Virtuoso: Chopin's Prelude in F Minor

Have you ever wanted to get up on a stage and sing a few broad and loud phrases to a sophisticated audience? That is what this piece suggests to me. Chopin's Prelude in F Minor, Opus 28, Number 18, suggests such virtuosity; hence the name, "Virtuoso". It starts with an angry argument that ends in a harsh, off-balance discord, based on F-G-flat. It repeats this argument and then goes into an arpeggioistic fit, followed by the same arguing line, this time in the sub-dominant key of B-flat minor. It then proceeds through a bunch of quarreling phrases, including some with a banging E double-flat in four octaves, and then it descends into the bass, where it mutters and fades into the final chords. It takes a bit of practice to get the running lines down, but once you do, you get a sort of satisfaction out of playing the phrases and then banging the keys when the downbeat chord occurs, sort of like punching a punching bag. It's a good piece to play if you want to boast about your piano-playing ability, or if you want to get some anger off your chest. Take your frustrations out on this piece instead of on your neighbor for raking onto your lawn, and you will be calmer and better able to deal with the crisis. This is one of his better preludes.

Autumn Idyll: Chopin's Prelude in A-flat Major

This is a magnificent prelude. Opus 28, Number 17 features luscious harmonies and harmonic transitions, a sonorous melody, and a majestic bass that at times reminds me of a huge organ at a cathedral, not to mention the 13 chiming bass A-flats in the last part of the piece that reminds me of a bell tolling out 13 o'clock. To me it reminds me of one of these gorgeous days in the autumn (or in the spring) in the park under the trees, sunny with moderately cool winds, that entice you to spend the entire afternoon out in the park sitting and admiring the nature that is around us. It is one that I learned when I was a child. The most interesting part was that with many of the chords, the left hand overlaps the right, so that if you are not careful, you stumble all over the place on the keyboard when you play it. It starts out with the melody in 6/8 time, or maybe a fast 3/4 waltz. It does have some unexpected transitions, such as E-flat to D-flat instead of the more usual B-flat 7. This tripped me up when I played it for my piano teacher - I kept wanting to play D natural instead of D-flat. It then goes four keys flatwise, and thus into sharps, into the key of E. The harmonies then go from one key to another - C-sharp minor, E7, D-sharp major, C-sharp major and so forth, finally winding up in an alteration between E-flat and A-flat minor. We then return to the main theme, but this time with the volume of an enormous church organ, as the bass hits the lowest keys of the piano. It then goes into a variation of the alternate theme, then goes back into a plain A-flat ending with its bell-like series of A-flats in the bass. This is a piece I want to hear over and over again, and I hope to hear it at a concert sooner or later.

Scurrying: Chopin's Prelude in B-flat Minor

Chopin's Prelude Opus 28, Number 16 runs all over the place and is not the easiest to master. It features jumpy triples of notes in the bass, and a scurrying around in the treble going up and down the black keys of the piano, with an occasional breakout to the white keys to provide the F7 dominants. I tried playing it and although I could get the general action of the running up and down the keyboard, I could not get it perfect, and coordinating it with the jumpy left hand is even harder yet. The entire piece reminds me of someone running around and scurrying all over the place, sort of like a mouse running all about the floor looking for cheese or for a place to hide from the cat. So I call this one "Scurrying". It continues for four pages of printed music scurrying almost non-stop until it drifts down into the bass, sort of like the mouse finding the hole in the wall, and then pum! pum! it's all over; he's in his hole. Chopin does not break any ground with this one with the usual standard harmonies of B-flat minor, E-flat minor, and F7th. But it still is an interesting one to listen to, and it will get your heart pumping.

By the way, I have now posted a web page consisting entirely of Chopin's Opus 28. Not all the links work on it yet, because this page will not go ahead of this blog. After I blog a prelude, I will also put it on the web page.

Storm: Chopin's Prelude in D-flat Major

This, along with Number 17 (A-flat) and Number 20 (C minor) is one of the more well-known pieces in Chopin's Opus 28. This one, Number 15, is usually called the Raindrop Prelude because of the constant A-flat eighth notes pitter-pattering in the bass like a light rain shower. The beginning and end of this piece are tranquil, something like the F-sharp or A major preludes, like a pretty day out in the garden. But that is not what makes this piece notable. To me the most characteristic part of this prelude is the middle part, a troubled C-sharp minor passage that reminds me either of a bad dream, or of the tranquil day represented by the rest of the piece interrupted by a storm, replete with thunder. I therefore call this one "Storm". It is the longest C-sharp minor passage in the Preludes of Opus 28, even longer than the C-sharp minor (Opus 10) Prelude itself. The song starts tranquilly, with a constant series of A-flat eighth notes, but then all of a sudden during a resolution from an E-flat 7 chord, it not only changes mood but name as well: the A-flats become G-sharps as the piece enters the C-sharp storm. The G-sharps keep pattering away, while an ominous series of chords accumulate in the bass. These eventually resolve into bangs, symbolizing thunder. The storm continues to rage, featuring a strange resolution from G-sharp minor to B augmented and back to G-sharp minor again. After the thunder reaches a climax, the rest of the C-sharp minor part develops melody, perhaps symbolizing the rainstorm and finally calming down and going back to the tranquil part as the G-sharps become A-flats again. The piece naturally has to flip-flop from flats to sharps when it goes into minor; else we have a passage in C-sharp Major (rare) or in D-flat minor (impossible). But to me this transition from flats to sharps also symbolizes the subtle and sudden change of moods from happy to sullen and back again.

It is not too hard to learn; the main problem is that many of the chords have overlapping hands - the highest left hand note is higher than the lowest right hand one. This can cause a good deal of stumbling while playing it for the first few times. This prelude is a good one to put into a program such as Cakewalk - I would insert audio thunderclaps to coincide with the musical ones in the middle part. Although I have found stronger storms in Beethoven's Pastoral Symphony Number 6, in Ferde Grofé's Grand Canyon Suite, in Igor Stravinsky's Le Sacre du Printemps or in Andreas Vollenweider's recording from an actual thunderstorm in his album Behind the Garden, I regard this as one of the better preludes of this opus.

Mathematicians done for at 50?

I have been hearing and reading about mathematicians not accomplishing very much after they turn 30. It is the youth of the mathematics world, it seems, that turns out the best mathematics and comes up with the best theorems and algorithms. Perhaps part of this image comes from mathematicians who are forever young because they died young: Eisenstein and Abel, for instance, or especially Galois, who was almost a child when he was shot to death in a duel at the age of 20. There are some exceptions; for example, the people who solved Fermat's Last Theorem were around 40. So what do mathematicians like me who are over 50 do? I say that it is the childlike nature of these young mathematicians that enables them to make great discoveries. They grab for the silly and ridiculous. They imagine things out of this world, such as five-dimensional manifolds. So if you want to be able to prove theorems well into your 60s, maybe the best way is to keep forever young, and keep a childlike attitude to life, as though it were all a game. Those of us who come up with the wildest ideas are those who will be productive into our 50s and beyond. You can see some of that in my writings, where I liken hat games to aviation maintenance and contra dancing to flipping mattresses. So just keep on playing, and maybe we will be productive into our old age. No, mathematicians are not done for at 50 - they keep on going like the transfinite ordinals, which keep on coming without end.

Throbbing: Chopin's Prelude in E-flat Minor

Opus 28 Number 14 is the first of Chopin's Opus 28 preludes in a flat key. It seems simple enough. The right and left hand parts are identical, except an octave apart. I was going to say treble and bass parts, but almost all the way through the piece, both parts are bass. So this prelude grumbles. It is relatively easy to learn, since you do the same thing with your left and right hands. Some of the notes are tricky to read, especially when a D natural greets you after an F-flat major chord. Shouldn't that be an E double-flat? But the hardest thing to get is the dynamics. Follow the crescendos and diminuendos carefully. The song is a continuous rise from soft to loud to soft to loud, giving it a throbbing feel, like a pain from an injury; hence the name. The piece keeps on going with the eighth notes non-stop until thump, it ends with a concluding octave E-flat. Not a good prelude to listen to if you hurt somewhere.

Bush's chances for re-election

I know I covered this subject recently, but Bush's officially throwing his hat in the ring today brings this subject up. So how can Bush's reelection be stopped? One source says the Democrats' best chance is health costs. If so, then this is something new in Presidential politics, for it does not appear among the 13 Lichtman keys. Others say that his anti-terror stands are popular. But what is really going to happen? As I said before, Bush has lost three keys: 4 (long-term economy), 10 (foreign/military failure), and 12 (incumbent charisma). He has gained 3 (incumbency), 1 (mandate), and 7 (policy). It seems to me that the most likely scenario for defeating Bush would be an economic sputtering in 2004 together with failure to achieve our goals in Iraq (set up a democratic, peaceful government) plus something else, like a charismatic Democratic candidate or a scandal hitting the Bush administration. These things need to happen else Bush wins. But see the previous item:

The Texas Democrats

It was an absurd sight. ALL of the Democrats in the Texas legislature running off to the next state like some sort of fugitives to prevent the Republicans from ramming through a redistricting plan that could increase substantially Republican representation in the House next year. To me the foremost thing that it says is that you can't require any more for a quorum to conduct business than you require for a bill or item to pass. For if not, then a group of people greater than an anti-quorum (1 minus a quorum) but less than the bill-passing requirement can run off into the woods and kill the item. Most quorums are a majority, but the Texas legislature has 2/3, making the legend of the Texas Democrats possible.

Could this lead to Bush's defeat next year? It could happen. Texas is now shown to be the laughing stock of the nation, so much so that it affects Bush the President. The economy does not pick up and things in Iraq don't do too well. In the meantime, the US congress considers doing what the Texas legislature did, and the threat of that causes people to examine Bush and his administration more carefully, perhaps unlifting a major scandal. Or maybe the Texas Democrats would secede from the Democratic party and form a third party getting a huge share of the vote. Either of these two scenarios will defeat Bush. Not likely, but look carefully at the consequences of the Legend of the Democrats who Ran.

Dream: Chopin's Prelude in F-sharp Major

Opus 28 Number 13 is a dream. It is a relaxed 3/4 piece with sustained chords suggesting a contented state. The middle section goes into some dreamy harmonies: first into C-sharp major, then into B major, then finally ending on an elusive D-sharp minor/F-sharp major ambiguous chord that does not resolve itself until the final chord. This piece is the last of the sharp key preludes in Opus 28. The next one would be in D-sharp minor, but here Chopin flip-flops into flats into E-flat minor, presumably because the leading tone there would be a natural instead of a double-sharp. The piece reminds me strongly of Chopin's Posthumous Etude Number 2, which is marked by a duple-time bass with bass notes that come up and down in an sine-wave pattern with a 3/4 treble. I call that one "Mercury" because to me it symbolizes the 3/2 pattern of Mercury's rotation and revolution around the Sun. This 3/2 juxtaposition appears also in Opus 28 Number 13, as does the sine-wave bass, in the middle dreamy section. This piece also has some interesting harmonies, such as E natural over E sharp in the middle section, and apparently Chopin at the end wanted to play some chords that are unplayable because they stretch more than a tenth. A good prelude to play just before going to bed. Tomorrow starts the flat preludes.

What's all this about Matrix?

In 1999 I was in a group of two men and two women who wanted to decide what movie to watch one night. The two movies that were offered were Sleepless in Seattle and Matrix. The women were interested in Sleepless in Seattle and it seemed intriguing to me. Matrix, though, was based on an intriguing idea. Look at the world you see. Hear it. Feel it. This is not the real world. It is enough like the real world so you can maneuver in it, get meals, find friends, read and understand integral calculus and so forth. But it is not the real world, but rather, what your brain perceives of as the world. If something could go in there and change the references of your brain cells, might not your brain think it is in an office building in a dot com in 1999 whereas the real world is a burnt-out hulk in 2199? That is the theme of Matrix and that is exactly how it starts out. However, after seeing the movie, I began to feel the women were right. This movie, although it was based on an excellent idea, was far, far too violent. Every time you turn out someone is threatening someone, or pointing a gun at someone, or shooting someone, and one scene shows someone shooting a gun and shows zillions of gun shells falling to the ground. I therefore rated it a bomb.

Now here comes Matrix Unloaded. Unloaded? That's gun talk. It seems to me as though this new movie is just as violent as the predecessor. And I hear lots of excitement about it. But I hear most of it coming from the movie industry and the media. They are really hyping this movie up good. No matter where you turn to, you get matrix. You turn on the news, you get matrix. You turn on Larry King, you get matrix. You turn on Phil, you get matrix. Even if you turn on sports, you get matrix. Matrix, matrix, matrix. And people are lapping it up good, as can be told by the box office figures and the predicted lines to get in the theater. So this movie is going to attract crowds far beyond what one would expect from a movie of this type. Already, the local newspaper rates the story plot a dud. I can predict by how the previous movie turned out and by the hype necessary to carry this movie to the movie fans, that almost certainly this movie is just as much a bomb as Number 1 was. I feel that on a scale of 0-10, it rates 0.8; i.e., a shade less than 1. If I see it, it will be while I have time to kill and it will be from a video tape, not in a movie theater. Matrix indeed. I'd like to invert this matrix and extract its eigenvector.

Agitated: Chopin's Prelude in G-sharp Minor

Here, in Opus 28, Number 12, is a fast and agitated waltz. First there is the rising strain of notes from a G-sharp minor chord, reminding me of a climactic buildup, misplaced at the beginning of a number, not the end. The buildup resolves itself, only to rebuild again. The waltz goes like this for a while, shifting keys a bit and building up to a big climax with its D-sharp minor chords. It then continues on and on, until it reduces to just two notes jumping back and forth. The waltz then resumes and ebbs away, only to have two sprightly octaves pop up at the end. It is not too hard to learn to play, although some of the chords are a bit of a stretch. There is also the problem of moving one finger of the right hand while keeping the thumb on the same note. I suppose one could dance the waltz to this, but it would be a bit more forceful than the usual waltz, because every one of the three beats is accented, not just the first one. As a waltz, this piece has somewhat of a Slavic feel, but that may just be because of the minor key. In any case, it seems to be the direct opposite of the previous prelude in B Major.

Contentment: Chopin's Prelude in B Major

This prelude, Opus 28, Number 11, suggests contentment to me, hence the name. It is a happy and resolved piece. Down under the contented exterior, there are some unexpected turns. These come out if you play the prelude. You stumble all over the place to begin with because the notes are not where you expect them. An arpeggio goes zigzag up and down then it unexpectedly goes up after an up. The pieces of the prelude do fit together into an organized whole. So this can be thought of as a Yin-Yang piece: there is a disturbance in the contentment. It terminates with a one-note solo (as do the preludes in D flat, A minor, and some others) followed by parallel fifths (Fx-Cx -> G#-D#), something the classical musical theorists say should not be done. So Chopin is breaking ground with this pleasant-sounding piece.

By the way, I am going to put all of these reviews of Chopin's Opus 28 on a separate web page and will tell you when it is ready.

Tricks: Chopin's Prelude in C-sharp Minor

This is one of those pieces that float around, not doing much of anything. It sounds like improvising, which has taken the greatest strides in jazz, producing what I call "deedle-deedle" jazz. Chopin's Prelude in C-sharp Minor, Opus 28, Number 10, is not so much deedle-deedle as it is a bunch of conjurer tricks. Imagine a magician appealing to the sky, causing a magic effect to drop down and achieve some paradoxical result. This is what this piece reminds me of. So I call this prelude "Tricks". It happens four times, and then suddenly it's gone, like the Cheshire Cat in Alice in Wonderland. It is not too hard to play; the fingerings in the downward "tricks" are what have to be learned. Altogether, a little frill of magic.

Incidentally, the key of C-sharp minor seems to be a favorite with classical composers, so much so that I call this the "classical key". Beethoven's Moonlight Sonata and Chopin's Waltz in C-sharp Minor are other pieces written in this key. It is said to be Chopin's favorite key, and it is interesting to note that the longest C-sharp minor passage in Opus 28 is not in this prelude but in Number 15 in D-flat (C-sharp's alter ego), the Storm, which I will review in a few days.

Sunrise: Chopin's Prelude in E Major

Chopin's Opus 28, Number 9, rumbles in the bass like an enormous church organ. It sets off a theme, then reaches a peak before settling down to a big climax at the end. Indeed it reminds me of a hymn, but its deep tones and its climaxing reminds me of something else - the Sun rising in the east. To me the notes suggest the lightening that gradually takes place in the sky before Sunrise before the Sun makes its grand appearance. It is fairly easy to play; the main difficulty would be to deal with repeated notes in the chords. This is a good one to play if you want something dramatic to play on the piano somewhere to catch someone's attention. It would be a good part of any church service, especially the prelude in the service.

Frantic: Chopin's Prelude in F-sharp Minor

Opus 28 Number 8 reminds me of some of the angry-mood pieces of Beethoven such as the Appassionata Sonata and the third movement of the Moonlight Sonata. This one has a driving melody in the treble with a descending triplet bass. It also has an obbligato in the treble written with small notes. When I hear the piece I wonder how one can move one's hand so fast on the keys, but I tried it once and found that the notes were selected to fit into the hand, so it is not that hard to catch its rhythm. Nevertheless, this is a difficult piece to play and I have not attempted to play it much. Instead, I put it into Cakewalk. When I do that I find that I have to double the melody notes, else they can't be heard over the din of the frantic obbligato. I feel that this piece sounds frantic, hence my name for it. Its discordant chromatic scales contribute to the agitation in the piece. It reaches a peak near the end and descends into a soft ending, finally concluding, like several of the other preludes, with three or four slow chords. To me this is the most Beethoven-like of Chopin's Opus 28 preludes.

Short and Sweet: Chopin's Prelude in A Major

This is the shortest of the preludes in Chopin's Opus 28. Number 7 is a brief waltz, that takes a theme and repeats it four times, following fairly standard harmonies, and ends in an A major chord. It comes, and then it is gone; too bad, because it is a really sweet number. Hence I call this one "Short and Sweet". At times I thought of continuing it but it is hard to do; it is like finding compounds of noble gases such as argon because the piece is complete as it is. This is the first Opus 28 prelude I have ever heard; I was only about 7 or 8 when I heard it the first time on a 45-rpm record that my parents had bought; it came with the Prelude in D Minor (Epic, number 24, which I will cover on 2003 May 27) on the same side, and that one seemed so complicated that I thought that it was forever out of my reach. I will discuss that later, but indeed I also learned how to play the A Major prelude. It is easy to play, but it needs to be played with feeling. One huge chord in the treble at the end of the third theme looks unplayable; the way to play the chord is to hit the A-sharp and the C-Sharp simultaneously with the thumb astraddle the two black keys. This means that the piece can't be transposed into another key without risking the playability of this chord. But no matter; the piece was made to be played in A Major and it stands as a completed work as it is.

Lost Love: Chopin's Prelude in B Minor

I don't know why Chopin wrote so many depressing preludes. They all seem to sound alike. They all could be funeral songs, it seems. Or wait. Maybe some are different. Chopin's Prelude in B minor, Opus 28, Number 6, sounds funereal. It sounds like someone grieving over a loved one that has been lost. So I call it "Lost Love". It could be a significant other that has left them for someone else. It could be a husband or wife that has recently passed away. It could even be for a person that has changed significantly, so they aren't the same person any more. That is what this prelude seems to me. It sounds different from the E minor prelude in that the E minor prelude is more haunting and pensive. It is different from C minor in that the C minor prelude is more formal and majestic. The B minor prelude may be written for the wrong instrument. Most of the melody is in the bass, so that this is really a cello solo. If you play it, the tricky part is to keep the right hand soft so that you don't hear its drone above the melody in the bass. Every once in a while the melody passes into the treble, so it is an interchange between the two parts. The piece does have a notational inconsistency. A note in a chord with a C sharp and an A sharp is written F double sharp, but later it is written G natural. This is causes by a notational paradox in the first instance; the note wants to be both F double sharp and G natural at the same time. Indeed this prelude is indeed a sad melody. Fortunately, tomorrow I will review a happier prelude.

Fits and Starts: Chopin's Prelude in D Major

This Prelude, Opus 28, Number 5, seemed like an ordinary enough tune, and I found it difficult to pin a name on it. Recently, though, I tried playing it. Playing this prelude requires coordination between the two hands and a few jumps of an octave or so. It is a continuous piece with an endless-seeming string of sixteenth notes, six to a measure. To me, when I played it and when I listen to it, the piece does not ever seem to get really going. It goes by fits and starts. It starts first of all with a melody oscillating between B and B-flat (Chopin is using blue notes! The blues had yet to be invented.) Then it resolves into D major, or does it? It starts wandering off again into B minor and continues meandering through a series of harmonies until it finally shoots up to a high D and then settles down to a couple of closing chords. It has a happy feel to it, and sounds pleasant, although its sudden turns keeps you alert. So I find that the prelude has a distinctive character after all.

Will the economy defeat Bush in 2004?

I saw in this morning's Richmond Times-Dispatch (2003 May 8) that Ross MacKenzie said, "Bush II probably cannot prevail in November, 2004, if the economy is further deteriorating or still stagnating - or not clearly recovering." Mr. MacKenzie is reasoning that if the economy turns or stays bad in 2004, then Bush II will be defeated in November, just like his father George H. W. Bush was defeated in 1992 because the economy was in a downturn.

I don't think that will happen. Bush II has two advantages over Bush I. Bush I did not make any innovative changes to Administration policy. Bush II has made at least two - the War on Terror and the Department of Homeland Security. Further, Democrats gained in the 1988 midterm elections, while Republicans gained in the 2002 elections. So while the economy sank the elder Bush, I believe that Bush II will still win in 2004 even with an anemic economy.

For Bush II to be defeated in 2004, other things would have to happen as well; for example, a substantial third party, a charismatic Democratic challenger, social unrest, or major snags in the rebuilding of Iraq. I believe that if two or more of these things happen, Bush will be defeated; otherwise, he will be re-elected. So in 2004, it may not be just the economy.

Moonlight: Chopin's Prelude in E Minor

Chopin's Prelude Opus 28 Number 4 has a haunting mood and slow changes in harmony that make it seem like the light from a fire or the light from shimmering sources, such as moonlight on a lake. Hence I call this one "Moonlight". The melody of this piece isn't much; it goes back and forth between two notes and then it descends. Then like a flute player trying to catch his breath, it pauses, then starts its plaintive melody again. This time it goes through a different string of harmonies. It then soars to a climax and descends into the three-chord ending. At each stage of the harmony, one or two notes change at a time, changing the chord: E minor, F-sharp diminished, F7, F minor 7, and so forth. Of course different notes could have been changed. In fact, this piece can be computerized. I once wrote a program to write a Chopin Prelude in E Minor Opus 28 Number 4 Variant by selecting random notes in the downward descents, which you can play by clicking the name. I only computerized the first half of the prelude; this MIDI file concludes with the original second half. The computer variant sounds pretty much OK but was more discordant and so had a more macabre feel. The computer could have chosen one of millions of Preludes, and in fact Chopin chose one of them and called it his Prelude in E Minor. It is fairly easy to play, but what is tricky is to get the emotion into it because it drags out a sense of melancholy in you and you feel it as you play the tune. It is a good piece to play on a soft summer night.