Thursday, 13 November 2014

5. Londonderry Air

This song was already familiar to me from a childhood spent in church. Apparently someone had taken this Irish folk tune and set Christian lyrics to it. So this prior knowledge of the melody meant I was always acutely aware of any mistake I made while tackling this piece. The cross-hand playing we did in Nobody Knows made a come back, but for me the most interesting and novel aspect of the song was that the score's given on three staves. J. T. assures us that, rather than making things more complicated, it actually simplifies things. It certainly makes things less clutteredand since clutter is actually an aspect of notation that bugs me, I definitely find this three-stave anomaly to be helpful. 

All in all, I think this song was good for me. I'm sort of conservative when it comes to flailing my arms all over the keyboard, and this song eases me into that. Apart from repeatedly crossing hands, a couple instances exist in which its necessary to walk arpeggios some distance down the keyboardnot too extreme, but graduated in a sense that makes it the perfect stepping stone for someone of my modest (but growing!) capabilities. 

I am utterly enamoured of the particular chord pictured abovethe one the diminuendo sign seems to also find necessary to point out. It's located in one of the final phrases of the song and consists (as is apparent) of two flattened C's, one flattened G, an A, and an E. It was murderous to read when I first encountered it because just about every infernal note has an accidental against it! But I was more than rewarded at the end of that effort. (Turns out to be an inverted B7 chord when all the key-signature dust clears.) And, if I recall correctly, my response to the combination was to find it at first peculiar and unexpected, then almost in the same instant it became interesting, and finally it settled on just being really satisfying. 

4. Toreador Song

Georges Bizet, what can I say? I had him in the second grade book aeons ago when we played Habanera. That was funI really loved that syncopated rhythm. And the learning never stops. I have not perfected this bullfighter's anthem by any stretch of the imagination. My current weak spots are a couple small jumps in the 4th and 5th bars. I kinda realise I just need to isolate and work on them though, because they haven't always been my weakest spots. What happened, I think, is that the polishing that I've done to the other areas have caused what I might have previously considered strong areas to appear weak by comparison. This is good, of course. It means progress is being made... but the song, as I currently play it, still sounds pretty horrible.

The good news is that the above double-time, backhanded-F-major-scale-that-starts-on-C is looking and sounding a lot better as of yesterday! Molto crescendo! Also, that trill-esque passage in bar 9 (repeated in bar 21) is looking pretty okay too in the right hand; if I could only get my left hand to keep up, I'd be set. Oh yeah, and how 'bout those acciaccaturas? They're coming along... It's a work in progress though, and I'm learning to be patient and allow myself the time I need to grow.

3. Musette

Musette on the other hand is a perpetual stumbling block for meso much so that about a decade ago when I first tried this piece, I gave it all up under the presumption that piano just wasn't my thing. (Dare I shake my fist at Bach?) Seriously though, I do like very much the modulation of volume and intensity prescribed in the piece: it's p  f  p  f alternating all throughout, and the contrast really works. Plus, that middle staccato section (below) is pretty sweet.

But... for the refrain with which the song begins and ends, I simply can't get both hands to simultaneously jump the measly octave and consistently land the middle fingers  on F# without at least one sliding off or hitting a neighbouring note. It seems to require a level of precision I haven't yet developed to perfectly balance my fingers on such a narrow perch while descending at the rate of however many feet per second is prescribed by the term giocoso. I've managed to do it a few times, of course. I've been practising it for almost 6 weeks, and I hit the right notes maybe 35% of the time (smh).

I could get discouragedI have donebut I no longer am. Instead, I've determined to make everything into a learning experience. Therefore, my current approach to this piece is to play it as fast as I can. Speed runs. My hope is that after several weeks at this ridiculous pace, when I finally get it back down to giocoso, the jumps will seem like a breeze.

Thank you, Bach :)


2. Melody

Luckily this time around, I found the courage to push past my incompetence in playing the first piece in order to tackle the second piece, (Robert) Schumann's Melody. For an intermediate player like myself (and one returning to the piano in adulthood after a long, loooong absence), I think this piece is a good exercise in developing hand independence.

The left hand notably doesn't just chip in with a harmonising note or chord now and thenonce or twice a bar, or something. Rather, it plays continuously throughout, even more so than the right hand, and provides (as J.T. himself put it) "a subdued, but ever-moving background." I actually play this somewhat to my satisfaction, though I'm still working out some of the transitions. The legato "singing tone" required of the RH complements my style of playing, I'd say. And thank God it's not too fast: cantabile and moderato are just my "speed."

1. Nobody Knows De Trouble I've Seen

This song was arranged by John Thompson (J.T.) himself, and it is a pretty easy song, I'd say. I mean, it's in 4/4 time and it's all crotchets and minims, with a few semibreves thrown in here and there... and yet for the life of me, I can't seem to play it right! It just never feels right in my fingers, and my timing's all screwed up. Now, I'm a person who prides myself on my innate sense of timing, so (ahem!) I think I'm just gonna blame a huge chunk of this problem on those arpeggios sprinkled over the piece. (Two consecutive ones are pictured above.) I can never seem to get them perfect the first time. Every time I play them, I have to practice them once or twice before they sound right. What's the answer... finger drills you say?  No argument there. I'm working on those, too...

Wednesday, 6 February 2008

stuff I don't understand: the story of e

Pi (π) and e are numbers. Strange and ethereal numbers that cannot be quantified. Because the phrase "be quantified" denotes the perfect tense, which implies a perfected action. Done. Complete. Finito.

Well, actually, finito means finite. But it still captures the anomalous nature of the situation because these numbers (π and e), though less than 4 and 3 respectively, cannot be said ever to end. It makes one wonder how anyone ever computed π, since it's defined (in words) as the ratio of a circle's circumference to its diameter. A ratio is by definition rational, is it not? Someone measured the length of a circle's circumference and its diameter and divided the first by the second. What's irrational about that? A rational number, after all, is defined as one that can be expressed as a ratio of two integers. Yet π is nothing if not irrational.

But this blog isn't about π. That's not the book I read. This blog is about e.

Let's say you have a curve that if the value of the function that defines it is checked at any given point of x (that is, what's y equal to at any given x?), you find out that that value is the same as the slope of the curve at that point. And what if this is true no matter what point you pick on the curve? This represents an exponential function--but not just any exponential function. It's the exponential function. The one that's related to e. The one we'll have to come back to shortly.

Now, we all know that functions are usually expressed in terms of x. Such as x plus two (x+2) or x squared (x2) or x cubed (x3). Usually if you work out these formulas by putting in a numerical value for x, you'll get a numerical answer back. Since this answer changes for every value of x, we usually just call it y till we know what it is for sure. Example: x+2 = y. But exponential functions are different. They have the variable (the x-value) in the exponential position. Like this: three to the x (3x) or four to the x (4x) or anything to the x (ax).

I wrote above about the slope of a curve at any given point (2 paragraphs up). It might seem strange to think of a curve having a slope at just one point, because the direction of the curve is always changing. (Actually, mathematicians usually call even straight lines curves, but let's think of the really curvaceous ones right now). Think of the slope as the general direction that the curve happens to be taking at that point. What if it stopped turning right then? Which way would it be headed? It's something like that. And it turns out that if you know a formula for a given curve, there's a way use it to find a new formula that will give you the slope at any time. (Remember, this e curve I described above is special. No other kind of curve would ever have given us the value of the slope at a point simply by finding out y. In fact, for a long time, no one even knew it existed.)

But exponential functions in general are kind of special too. When you follow the method for finding the slope-at-any-given-point (which math people call the derivative), you just end up with the function you began with multiplied by some constant. The value of that constant would depend on the function we started with in the first place. So someone brilliant thought, what if we could find that number that when it's at the base of the exponential function (as 3 is at the base of this exponential function:
3x) the constant that comes back to multiply it in the derivative is 1? What if we could find that number? That would mean that we found a function whose derivative (slope-at-any-given-point) is itself (since anything times 1 is itself). This is a HUGE deal, because that would make it so much easier to work out a bunch of high-level mathematical things that I don't even know about yet.

It turns out that number does exist somewhere too. And since the constant that comes back to multiply
2x is about 0.693 and the one that comes back with 3x is about 1.099, then they knew the number they sought had to be between 2 and 3. Trying a whole bunch of different numbers in between brought back the answer 2.7182818284 (continuing forever), which they shortened for mortality sake to "e". So ex is our special function whose derivative is ex.

This was my first introduction to the number e.

Tuesday, 28 August 2007

a pertinent idea

The idea expressed below demonstrates the spirit of life which, like Henry James, does routinely include tragedy and doesn't offer happy endings "at any cost." Interestingly, this passage was clipped from a blog entitled The Art of Fiction by Mauricio Salvador:

"Como diría el narrador de Muerte en la tarde, de Hemingway: 'Señora, todas las historias, si continúan lo suficiente, terminan en la muerte, y no es un auténtico narrador de historias quien se lo oculta.' Y Philip Roth, sin duda, es un auténtico narrador de historias. "

A crude translation: "Like the narrator of Hemingway's Death in the afternoon said: 'Madam, all stories, if they go on long enough, end in death, and he who tries to hide that is no true storyteller.' And Philip Roth, without doubt, is a true storyteller."

I've left only to add: Y Henry James, sin duda, es un auténtico narrador de historias.