some interesting letters. Schumann, as you could expect, wrote up a storm, but Mozart gave him a good run for his money. Once I had read this book from cover to cover, suddenly I had an actual mental image of what these guys were like. It was startling for a kid of sixteen to realize that they were quite distinct personalities. (OK, so I was a pretty retarded sixteen year old.) Then I happened to get my hands on an enormous book called the Oxford Companion to Music, which had actual engravings of the masters, enormous full-page portraits of Bach, Handel, Mozart, Brahms, Wagner, and so forth. And Mendelssohn. I was beginning to take Mendelssohn seriously. I had heard the famous violin concerto, of course, but I had assumed that old Felix was a two hit wonder, at most. But as I grew more interested in his stuff, I began to take note of the pictures available of him. About this time, too, my high school principal had given me a book to read called Johnny Tremain, which was all about Paul Revere and the revolution. I began to get interested in people such as Benjamin Franklin, George Washington, and William Jefferson. Abraham Lincoln followed soon after. Years later, it was as I was watching Little House on the Prairie on television that it struck me: half the guys were dressed in knee-length breeches, like Franklin and Washington and Bach and Handel, while the more affluent storekeepers dressed like Lincoln and Mendelssohn. By this time I had seen a portrait of Oscar Wilde, and he looked as like Felix Mendelssohn as made no difference to me. [The knee-breeches were going out of style, and the full-length pants were new, and initially more expensive. Eventually, people wore pants most of the time, while they used their old breeches for farmwork, etc. You see this too in the Little House on the Prairie tv series, where breeches were worn for work, and pants for Church, for instance.] So it is that my insight into history, which was based on the idea of contemporaries, was sparked by my interest in fashions. 

Soon afterwards, I became interested in the middle ages, the early renaissance, and ancient Greece and Rome, all spearheaded by my interest in clothing. (I'm by no means a natty dresser; for me fashion is the study of the clothes of other people than myself.) What people wore explained a great deal about what they did on a typical day: fighting, or keeping the weeds down, or bringing in a catch of fish. 

Yet another dimension was opened up when I began to be interested in the History of Mathematics. It so happens that the History of mathematics is less important to mathematics as such than the histories of other subjects might be to them. Mathematics at work is in an eternal present, which has subsumed all foregoing understanding of the subject. Still, it is intriguing to learn what the fathers of the subject dreamed up to accomplish something that is done today in quite a different way. As one learns about mathematicians of the past, their costumes and portraits, too, establishes each of them as a contemporary of a musician or a politician, or an author or philosopher. These isochronous layers, to coin a phrase, serve to make sense of the motivations and accomplishments of all these important figures of the past, in whatever field they worked. It is similarly interesting to analyze the stories of the Bible in terms of the level of development of the culture in which they were set. Abraham, for instance, was a stone-age nomad, and his sacrificial knife is often depicted as a flint implement. By the time Solomon came around, they were bronze-age, and presumably there are biblical sources that will establish the precise chronological and cultural facts, in terms of religious specifications of how things were to be done. (I'm keeping a straight face here with some difficulty, but that's why it's called a religion, because it doesn't make much sense.) The Romans, of course, were ultimately deposed by iron-age barbarian warriors, if my memory serves me right, and at least the current thinking in the world of speculative fiction is that the greatest legendary weapons of ancient heroes were probably forged from meteoritic iron. 

As always, the anthropological implications of the various lifestyles, from hunter-gatherer, to nomad, to farmer, inform the stories one reads. Thus History reveals itself as the ultimate application of the principle that connections are the path to assimilating information into knowledge. To the consumer, History is simply a matter of structuring facts and events into some semblance of cause and effect. (To the purveyor of history, the Historian, it is much more: it is a matter of persuading one's readers of one's prejudices, and is a subtle skill. But since they make money out of it, they can do their own damn writing and not look to me to do it for them.) 

To end, The Mists of Avalon, by Marion Zimmer Bradley presents the legendary King Arthur of Britain as one of the earliest kings of the post-Roman era. Her point of view makes amazing sense of the clash of the pagan and the Christian influences in the story. To a Briton, the Arthurian legend is probably connected with various landmarks, the legend of Joseph of Arimathea, Salisbury Cathedral, and the Holy Grail legend, which would serve to place it in a vaguely historical context. For me, though, it was Mists that provided that invaluable service. (Many critical reviews of Bradley's novel focus greedily on the fact that it was supposedly a feminist perspective on the Arthurian legend. In fact, Bradley does far more than simply provide a feminist perspective: she presents the action from the point of view of Christian expansionism, a potent force which complicated the gender issues in many ways. But from our vantage point in the 21st century, it is no longer necessary to use feminism as a crutch to bolster an analysis of a literary work. Feminism should illuminate everyone's thinking, rather than that of a few isolated feminists.) 

Hardest of all, in studying history, is to understand the mind-processes of the protagonists, carefully allowing for the fact that the intellectual environment of another age is simply different from ours. Genocide, for instance, is abhorrent to us. But that attitude is the result of history. As we go backwards, we must judge genocide by Hitler differently than genocide by Genghis Khan, or the Crusades, or the Aryan Invasion of Asia, or Cortez in Mexico. Though abhorrence is inevitable, the same abhorrence for the same crime at different historical times simply becomes an obstacle to understanding history. 

Archimedes, who could be wrong

Dreaming: Wagner's Songs

Unlike most other composers who wrote for the voice, there are few instances of Wagner's writing available for the concert stage; if you want to hear just a single item for a tenor, for instance, you have to hear what is delightfully termed a bleeding chunk from one of the operas. (One of the opera, we should say; opera is the plural, after all.)

There are a few notable exceptions, such as The Prize Song from Die Meistersinger, sung here by the celebrated Canadian tenor, Ben Heppner. (This is the song of a youth, smitten with love. In his defense, we must note that Ben Heppner has been singing this role since he was a young man, with great success.) Here is another rendition by Peter Anders, in which the orchestra has been captured better than in Heppner's live version.

Because Wagner wrote his operas in a seamless style, not wanting it broken down into "musical numbers", as are Broadway musicals, for instance, and certainly Italian Opera, it is hard to slice out a "song" from the continuously evolving melodic texture of the opera. He found the choppy style of recitative, aria, bridge too artificial. In fact, Wagner wanted to create a single art-form that encompassed art, music, poetry and drama seamlessly all in one. In a Wagner opera, the protagonists declaim their heroic utterances as if they were instruments in the orchestra, in contrast to earlier styles of opera, where the orchestra backs down to the role of an accompaniment when an aria takes place. (Note that Wagner's artistic ideas have the potential to be realized in Cinema. My Fair Lady, for instance, despite its sectional structure, comes close to this almost seamless unity of visuals, text and music.) As a result, the vocal music of possibly one of the greatest composers for voice is unavailable for enjoyment in the concert hall. Almost.

It so happened that Wagner had an affair with one Mathilde Wesendonck, the wife of a banker. She was a poet, and she gave him a number of her poems, to set to music. Wagner did this, and there is a set of five songs --Lieder, as they are called in German-- and they are beautiful. [A portrait of Madame Wesendonck is at above right.] The songs were originally for voice and piano, but were later orchestrated in Wagnerian style by Felix Mottl, and were recorded by such famous Wagnerian mezzo sopranos as Kirsten Flagstadt, and clips are available on YouTube. Much later, a light scoring of the Lieder was undertaken by Hans Werner Henze, for chamber orchestra and voice. A beautiful example is by Marjana Lipovsek. (I'll try to upload a clip one of these days.) A videoclip of Der Engel (The Angel) sung by Silvana Dussmann is available on YouTube.

[Added later: Der Engel sung by Waltraud Meier.]

Arch

[P.S. : None of the links work, because of an "upgrade" to the blogging software!  Gotta love it.]

BBC Composers of the Year for 2009

Apparently the BBC has decided to select four composers for the year 2009: Purcell, Mendelssohn, Haydn, and Handel.  

Purcell -- Henry Purcell (1659-1695) was the earliest of these composers, and the one who can be considered most British of them all. (There appears to be nothing anniversarial about his selection for the year 2009.) He is clearly one of the most brilliant composers of the time, and the British are fond of declaring that it was just bad timing that prevented Purcell from having as large an impact on western music as Bach himself. This is probably true; just as Bach did, Purcell delighted in writing beautiful dances for orchestra, (some of them featured in Jane Austen films, e.g. Pride and Prejudice), and in the pleasure of complex harmonies. Ayres for the Theatre is a collection of dance music and concert dances intended to be played between the acts of plays in London. [Here is an excerpt from the music for Abdelazer, immortalized as the theme in Benjamin Britten's Young Person's Guide to the Orchestra.] Just like Mozart some years later, Purcell loved the theatre, and spent so much time there that he was locked out of his house one night by his wife, and subsequently died of pneumonia (or something similar they had at that time. Pneumonia had not been yet invented. Ancient diseases, as you know, dear reader, were not as good as modern ones.)

Note: a popular march called the Prince of Denmark's March has long been attributed to Henry Purcell, though it has since been established that it was composed by Jeremiah Clarke. This error puts hardly a dent in Purcell's amazing output. One of Purcell's greatest works is a masque called Dido and Aeneas, which contains some lovely music. He also wrote incidental music to Shakespeare's Tempest, as did Thomas Arne and others.  

Handel -- Georg Friderick Händel was a contemporary of J.S. Bach, and lived in Halle, in Saxony, not far from where Bach was born and lived most of his life. In contrast to Bach, Handel traveled south, through Italy, finally arriving in Britain. While he traveled, he absorbed all the music he heard, and in fact his musical writing was a wonderful synthesis of German and Italian styles, with the Italian sensibility predominating. (Bach admired this style, and adopted it as far as he could in his arias, with moderate success. Apparently his German tendency to work a theme extensively got in the way of the leaner profiles required by the Italian style. Don't quote me on this; I'm not an expert.) We know Handel best for his oratorio, Messiah. He wrote brilliant operas, though, whose quality exceed that of Messiah by many estimates, as well as other oratorii, such as Israel in Egypt, which I have heard nominated to be his greatest work. The Watermusic Suites and the Music for the Royal Fireworks are delightful, grand works for royal celebrations, the kind of thing the British aristocracy love so much. Handel's music deserves to be heard more than it commonly is.  

Haydn -- Franz Joseph Haydn was an Austrian composer of great significance. The year 2009 marks the 200th anniversary of Haydn's death. The vast majority of his music was composed at the court of the Esterhazys, a wealthy aristocratic family. Haydn, in retrospect, was very much influenced by a couple of visits to Britain, at which time he heard the wonderful works of Handel, as well as the British national anthem, which he admired greatly. Subsequently, with the encouragement of one Baron Gottfried van Sweiten (whom you can see in the movie Amadeus, having been a popular visitor at the Viennese court), Haydn composed his last masterwork, The Creation (Die Schöpfung), which is claimed to be one of the last of his works he heard performed. (When I see that German title, I keep thinking: when the going gets tough, the tough go Schöpfung.) [Here is a clip of Nun beut dir Flur das frische Grün, a lyrical aria that expresses the delight in the verdant woods.  Note 2018/4/9: Blogger has eaten all the video links that had been inserted in these posts, and any you are seeing in these early posts were repaired by me just today, and only a bare minimum have had the treatment.] Haydn also wrote the national anthem of Austria, whose tune is still used in the present German national anthem, and is a model of restrained patriotic musical rhetoric. (The clip features modified harmony.) One must not forget to mention a couple beloved concertos for the 'cello, as well as a trumpet concerto, also played as a concerto for recorder, oboe or flute. And finally, it was Haydn who perfected the classical string quartet, much admired by Mozart. Mozart was born after Haydn was born, and died before the latter, and the two men were musically much influenced by each other to the good. And Haydn was one of Beethoven's teachers. In Haydn's vast output are also numbered a hundred symphonies, a genre that he helped develop, along with the sons of J.S. Bach, in particular Johann Christian Bach. In recognition of his contributions to music, Haydn was granted an honorary doctorate by Oxford University on one of his journeys to Britain.  

Mendelssohn -- Felix Mendelssohn-Bartholdy was born to a Jewish family that converted to Lutheranism in the 18th century. 2009 marks the 200th anniversary of his birth. A renaissance man, Felix, together with his sister Fanny, were adept in numerous areas, including painting, literature and music, and had wide interests in all areas of Art. Felix began composing at an early age, and one of his most celebrated compositions originated at around the age of 15, or possibly earlier. The Octet for Strings is a lively work for eight stringed instruments -- four violins, two violas, and two cellos. (Some modern performances add a double bass, as far as I know not in the original scoring.) Its Scherzo, the third movement, is justly famous. Two of Mendelssohn's string quartets are gorgeous, and delightful to play. As did other German composers before him, Mendelssohn traveled through Italy, and eventually to Britain, and Scotland. He was much impressed by the natural beauty of Scotland, which he celebrated with the Hebrides, or Fingal's Cave overture. He wrote several overtures, all still in the orchestral repertoire, and numerous chamber works, and vocal pieces, such as On the Wings of Song. [Clip: Victoria de Los Angeles.] His overture to A Midsummer Night's Dream is one of his most famous compositions, in addition to the magical Violin Concerto in E minor, and his last few symphonies. Long before these last symphonies for full orchestra, he had written symphonies for strings only, to be performed at private musical evenings in the Mendelssohn home with their family orchestra. The British have a particular fondness for the composer, even if his music is not considered as British as that of Handel and Purcell. Still, his oratorio Elijah was a regular offering in Britain through the last century.

A lovely aria from J. S. Bach

I have heard this aria (solo vocal movement) many times, but it was only recently that I began to really notice it. This is a recording of Andreas Scholl, on YouTube. I looked up the piece on Amazon, wanting to buy an Mp3 of it, and one of the more beautiful renderings of it is by a French mezzo soprano called Guillemette Laurens.


Another offering of this aria is by one of my most favorite sopranos, Magdalena Kozena. Unfortunately, it is taken too fast, making the words come out as rather a tirade, whereas it is probably intended to be a reflection. Another treasure hiding in YouTube is a recording by Alfred Deller, one of the earliest of the celebrated counter-tenors, and you can hear why he was so celebrated. Janet Baker, one of Britain's most precious voices, a woman with an austere and disciplined lyric talent, has recorded this cantata (BWV 170) for EMI, and I'm eagerly awaiting its arrival. Unfortunately it is not available on YouTube. I listen to the music, and it is almost as if Bach is trying to explain something so earnestly that he is in pain. The song is about renunciation, that true peace is not obtainable except in god. The music alone seems able to give some inkling of this sentiment. The solo wind instrument is a sort of oboe that was just going out of favor at the time of Bach: the Oboe d' Amore. Now, of course, the instrument has been revived, especially for use in the music of Bach and his contemporaries.

Archimedes

Archimedes meets Myers-Briggs

It might delight my readers to know that your favorite blogger (I know, I know, ok, second favorite blogger) is of type ISTP: The Mechanic, according to Typealyzer, a website that analyzes a blog and tells you what sort of person the blogger is. Yours truly is...

The independent and problem-solving type. They are especially attuned to the demands of the moment are masters of responding to challenges that arise spontaneously. They generally prefer to think things out for themselves and often avoid inter-personal conflicts. The Mechanics enjoy working together with other independent and highly skilled people and often like seek fun and action both in their work and personal life. They enjoy adventure and risk such as in driving race cars or working as policemen and firefighters.

Maybe these guys know more than I know about myself. I am one of the biggest chickens you ever saw; firefighting--I think not. And I am not the artistic type, apparently. But, you know what? I did submit the blog of an artistic friend of mine, and it did come back with "artistic, soft-hearted type," which does describe this particular person frighteningly accurately. So there you have it. Pretty soon the Internet will know exactly how to sweet-talk us into what it wants.

[Added Later:] I decided to independently verify my personality according to the Myers-Briggs Type Indicator. (The subject was initially studied by a mother-and-daughter team in the early 1900s, and developed partially with an eye to placing women in effective wartime jobs.) According to an on-line test by HumanMetrics I am an "ISFP", that is introvert, sensing, feeling, perceiving. This is all very alarming to a trained mathematician such as myself. We do not sense, we do not feel, we do not perceive, we KNOW. Golly gee, this is embarrassing in the extreme. However, I was somewhat mollified by the list of other folks in the same category, namely: Princess Diana, J.K. Rowling, John Lennon, Florence Nightingale. These are four of my most favorite people. [Important note: Florence Nightingale was one of the matriarchs of modern statistics.]

2018-4-10: This just in: I repeated the Typelyzer test, and we have been re-allocated to INTP.  I also submitted Archie's Archives, our companion blog, and that did come in as ISTP.  So I guess I'm more mechanical when doing music on the radio.  No wonder the radio station went on the fritz...

Archimedes, always the cynic. The Mechacynic.

Rachmaninov: Symphony No. 2

Listening to the early morning syndicated program featured by my local Public Radio station, I was startled to hear a very familiar melody. I had heard the announcer's introduction and registered it subconsciously, but had not grasped it completely. The words that popped into my mind each time the melody returned were: "Never gonna fall in love again!" In contrast to the determined sobriety of the words, the tune was quite jaunty to begin with, though it retreated into a rather injured melancholy, only to make a sally again with some slight optimism, and so on. Of course, I had to find out more.

As soon as I could wake myself up enough to get on the Internet and find out more, I discovered that the playlist of this early-morning filler program that was aired before Weekend Edition was not published with the same meticulous care as were those of the NPR programs and those created at the local studios. The only clue I had were the words "Never gonna fall in love again," and I didn't know for certain that it would be "gonna" rather than "going to". As it turned out, I myself knew at least two songs that had many of those words in them. Google gave numerous references, including songs by New Kids On the Block, and so on. What I needed was a source that would play the songs right away. The next stop was YouTube, and within seconds I had a hit with Eric Carmen. This was the song I remembered, a jaunty tune, with rather peevish lyrics that expressed the unworthy feelings many of us experience at the demise of a love affair. The sumptuous sound of the orchestral version I had half-heard while still asleep, with its broad repeating sequences was in weird contrast with the popular song, though the song faithfully retained the harmony of the original. Going back to Google, I was sent to Wikipedia, which had not only an article on Eric Carmen, but on this specific song, with a pointer to Sergei Rachmaninov's Symphony No. 2.

Of course I had to narrow down the actual movement. Going back to YouTube, I found several clips of this symphony, and I finally hit the jackpot with Movement 3. It was precisely this movement that I had heard; a sweetly earnest assertion of youthful desire, still not in the stage of disappointment expressed by Mr Carmen. The youthfulness of the Rachmaninov movement is actually quite comparable to that of the popular song; but where the symphonic movement is romantic and positive, the song is ambiguous and negative. Still, Mr Carmen has to be congratulated on a song that deserved better than it got, in my opinion. And he deserves a lot of appreciation for pointing me in the direction of Sergei Rachmaninov's Second Symphony.
Archimedes

Leonhard Euler: Mathematical Genius

It is strange, but true, that not a lot of people enjoy reading about mathematics, or doing pretty much anything with it. This post is aimed at the exceptions, and especially those who are on the edges, just becoming interested in the subject.

In the early 1700s, mathematics had just taken off like a jet plane, shortly to be more like a rocket. Newton and Leibniz had just invented Calculus, and Johann Bernoulli, a brilliant Swiss mathematician, had turned his mind to inspect everything that the theory could do, and had asked the big theoretical questions that would drive the engine of mathematical discovery in the next hundred years or so. It was an exciting time in which to be a mathematician.

William Dunham, of Muhlenberg University has made a particular study of Leonhard Euler, one of the greatest mathematicians of all time, born in Basel, and a protegee of the famous Bernoulli. In his book "The Master of Us All", Dunham describes some of the most accessible and interesting of the discoveries of Euler, making a point to underscore the intuitive methods Euler used, which though not acceptable as formal proof today, reveal the amazing mind of Euler.

To the layman, the idea of an infinite series might be a little strange. An infinite series is simply an addition of an infinite number of terms. Generally, a sum of infinitely many terms will produce an infinite number. However, if the numbers are very small, the sum could be finite. Such finite-valued "infinite sums" can be highly useful; many useful numbers can be approximated as "truncated"infinite series (infinite sums of which only a finite number of terms have been added; what is omitted is carefully calculated to be less than an acceptable error tolerance).

Consider the infinite sum 1/2 + 1/4 + 1/8 + 1/16 + .... With a little thought, it can be seen that this sum can never be greater than 1. As Zeno observed, if you walk half a mile, then walk half of the remaining half mile, and then half of that, and keep doing this, you'll never walk more than a mile. In the chart below, the blue bars represent the terms that we want to add up, and the pink bars represent the running subtotals. As you can see, the subtotals approach 1, and rise no higher.


In contrast, the series 1 + 1/2 + 1/3 + 1/4 + ... can be seen to be infinite. Observe the sums climbing steadily. (They do slow down, but not enough to make the sums approach a finite value.)


It is harder to show, but the series 1 + 1/4 + 1/9 + 1/16 + ... , (the sum of the reciprocals of the square numbers, 1, 4, 9, 16, 25, ...) is a finite sum. (See below. The sum is about 1.64.) The story of how Euler showed that it adds up to the unlikely value of (Pi)^2/6 (Pi squared divided by 6) is entertainingly recounted by Dunham in his wonderful book. This derivation is characteristically Eulerian!

The discovery above is topped by a result that connects an infinite series consisting of the reciprocals of the squares of the positive integers on the left, with an infinite product of factors of the form (1 - 1/P^2) on the right:

Bill Dunham's book, beautifully written, combines stylish exposition with absolutely fascinating content. Euler, a contemporary of J.S.Bach, showed a similar brilliance and creativity to the musical genius, and both had similarly enormous influence over the development of their respective areas. Both had many children: Bach had 20, and Euler had 13, and in each case, only a handful lived to adulthood. Finally, both were afflicted with diseases of the eye. While Bach died at the age of 65, Euler lived to be nearly 80.

Arch

The Youthful Johann Sebastian Bach

Johann Sebastian Bach, one of the fathers of modern harmony, was born in 1685 (a few decades after the Pilgrims landed on Plymouth Rock--though I could be wrong about this) and lived to the age of about 65. Though by modern standards, this was a rather brief existence, because of the limited number of distinct portraits of him that are available (actually just one original portrait, of Bach at the age of about 50) we have an image of the composer as a grumpy-looking, serious, dried-up, aged, authoritarian fellow, a father of 20 children (21, if you count P. D. Q. Bach, which you should not, if you know what's good for you) and the teacher of numerous other young men. From his letters, we also get a plaintive whining tone, which has attached itself to the perception of Bach by those who know of him mostly as an important historical musician, rather than a beloved composer of miraculous, inspired pieces.  

In contrast, for those whose perception of Sebastian Bach (the Bach family was enormous, and to them, he was Sebastian, since there were lots of Johanns in the family) is based on his actual music--rather than his reputation or his letters-- the personality that comes through is entirely different. To us (and I count myself among this blessed number) he was a guy who lived for music, who knew he had far better musical instincts than anyone else whom he was acquainted with, just as confident of his abilities as Mozart was to be a few decades later, but who had little leisure in his busy day in which to dwell on his own brilliance. There were a few things that he could thank God for besides his talent: that he had a wonderful and talented wife, who gave their children a measure of her own gifts in addition to those of their father, and the fact that he earned his living essentially in the service of music. (One shudders to think what his life would have been like if he had to paint houses for a living, for example. P.S: Not that housepainting is an unpleasant occupation. Rather that Bach would have had no access to an organ, for instance.) Among other things, this meant that he usually had at his disposal moderately good musical instruments on which to play. That many of Bach's mature musical works are somber and serious cannot be doubted, even if they were imbued with the amazing melodic, harmonic and rhythmic energy that keeps them an important part of the 21st-century repertoire. It is possible to contrast badly-played Bach with more rhythmically interesting Romantic period composers to the detriment of Bach, but this is not to say that rhythmic sophistication was absent in Bach. Quite the contrary. Some critics give Bach credit only for his harmonic skills; this is also a mistake, since Bach's melodic skills are unsurpassed, even in comparison with such fabulous melodists as Chopin, Mendelssohn and Rachmaninov. The reason I was suddenly inspired to actually write about a composer who is easily my favorite today, of all days, is that I was trying to play one of my favorite organ fugues, opus S. 545 in C major. The catalog of Bach’s works is not chronological, but rather based on categories; the entire set of cantatas were catalogued first, and so on. (The organ fugues seem to have been catalogued by key, so that 543 is A minor, I believe, 544 is b minor, and 545 is C major.) I first heard the C major fugue on NPR early on a Sunday morning, and it seemed to me that I had heard it before. To this day I do not know whether I might have heard it as a child, but it seemed somehow interesting. Having listened to it for years, now, I begin to realize that it is a very youthful composition; it is drenched with youthful optimism, romance, happiness, pride, grandeur, a carefree quality that is utterly and captivatingly naïve and infectious. The writing is redolent with parallel sixths, where the parts go together in the same direction, the highest ‘voice’ going in parallel with the ‘tenor’ or the ‘alto’ voice. (If you need an example, the first few notes of (the verse of) “If I fell” by the Beatles is one.)  

This three-minute fugue is widely available in any collection of Bach organ preludes and fugues; in particular the CBS recording by E. Power Biggs is a good one; it has good pace, and the Harvard baroque organ has a nice clear tone. I have uploaded a MIDI-based sound-file made into a video, which will serve as a minimally acceptable substitute for a good performance. In an actual performance, the organist will vary the tone enough, so that it is a little easier on the ear. In this one, the software gives a uniform organ tone, which you have to endure for the sake of finding out what I’m talking about. Above all (in my opinion--I'm not a scholar, and I don't know, off the top of my head, what year this fugue was composed according to the scholars), this fugue shows Bach as a young man. This work could only have been written by someone in his twenties, in my humble opinion; someone whose native optimism has not yet been dented by the vicissitudes of 18th-century life. Listen and see whether you agree!


Archimedes

Words are your Friends: The Joys of Etymology

One of the earliest experiences of an intellectual nature that I remember had to do with a Sunday-School lesson. Our Sunday-School met all together first, at around seven in the morning, and a sort of devotion was led by the Superintendent, after which we broke up into individual (age-specific) groups. The lesson I remember had to do with the etymology of the word "sincere". You can look it up: it comes from the roots "sine" without, in Latin, and "cere"; wax. The root "sine" gives us lots of words through the French cognate "sans-", such as sans-culotte, which one rarely uses, and of course Shakespeare's "All the world's a stage" speech (from Hamlet, I presume? Or perhaps I presume too much?) Sinecure, is also a word rarely used these days, and means an occupation that does not involve a great deal of responsibility. "Cure" must derive from the same origins as "curator", but that's only a guess. "Cere" is worth some investigation, since it sounds so much as if it has some relation to 'ceramics', and 'ceremony', and the goddess of the Earth, Ceres. Our month of January comes from the Roman god of beginnings, Janus, who was said to have two heads, one looking forwards, and the other looking back, and as such appropriate for being the patron of the new year, with its retrospective and prospective aspects. (There you have three words with the "spex" root [Wiktionary] meaning "observer", one who looks.)

I wish there were more of an etymological component to modern American education. In tandem with the American tradition of doing things differently than the rest of the world, there ought to be a moderating interest in those inquiries that look at connections with the rest of the world. We do not serve our children well if we give them the illusion that all good things that we enjoy were invented right here by Americans. The interconnectedness of all things is one of the greatest lessons one can learn, and Etymology draws on language, history, literature, vocabulary, and cognitive skills. One of the few areas in which there appears to be etymological interest on the part of the general public is about internet-related terminology. The etymology of blog is often talked about (evidently a contraction of Web Log). There is an interesting account of the origins of the phrase "suss out", which is used to mean 'check out' at the Grammarphobia Blog. How does the mind work? On the surface, we think of our brains as being simply fact-collecting organs, but more accurately, the brain collects facts, and connections between them. Collecting the facts is the easy part. What help we can give with the rest of it is sorely needed, and sadly absent from the experience of many of our youth. (I was trying to locate good further reading for the interested reader, but was frustrated by the aggressive tendency to classification that cognitive psychologists seem to have.

There is a theory that has been co-opted by a teaching philosophy --at least according to this site-- namely "constructivism". Unfortunately, they have made a part of their creed that any sort of testing is against the objectives of learning. While this is true to some extent, it does make it hard to call oneself a Constructivist if one does need to administer tests and evaluations. As a result of this fragmented nature of the theory of cognition, for many years it has been an unpopular area in which to specialize.)

To summarize, careful expression, careful use of words, the careful measured thought, all these things should have a larger share of what happens in this century, if we are to have a better public life for all of us.

Archimedes, hoping for a more articulate Presidency

Miriam Makeba

Soon after singing at an anti-Mafia rally in Italy, Miriam Makeba is dead at age 76. This charismatic and courageous woman was found by the cause of anti-apartheid, and was exiled from her native South Africa for twenty years, which she put to good use in spreading the word about conditions in Africa. Musicians, social historians, Africans, and those of us who were molded by the amazing ideas and movements of the sixties will miss her greatly. May she rest in peace, and may she never be forgotten.

Archimedes

Why Taxation is Reasonable

Of late, it has become the fashion that Americans Hate Taxes. If one hates something, one must look carefully into what it is about it that one hates. In his blog, Mano Singham carefully explains the role of taxes in society, and why one should look carefully at anyone who earns a good living, but hates taxes. His explanation (link no longer available) is based on levels of need.

1. If I find it hard to keep body and soul together, it would make no sense to pay taxes at all. For the poorest Americans, paying taxes is something they would rightly resent.
2. If I earned more than I needed simply to keep body and soul together, if I had a little more money, Mano Singham points out, I would be interested in such things as security, a decent police force, decent schools, decent services which I could not afford by myself. It makes no sense to return my taxes to me and withdraw the security provided by the community, unless I was so wealthy I could hire my own private security service. So, at this level of income, it makes sense to pay some taxes, for these benefits.
3. Once my level of income rises still higher, Mano Singham speaks for himself: it is satisfying to know that by paying higher prices for groceries, for instance, that agricultural workers would earn a better wage. In other words, he says, for some of us, the satisfaction of alleviating suffering and hardship is something that we would be willing to pay taxes for.
4. [Added later]: such things as airports and stadiums, often built at taxpayer expense, are usually only enjoyed by those in fairly high tax brackets, or more frequently enjoyed by the wealthy. In addition, there are publicly funded resources that can be used only by a very few, such as luxury accommodations at airports and national parks. This list is by no means exhaustive; I suspect that there are things the wealthy can enjoy whose existence the rest of us are unaware of. The better off you are, the more you can enjoy what the government provides, and so the tax system should tax those of higher incomes at higher rates.

Mano Singham's beautifully, clearly and lucidly presented explanation of the costs versus benefits of taxation from the point of view of the socially conscious individual can hardly be improved upon. What is dismaying is that many of us have friends who are so comfortable saying that the needs of those less fortunate than ourselves are not an important consideration when it comes to complaining about taxes. In short, they say, there is so much waste in government that it excuses the blanket condemnation of taxes altogether.

Archimedes

Who is In the Middle Class?

In his blog, Mano Singham asks this very question. Dr Singham observes that political candidates in the US often claim to be on the side of the "middle class", but every administration manages to help only the very wealthy, and appease what most of us think of as the middle class by giving them a few crumbs. How is this done? By making people who earn around $30,000 a year feel a kinship with those who earn more than $250,000 a year. Of course it's all relative; Bill Gates probably thinks that anyone earning $250,000 a year ought to get Social Security (I'm just kidding; he's probably a very hip guy), but each person considers him or herself as a person of very modest means.

The State of the Union

The President-Elect, Barack Obama, will be inaugurated in January. But it isn't too early to put forward an open letter to the nation, spelling out what should be done between now and that moment. With all humility, and recognition that the Supreme Court has become comfortable with interfering in the electoral process, thus reversing the will of the people, the President-Elect could, without appearing too eager to take office, or usurping the prerogatives of the Electoral College, set out some principles for whomever should be president in 2009:

1. A word of reassurance to the troops in Iraq, Afghanistan and elsewhere would not be out of place. No matter what the detailed plans should be for their final repatriation, if that's the word I want, they deserve some word from the new people in Washington, even if they have not yet taken the reins.
2. A few words to the Congress might be in order, for surely some furious activity is planned there, for the days between now and the end of the year! Warning or encouragement, either could be of value, and a reminder that the nation is watching.
3. A few words to the newly elected Governers may be appreciated. It may be too early to proffer advice, but kind words now will be remembered when help is needed presently.
4. A few words to the people will be welcome. It is right to rejoice in the victory, but not too soon to set a tone for the next few years.
5. Words of warning to certain sectors of the business world might be in order. It is time to call a stop to the freeloading that has gone on in certain quarters, in the name of free enterprise. If free enterprise is selling stocks in political figures (something I still find difficult to believe), perhaps the term should be redefined. I cannot help thinking that the futures market should be examined closely, for its contributions to the instability of the economy.
6. Finally, a greeting to those who deal with the youth of the nation, who train the minds of our young citizens, and shape their attitudes towards duty, service and privilege. Perhaps it is time to veer away from the path of creeping elitism and lowered expectations. We need a more practical solution to low achievement in schools than the suave legislated excellence of recent administrations. There is not one single cause for ignorance among American youth, and we should not proceed as if there were just one enemy of education. Teaching requires work on the part of students, teachers and parents, all three, and there is no way to achieve excellence by imposing additional burdens on just one or two of these parties.

Archimedes

The Beauty of Kathleen Ferrier

Every once in a while I'm reminded that Kathleen Ferrier is dead, and I fall into a state of misery, ignoring the fact that I never knew her, never saw her in a video clip, and only shared the planet with her for a little more than two years. More than the voice which has been within arm's reach for most of my life, and the fragrant personality that every piece of memorabilia radiates, I also, in my pathetic male way, mourn the loss of her wonderful face.

When I was a kid, I could never understand the adult preoccupation with dimples. I knew some kids with deep dimples, who were almost literally a pain in the butt. But now that I am come to man's estate, I can see a little of what the fuss is about. Let me put it this way: if I were to be a girl (which I am not), that's whom I would like to look like.

There are several vocal pieces I love that I can almost only bear to hear sung by Kathleen Ferrier; most of them are on the album Kathleen Ferrier sings Bach and Handel Arias. One in particular, one of the most joyful arias ever written, is from the Handel Messiah : "O Thou that tellest glad tidings to Zion" heard here in a Google video. This particular recording uses an enriched version of Handel's scoring, very possibly that by Ebenezer Prout. On that same recording with Sir Adrian Boult is the gorgeous Bach aria: Qui sedes ad dextram Patris, from the mass in B minor.

It is interesting how protestants such as Bach addressed these ancient Latin prayers composed by clergy a thousand years ago; clearly, to at least some of the leaders of the early church, the day of judgment was very close indeed. The prayer says --and some of the fear in it still remains after millennia of comforting familiarity: O Thou that sittest at the right hand of God the Father, have mercy upon us! I am not a believer; nevertheless the appeal can be very poignant, depending on who makes it. To the first century clerics who first wrote the prayers of the Mass, the confidence that Jesus had promised to intercede for mankind must have warred with belief in the fearful end of the world, and the accompanying judgment. To Bach, for whom the goodness of Jesus was, with the consolation of music, the only relief from the misery of his life and the cruelty of his world, the prayer was at once an opportunity to practice his compositional art, as well as an opportunity to praise god. To me, it seems as if the beautiful aria is not a personal plea, but an offering of beauty, where the rhetorical aspects of the melody are an offering to god, carefully wrought, and sincere in the context of religious drama. To Kathleen Ferrier, I doubt that the feelings of Bach and the author of the prayer meant too much. She probably allowed the emotions in the notes to suffuse her, determined to persuade her audience of the beauty of the aria, and to give her fellow performers of her best, so that the whole work, the recording, could be as good as she could personally make it, and sincerely, from her heart. Listening to it, it seems effortless, but in the footnotes we read that she had already been diagnosed with cancer. We can never know, but it is possible that the illness did not color the performance except as a hindrance to doing even better. I have never seen so many photographs of a woman who smiled more readily with her eyes. There is a youthful photograph of her, as young as nineteen, possibly, with the marks of braces still on her teeth, with the same smile on her face with which she graced photographs all her life.

Janet Baker recounts hearing of the death of Kathleen Ferrier, and her feelings at the realization that she could never get to know her. I can only guess how universal that feeling was, but it is certainly how I have felt every once in a while, especially when I see that wonderful smile.

[Added later:
It is said that, even if everyone she knew was not exactly in love with Kathleen Ferrier, at least the horror of hearing the news of her death was a serious shock to everyone.  The recordings in the album Kathleen Ferrier Sings Bach and Handel Arias, in Mono, were literally the last recordings she ever made, for she died very shortly afterwards.  Adrian Boult, the conductor on the record, was so grief-stricken that he had not made a stereophonic recording for the album that he placed a large speaker on the middle of the stage, conducted the orchestral accompaniment all over again, and recorded it in stereo, with Ms Ferrier's voice coming out in Monophonic sound in the middle.  This was considered sacrilege at the time, and for years to come; of course purists would consider practically anything sacrilegious.  I for one would love to get my hands on this fake stereo version.]

Archimedes

Harry Potter and The World of Children's Books

It seems clear, at this point, that the Harry Potter books, and the Harry Potter Phenomenon generally, has given children's books a fillip that was sadly needed for decades. You may disagree with Jane Rowling's metaphysics, or with her educational objectives or social consciousness or whatever, but you can't fault her saying that she writes a boring book. I'm willing to bet that there must be a million young readers out there for whom Harry Potter was the first book they read voluntarily. There must be a vast number who began reading Harry Potter under duress, but continued to read voluntarily. The hardest thing to do, and believe me, I know first hand, is to get a kid to start reading. You pick the wrong books, or she has the wrong interests, or there just aren't any interesting books, or her friends don't read, so she doesn't, either, or she despises her friends and they do read ... you can ring the changes on that ad nauseam. So even if kids are reading books that you'd rather they didn't, they are reading, dammit, which is a huge improvement over not reading at all.  

Is our adult preoccupation with reading a temporary 20th/21st -century phase? Will 25th century adults bemoan the fact that kids don't watch enough TV? Is there something special about books? Because I enjoy writing so much (hence this blog :) I assume that there is some benefit to reading and writing, both to the writer, and to the audience. When writing, you have to force your nebulous thought into words, and you begin to realize that you have linguistic resources that you did not dream you had! Language, especially written language, is a resource that one must never undervalue. I wish I had the skills to persuade everyone of the truth of this, but it is only an instinctive feeling, a gut conviction, at the moment.  

It's surprising how the Harry Potter books have caught on in America. Perhaps the wonderful movies have contributed to the overall phenomenon, but why did the books catch on at first? They rely so much on the British boarding-school phenomenon, to which most Americans are strangers (except for the few who have read boarding-school books, and I can't even think of a few offhand--I belong to the generation who read Billy Bunter and Psmith stories from books handed down from uncles and aunts). The idea of a mixed boarding school (girls and boys) is unfamiliar, but I imagine in this enlightened age such a thing is not impossible. Perhaps they have been around for decades; gosh, I'm such a dinosaur.  

Rowling is a master at characterization. There's absolutely nobody better. The plots are not as satisfying as I'd like (or rather, The Plot isn't as satisfying, I should say). It all goes to show that, really, the plot is only a minor component of the entire work of fiction. Brilliant books have been written with very sketchy plots. Rowling's characters are so real, that to this day it seems as though Hermione Granger in the books and Hermione in the movie (Emma Watson) are two different characters entirely, both of whom share Harry Potter. Honestly, I can't see Emma Watson in the role for the movie of the last book (Deathly Hallows). She just gives the impression of being too much in charge and unflappable, while the Hermione of the book seems at the end of her tether, and only hanging on by a thread. Let's see Emma Watson hanging on by a thread, then, and I'll believe she can do it. There are other authors who have been plugging away at the young adult audience over the years, with some success, if not as spectacular success as that of Rowling and Potter. Tamora Pierce is one, a particularly good writer, even if not as brilliantly gifted as Ms Rowling. Arguably, some of Pierce's stories are more satisfying than any given Harry Potter book, but the Harry Potter books are to Tamora Pierce's books as a Hollywood blockbuster is to a wonderful little Indie film. A lot of work has gone into the style and the stylishness of the Harry Potter books, and we can't all be J.K. Rowling. On the other hand, Tamora Pierce has written a score of books, many of them very, very good, and as far as we know, J.K. Rowling has not gone beyond Beadle the Bard, which is still squarely in the Potter universe. But she has plenty of time in which to prove that she is not just a 7-hit wonder.  

Archimedes

The End of The Art of Fugue (Der Kunst der Fuge)

I never took YouTube seriously for years, until I got interested in ballroom dancing. Then I discovered a video clip of a tiny couple dancing on YouTube, and was totally hooked! I still probably go to YouTube less frequently than most, but I decided to report on what I have found.

 Glenn Gould is represented well, mostly off TV appearances, with his humming very clearly audible. (I have not heard the humming on disc, though as I reported, I'm a little hard of hearing.) In addition to most of the goodies, Gould plays the Bach Contrapunctus no. 14 from the Art of Fugue, a very moving performance, the humming notwithstanding.

The Art of Fugue ends with a famously incomplete piece, Contrapunctus 14. For most lovers of the music of J.S.Bach, this is a difficult moment. The surviving fragment of this last fugue (Contrapunctus simply means fugue with some extra connotations that are unimportant) is such a wonderful achievement that the fact of its incompleteness is heartbreaking. The first fugue --a jewel itself-- introduces the main musical theme of the entire set of fugues which constitute The Art of Fugue, assigned the opus number 1080. This theme appears inverted and altered in many interesting ways, but then other themes are also introduced, until there are four in all. [It is now believed that the] last fugue was supposed to be a fugue in all four themes, a so-called quadruple fugue, [though for many years it was identified as merely a triple fugue, following the designations of early scholars, notably the sons of J.S.Bach].

The fugue is both an intellectual exercise and a musical form. A musical form is simply a holding-structure for a piece of music, to make it easier for the listener to cling to points of familiarity in the musical narrative. Thus form makes music more listenable. A fugue, an essentially minimalist concept, is a piece of music based on a single motif (the subject), whose intermittent arrival in one part (or voice) or another provides the familiarity that makes the piece accessible. But the temptation to make a clever fugue is almost irresistible, so that an amateur could write a fugue that is correct, but which does not make for pleasant listening. (Note: the way in which a fugue subject pervades a fugue must not be taken to be an indication that every one of the subject entries must be emphasized and recognized. The subject provides a texture that is just as satisfying --or more satisfying-- than the satisfaction of recognizing an entry. The presence of the subject is felt rather than actually heard, and the connoisseur of counterpoint will have learned this pleasure.)

Bach's 'last' fugue, on the other hand, is first and foremost a piece of beautiful music. It starts out with great dignity, even solemnity, and becomes a mighty protest against the universe. Then, as it gathers strength to repeat a new and more terrible argument, it collapses into a lonely tenor voice, which suddenly finds itself utterly abandoned by the remaining voices. There are stories that Bach died while working on this piece, but this is contradicted by a fair degree of evidence. It is not the sentimentality of Bach's death and his inability to complete the work that is tragic. Rather it is the fact that a completion simply has not come down to us.

Some writers (notably Christoph Wolff) have argued that The Art of Fugue was a work begun a lot earlier in Bach's life, and that perhaps the last fugue had been completed, but has been lost. It is also possible that Bach did not like his completion, and left the truncated fugue as a challenge. For those interested in the subject, there is a completion by Donald Francis Tovey that is conceded to be learned, but widely regarded as unsatisfactory. There is a completion by Lionel Rogg, which I have not heard, and also one by William Malloch, which I have. This last is rather an irreverent and playful arrangement of the whole Art of Fugue which leaves one both bemused and amused, and is thoroughly worth hearing. (One of these days I may have the courage to upload it to YouTube myself.)

Searching for Art of Fugue, or Die Kunst der Fuge, and Bach, or maybe BWV 1080, you get many hits on YouTube. Some of the best clips are of Musica Antiqua Koln (with Reinhard Goebel). There are two clips of Contrapunctus 1 by recorder ensembles, both Japanese, and an uncredited Organ version that is mechanical enough to be derived from a MIDI file.

A piece that is --at least thematically-- quite unrelated to the Art of Fugue is the Chorale Vor deinem Thron tret ich hiermit. This is a fairly well known tune sung to words less familiar to English congregations. The original tune is an alternative to "The day thou gavest, Lord, is ended." This chorale was (as I understand it) written on the lower half of the page on which Bach's unfinished 14th fugue ends, and was presented by Bach's son as the last thing the great composer ever wrote. It is certainly something that Bach may well have wanted to do, but on our deathbeds, few of us have the strength to make the wonderful gestures we would like to make. But the wonderful blend of arrogance and humility that we see in Bach from this distance in time is neither diminished nor increased by whether he wrote the hymn below the fugue on the manuscript.

Archimedes

Liszt's Transcendental Etude No. 10

I watched this clip of Cziffra playing one of Liszt's Transcendental Etudes just a second ago. It humbles me that there is so much music that I am not aware of, and with which I am completely not in tune. I could appreciate the brilliance of the performance without being touched by the music. The fact that the man had such technical mastery was amazing. The pianism was undeniable. But is it music? There are pieces by Liszt that I love. But there is a point, a level of brilliance beyond which my appreciation does not go.

Arch

Rites of Spring

A couple of weeks ago I decided to read Jessica Duchen's first (?) novel: Rites of Spring. The book arrived late last week. The novel, for the most part set in contemporary London and its suburbs, had a number of wonderful characters, all of them sympathetic, especially Liffy (Olivia) a twelve-year old who wants to dance professionally, and lives Ballet. There are a pair of twin younger brothers, usually noisy and obnoxious, interesting and colorful parents, grandparents, an aunt hopelessly in love with a concert pianist.

The first part of the novel --all I have read so far-- chronicles the gradual falling apart of Liffy's comfortable world, and for various reasons, the worlds of everyone around her. The rest of the novel must salvage something for most of those who survive this multi-dimensional upheaval, or I will never forgive Jessica Duchen. I suspect that Liffy will be the price that has to be paid for the redemption of the characters and their situations.

As in Rebecca West's The Fountain Overflows, we witness the suffering of people of greater than ordinary sensitivity, especially when their relationships go wrong, and they find it impossible to communicate. When dull, ordinary people suffer due to their obvious mistakes in communication, we can sigh, and point the finger at their dullness, and at their limited communication skills. But when bright, scintillating people get their wires crossed, or allow their too-sensitive perceptions to interfere with connecting with those they love, and when their enormous needs battle their satisfaction with what they have, one is at a loss for a simplistic recipe for a way out.

I often feel put upon in these novels where everything goes wrong. In the present instance, though, I have to admit that everything that does spiral out of control does so very plausibly. It is chock-full with emotional action, as if Ms Duchen is packing it with ten stories for the price of one. They all have the ring of truth, the stamp of an eyewitness, and perhaps in years to come some enterprising graduate student will greedily deconstruct this work, revealing it to be at least semi-autobiographical. [Added later: the story is based on facts, but is not autobiographical.] It is this note of truth which makes it unreasonable to point at the seeming clutter of the action. Often it is the clutter of life, the myriad oppressive details that drive one to the depths of despair. At this point in my reading, we are approaching the depths. I would like to recommend this book at this point, even while anticipating the worst. Never have I been less proud of being either a liberal or an intellectual. It remains to be seen whether either characteristic can bring some resolution to the mess towards which things seem to be heading.

[Added later:] Having finished the book, I must say that I join the host of critics who have applauded it. There is great humanity in it, and though the main protagonists have been brought low, they save themselves in believable ways. And I'm delighted to report that Liffy survives the novel with most of her sweet character intact. Despite being the principal voice of the novel, Liffy manages to be a relative unknown. We see deep into her mind, and we see her watching everything else, but at the end we are left feeling that we don't know her very well. (Or that we do, and there isn't much to know.) I can't help contrasting her with Paloma, the young person in Hedgehog, and they do provide as great a contrast as possible in two characters with whom I have great, great sympathy. This book does not set out to give us lessons in life. But there are little thoughts that Ms Duchen could not help putting in there, and I leave them to you to discover. Living in this age is a challenge, and for a sensitive child, growing up in Western society is difficult indeed. This book is a chronicle of what might be considered a narrow escape.

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Talking about Sonata-Allegro Form . . .

A few weeks ago I wrote about First Movement Form, or how classical symphony first movements were traditionally constructed. The example I used was Eine kleine Nachtmusik, Mozart's serenade for strings in G, actually not a symphony at all. Learning first movement form decades ago at the feet of Thomas Schippers, and the Book of the Month Club and their Musical Appreciation series of vinyl records, one of the earliest symphonies I learned to analyze was Beethoven's famous 5th symphony in c minor. I tried, in my article to explain how two themes are presented, the first theme regarded as the 'masculine' theme, the second theme regarded as the 'feminine' one, after which there is a Development section, after which came the Recapitulation, where both themes are re-stated. Beethoven's Fifth Symphony opens with the famous four note theme. After this is formally presented with a certain amount of repetition and extension and other rhetoric, there comes the second theme, in the key of E Flat major, played by a Horn. Brass instruments at that time, you may have heard, were not chromatic, except for trombones (and slide trumpets, which were not commonly used in concert music). The theme was written to be playable on the horn in E Flat. When a piece is written in a minor key, such as c minor, the second theme is most often in the major key that has most of the same notes, called the Relative major. The Relative Major for C minor is E Flat. If you listen to the first movement of Beethoven's Fifth, and listen carefully to the two big chords just before the Horn theme, you will realize that there is rather an abrupt change there, in order to continue in the relative major. It is an unusual chord sequence, from the F sharp diminished seventh to the B Flat major seventh. Well, the movement goes on its determined way, and finally we come to the recapitulation. Now, of course, the two themes must both be played in C minor. Oops; the Horn can no longer play it, because an E Flat horn cannot play in C minor, or at least could not play it, in Beethoven's time. This was not an insurmountable problem; no doubt there were horns that could play in C, but Beethoven chose to do something creative: he gave the recapitulation of the second theme to the bassoon! Hearing the bassoon play the horn theme is eerily fascinating. It is clearly the same theme, but it has a sad dignity now in place of the jaunty challenge issued by the horn. However, in the late nineteenth century, and the early twentieth century, conductors made the horns play the recapitulation as well, in defiance of the written music. The reasoning was that Beethoven had written the music for the bassoon as a second best, since the horns could not play it. Modern horns, of course, are essentially chromatic, and can play the notes without turning a hair. So why not let them? Each of us must decide for ourselves whether it makes better sense to let the bassoon play the theme, or let the horns. It is hard nowadays to actually find a recording in which the horns play the recapitulation, since most people are on the side of the bassoon. I will try to find a clip with the horns, and post it here. [OK, mission accomplished.] Here is the second theme played in the Recapitulation by John Eliot Gardiner's Orchestre Revolutionaire et Romantique. This recent (1994) recording features the bassoon. There is some lead-in stuff to orient you. Note that the bassoon, though it has a distinctive voice, is not a very familiar voice: Gardiner, 1994 Here is the same spot, the second theme in the recapitulation, played by Herbert von Karajan and the Philharmonia Orchestra in the 1950s (?). In this performance, it has been given to the horns (more than one, obviously, playing in unison), as I said, in contradiction to the music as written by Beethoven. Still, even without the drama of using a bassoon, the music is effective: Karajan, 195x Arch.

Glenn Gould, prophet of the piano

Today is the birthday of the wonderful Canadian pianist and keyboardist, Glenn Gould. Oh Lord. I had heard that Gould was a genius, and that he sang along with his piano playing, but this is the first time I have actually heard it! (My hearing is not very acute.) I'm referring to the YouTube clip to which the title of this post links. I first heard Glenn Gould playing Mozart's sonata in C K545. It was played incredibly fast, but with such a crisp sound that it was fascinating to listen to, especially the first movement. I listened to a cassette that I made with that recording (borrowed from the Carnegie Library in Pittsburgh, which I must thank for getting me started with nearly half of my interests within classical music) on and off for a decade. I eventually began to collect digital recordings, and learned that not only did Glenn Gould not like to play Mozart, he loved playing Bach. I had come out of my teen years firmly convinced that Bach simply had to be played on the proper instrument, namely the harpsichord, or maybe an organ, and even then not just any organ. I was as doctrinaire as they came, and deplored the use of modern, large organs for Bach trio sonatas, for instance. At about the time I discovered Glenn Gould's Mozart, I also discovered a percussionist called Brian Slawson, whose album Bach on Wood had a couple of fabulous cuts that had been played on the radio, and taped by me. (It was during a trip to Yellowstone, and I was just barely able to tape the piece on a little boom-box we had along!) It never rains, but it pours. After Walter Carlos's Switched-On Bach in the sixties (which I did like very much, some cuts more than others), I was ripe for this new interest in unusual recordings of Bach, or at least recordings of Bach on "unauthorized" instruments. Many people will agree that Bach is especially fine played on odd instruments. Brian Slawson's album (which he has now followed up with Bach Beat, which features the incredibly slimy Das Roach, as well as the beautiful original composition Elegy) shows just how many alternatives there are, even within the class of percussion instruments, for instrumentation. Stefan Hussong plays Bach on the accordion, and has made some lovely recordings. I'm having to figure out, in real time, why Glenn Gould sings here. Watching the video clip, it is clear that it is the rhythm of the Bach piece that has caught his attention; the syncopation, the excitement of some figure that he wants to emphasize. It takes a while to realize that Bach was not only about the four-square sewing-machine rhythm that seems to define a lot of Bach's music. That's only on the surface. Inside, there's all sorts of mayhem going down, inner voices clicking and clacking against each other, especially in the keyboard works, one of which Gould was playing (or rehearsing) on film. I had been willing to concede that he was a genius --I'm willing to concede that practically anyone is a genius, as long as they leave me alone-- but now I'm seeing exactly what kind of genius he was: someone who thoroughly appreciated the beauty of complex rhythms. Mozart's allure for me was not one built on complex rhythms. If complex rhythms (and probably complex harmonies, too) were what drew Glenn Gould to them, it becomes more clear why he liked Mozart a lot less than he liked Bach. Mozart, it seems to me, put nearly all his eggs in the basket of chromatic melodies. There was a lot of harmonic support for his melodies, without a doubt. But because all his energy was focused on making that one melody be the princess of the piece (not all the time, but certainly most of the time), rhythmic complexity did not have a large role to play. (It is unbelievable how much Mozart was able to do with so little.) In contrast, Bach gave you your money's worth. Someone wrote that Handel, for example, would write just enough for the effect he wanted. He was writing for his audience. Bach, on the other hand, wanted to write until the potential of his musical material was exhausted. An interesting example is an aria from Cantata 68, a well-known soprano song learned all over the world, called (in translation) My heart ever faithful. The aria is a perfectly normal one, accompanied by a sort of mini-cello, which has a vigorous counter-melody, one that Glenn Gould is sure to have appreciated. Anyway, the aria full of pietistic joy and exhaltation, comes to an end. and then, totally out of the blue, the music continues, with the violin and the oboe and the cello going full tilt for a full minute or two! No one can explain why this goes on, because the aria is over! This is sheer exuberance. Bach has this neat rhythmic theme that he has not exploited, so he has to make it live it's musical life! He was as pro-life as it is possible to be, in a strictly musical sense. There are times, though, where Bach brings something to a close, and you wish he would keep on going. Glenn Gould became famous for his performance of the famous Goldberg Variations, and now they are talked about by practically everyone who craves insider status into Bach music. But the Goldberg Variations are justly well known, and worth listening to. Finally, Glenn Gould recorded the Art of Fugue, by J.S. Bach, long considered his last composition, using both piano and organ. It is a fascinating interpretation of the Art of Fugue, which does not have any instrumentation associated with it. Archimedes