Thursday, November 12, 2020


In our last episode, I discussed the way in which Beethoven's Für Elise can be felt according to its original 3/8 meter or alternately in 6/16. (Tip: The most fun is try to hear both at once!) Each option includes six 16th notes per bar, but the former groups the 16ths in three pairs and the latter groups them in two sets of three. After creating my little re-metering, I flashed back to an even earlier and even more iconic piano piece associated with children which can also be heard as 2x3 or 3x2. That's right, after chopping up Für Elise, today we'll be considering the most chopped piece ever: Chopsticks

A little research has confirmed that the closest thing to an original version of this music, which has surely been played many different ways as virally transmitted from child to child, uses the waltz-like 2x3 pattern:

You can hear it played in the 1946 Academy Award winning "The Best Years of Our Lives" here, with Hoagy Carmichael counting in "1, 2, 3." [video should begin at 2:09:53]

[If you need more waltzing chops, Liberace awaits you. He eventually ends up in duple meter.]

Of course, the version which was somehow known to every piano-adjacent child in America before the Internet and Tik-Tok introduced instant virality, would just feature the top staff above, played by single fingers of each hand in delightful contrary motion. Its appeal is surely in part based on the fact that the performer needn't worry about controlling independent digits (or hooks in the film clip above), with their relative strengths and weaknesses.

But getting back to meter, after a few Facebook conversations, I'm guessing it's true that most young piano pugilists feel these six-note repetitions in three groups of two rather than in two groups of three. I know I did. Like so:

[Just ignore the left hand in that quick re-alignment.]

So, here's a very famous melody which is probably meant to have the beat subdivided into threes (waltz feel), but which is maybe better known among children pounded out in groups of two or perhaps even "groups" of one! This makes sense since it requires a bit more musical and technical subtlety to group repeated notes in threes, with the second and third note of each group thus needing to be lighter. 

One of the tip-offs that the song should be felt in two groups of three (what I'll call a 6/8 feel) is the middle section which has a metrical pattern that is clearly 6/8. And this is what interests me most. That I, at least, learned this song with a 3/4 feeling, but switching to 6/8 in the middle and right back to 3/4 for the return of the opening. More or less like this:

This is as opposed to the more authentic and graceful (but somehow less interesting) through-waltz feel:

Notice it would be particularly awkward to play the entire piece in 3/4, though I've attempted to show how that might feel with my obnoxious percussion here:

And finally, I couldn't resist doing a more fun mixed-meter version inspired by Leonard Bernstein

I think that's all I have to say about that, and though I have already written about another kid-repertoire standard in the past, don't expect a feature on The Knuckle Song any time soon.

However, I shall be returning to Für Elise very soon as I'm finishing up a project I've had in mind for years. You've been warned.

Thursday, November 5, 2020

Variations on Beethoven

When I last blogged here, I wrote about a composer celebrating his 250th birthday in 2020 - and it wasn't Beethoven. Well, today I'll give Beethoven his due. Or at least half his due. In an effort to get the blog back in gear, I'll keep this pretty short, but maybe return later to a few of the ideas raised here.

Today's two projects were both inspired by something very non-Beethoven. A Facebook friend linked to this cool video in which an iconic Michael Jackson song has been manipulated in an unusual and surprisingly effective way. As the video title says, each off-beat of the song has been removed so that things proceed twice as fast, with words becoming fairly nonsensical, and the melody....actually, it's not such a melodic song, so the melody doesn't sound so off. The song is probably driven by its bass line more than anything, but that also survives the extreme surgery, and....well, give it a listen:


It has tremendous, driving energy (inherited in part from the original, of course), and it's also over surprisingly quickly! As the day went on, I started thinking about this idea of cutting out half of each measure - and was a little sad I'd never thought to try this trick on my own. I did once write about a "musical storyboarding" concept in which I made recordings which skipped quickly from the beginning of one section to another to help give an overall feel for the structure of sonata form works. And I've made other experiments in speeding quickly through recordings, with the same idea of getting a quick, bird's-eye view.

In the case of the Michael Jackson song, I was partly just impressed that a recording could be edited so cleanly, and that a song with words could come across as not too absurd sounding when sliced and diced. However, I quickly realized that many musical structures might work just fine with measures chopped in half since so much music only changes harmonies once or twice per measure. For no particular reason, the first music that came to mind for a quick experiment was Beethoven's Xtremely iconic Für Elise. 

Because this little piano piece is in a triple meter (3/8), my first thought was that I would remove the final third of each bar, but after a quick look, I realized that so much of the figuration groups 16th notes into half-bars. This meant that converting 3/8 to 3/16 might actually work, and in fact, the music - or some subset of the music - survives remarkably well. The effect is to strip  down Beethoven's flowing writing into something more elemental, almost like a Schenkerian reduction. For this little project, I chose to work only with the A section. In the video, you can view it first in the original context, with eliminated notes whited out. Following that, you can hear the same (synth) performance while viewing a newly created score in 3/16.

So, yes, I do think this works pretty well, and it feels a bit like a "found music" thing. This humble little piece has been hidden in plain sight within Beethoven's canvas. I didn't so much write it as discover it.

But I also discovered something else. The experiment made a bit more plain something I hadn't thought about so much, which is that though Beethoven's composition definitely functions with a subdivision of three beats to the bar, the groupings (often defined by the hands playing) often appear as two groups per bar, and the little reduced version I created actually treats the groupings that way. 

In other words, the music has switched from basic groupings equalling an 8th note to groupings equalling a dotted 8th note. 

Whatever factors have gone into making this such a notoriously well-known work, a case could be made that part of its real charm comes from the way Beethoven's patterns glide back and forth between groupings of two and three. I'm not really arguing that the music should be heard with groupings of 3 16ths as primary, but I couldn't help wonder what that might sound/look like.

So, my final little project today was to re-notate the entire piece in 6/16. 6/16, like 6/8, implies that two beats are felt per bar, whereas Beethoven's 3/8 suggests three beats per bar. It would be a fun experiment to perform the whole thing with that in mind, but to make the point more obvious here, I added a little background percussion to make explicit where the beats now fall as my robo-pianist supplies the artistry.

And it all works, with some charming syncopations along the way - until we arrive at the climactic triplets in m. 78. (I never liked that part in the original anyway!) At this point, the jig is up, as it were, as the two-beats-per-bar percussion creates an odd conflict against the nine triplets per bar. But, it's also an exception that otherwise proves the rest really does kind of work.

This "performance" is pretty brutally unmusical, but it makes its point.


If the distinction between "three beats per bar" versus "two beats per bar" is confusing, here's what the original would sound like with a drum-part emphasizing the more natural feeling of "three beats per bar."

And that's all for now, but there's more 2020 blogging ahead. Stay tuned...

UPDATE: I should've done a quick search before posting, but have now realized there's at least one rendition out there of Für Elise with a 6/16 feel, and it's from an album I've definitely listened to before: Don Dorsey's "Beethoven or Bust" from the late '80s. My favorite track there has always been the "Western" version of the Scherzo from the Sonata, Op. 31, No. 3, but I just checked and found there is indeed a Für Elise given the same two-beats-per-bar treatment I do above. The main difference is that the beat only drops when the left-hand bass line comes in, so Dorsey's treatment allows the ambiguity of all those introductory figures to remain. This is surely another part of the charm of Beethoven's original. Whether or not the main "tune" is heard as 3/8 (correct) or 6/16 (for fun), all of those winding figures defy clear metrical categorization (unless someone like me inserts insistent percussion). In thinking more about this, I've realized that for many years, I always heard this music with the beats more or less as follows:

It's less important whether the first note is heard as a real downbeat than that the feeling of three beats per bar doesn't arrive until the second full measure; and Beethoven keeps obscuring that feeling between phrases.

Monday, May 25, 2020

The one about the other guy having a 250th birthday year

As with so many blog posts in the past, I'm here again due to the wonderful world of Facebook discussion threads. In this case, a pianist friend and her conductor/oboist husband were wondering about examples of music in 5/4 time that pre-date the second movement of Tchaikovsky's Symphony No. 6. As it happened, I had been dabbling in this trivia a few weeks before - specifically on "May the Fourth Be With You Day" when another Facebook friend posted this (which actually refers to a Paul Desmond tune made famous by Brubeck);

I fairly quickly responded with a couple of improvised responses to that from Holst and Tchaikovsky:

So, my knowledge of famous 5/4 music also basically went back to Tchaikovsky, but I did sent along a link to this very useful Wikipedia page on quintuple meter which I had run across while investigating May 4. My friends wrote a bit later to make note of an unusual fugue in 5/8 they'd found there written by Anton Reicha. Did I have a clear sense of who Anton Reicha was at this point? (This was five days ago.) Not really. I think I remembered him as someone who'd written wind quintets (true!), though I wouldn't have wanted to be held to that. Contemporary of Beethoven? I feel like maybe I would have guessed that as well, but wouldn't have been surprised if I'd been off a hundred years either way.

My friends also sent along the only YouTube link they could find of the Reicha fugue, and though it seems to be a generic synth rendition (with a mystifying picture of a bunnies for the video), I started listening. At first, in part I'm sure because of the synth sound, it seemed forced and weird, but as I kept listening, I started to get into the swing of it. I listened to it at least two more times on a walk, found a couple of early 19th century editions on IMSLP, and suddenly was in the midst of obsession.

So to back things up, since I shouldn't assume anyone knows much about poor Mr. Reicha, he was indeed an exact contemporary of a VERY famous composer also born in 1770. In fact, Reicha and Beethoven were fellow students and orchestra members in Bonn and later friends in Vienna. Reicha was also a pioneer of the wind quintet and an important teacher of composers such as Liszt, Berlioz, Gounod, and Franck. (Not too shabby). He also wrote a good bit about theory and had some very adventurous ideas about going beyond usual procedures, for example in the writing of fugues. The 5/8 fugue that brought me to this point was published in a set of 36 fugues which push all sorts of futurist boundaries. For whatever reason, though some of his ideas may have been influential (Beethoven became fugue-obsessed in his late years and Liszt was a pioneer in pushing tonality in ways that are suggested in this little fugue), Reicha did not make a big name as a composer, and aside from the wind quintets, he exists pretty much on the music history periphery. (Sadly, his February 250th birthday has already passed, but he still deserves some 2020 attention.)

Although the "ahead of his/her time" metric is not always a sign of greatness, it is remarkable that this 5/8 fugue dates from 1803 (or earlier). I don't know of anything from the period that sounds like it. Curious that the "old-fashioned" genre of fugue should be used for such experimentation.

I'll perhaps write more about it in days ahead, but its quirks include:
  • Being written in the unusual quintuple meter, which Reicha actually indicates as 3/8 + 2/8. 
  • Beginning in A Major but not really being in any particular key. For whatever reason, it ends in F Major. 
  • Having a long, meandering subject which, bizarrely, involves a single triplet and some afterthought sixteenth notes. The triplet is odd in part because the composer makes a point in the preface of being sure the performer doesn't interpret 8ths grouped in three as triplets. And then tosses in a triplet that's not easy to feel in time. But it's also just odd. 
  • Having successive entries of the fugue subject come in at pretty much whatever interval he felt like. The second voice enters a tritone above the first, for example. I guess this is the kind of thing he and Beethoven argued about. (There are eleven entries of the subject, all in major, and they begin on the following pitches: A, E-flat, G, A-flat, F-sharp, A-flat, B, E-flat, C, A-flat, F. Note that the most common is A-flat, and that A never returns!) 
  • Having long passages which modulate freely.
So, yes, it's a quirky fugue, but I have also found it irresistible. Although some of the writing for piano doesn't take best advantage of piano sonority, the notes lie very nicely in the hands, and even though I've now played through it many times, it still feels surprising and even magical. Unlike the inexorable logic one finds in a great Bach fugue, Reicha sometimes seems to be composing on the spot. That nonchalant final cadence in F Major could almost be inspired by someone saying, "Anton, time for dinner!" I still find the meandering tag of the subject (with the triplet and sixteenth notes) to be a little unnatural to the musical discourse, but he just kinda rides with it.

And that's what I'll do here as well, rather than try to analyze every chromatic alteration. Unfortunately, the two early 19th century scores available on IMSLP are both rather poorly engraved, and so I couldn't resist the siren song compelling me to re-engrave the whole thing. I decided to let Reicha keep most of his curious spellings (he likes having one voice in sharps while another is in flats), but there were a lot of spacing issues and also some poor choices about how the voices are arranged across the two staves. He's just one example of a passage that I think is much clearer in my version:

So, although I'm still at the work-in-progress stage, both with the engraving and the performance (on my poor piano which really needs a tuning and re-voicing), I'm releasing this into the wild because I think this is such charming and unusual music. There are at least three commercial recordings of this fugue (here and here and here)*, though they don't seem to be available on Youtube. (Actually I just discovered that the third is available on YouTube Music. It's very fast!) I have listened to all three, and they are fine. But this one says more closely what I think - based on my five days of Reicha expertise!

* Those three linked recordings go from slow to medium (my tempo) to fast. For some reason, on the first album linked, this fugue is listed as #9. I believe all of these pianists play the triplet in the theme a little more slowly then I do, which means I'm probably rushing; but I prefer that sort of headlong falling-forward feeling leading into the 16th notes.

Addendum: A few more observations about my edition and performance. All of the commercially released recordings have the A on the downbeat of m.24 re-articulated, although it is tied from the previous measures in all of the 19th century sources I looked at. This 20th century Barenreiter edition (kind of sketchily uploaded to IMSLP) does not have the tie, and the editor probably had good reason, but I like effect of that tie as it helps this transitional phrase elide more elegantly with what came before.

This brings up a broader point which is that I LOVE that Reicha does not include many articulations or dynamics - in fact, I wish he'd included fewer. I think there's a lot to be said, in music like this, for letting the performer make those decisions. My own set of fugues from the Summer of '18 has no such markings, and though this might be mere laziness on my part, I love the sense of adventure that comes with a good fugue. I play Bach fugues in church many times a month, and I make all sorts of idiosyncratic decisions related to tempo and articulation with them. Many different solutions can be satisfying depending on the context.

Saturday, May 2, 2020

Signs and Magic

[If you don't feel like reading a lot, there's a fun new game about 2/3 of the way down. I LOVE burying the lede.]

There's a throwaway line in the article I wrote for the Boston Musical Intelligencer last week which I've found myself thinking about ever since. After boasting that my "blog combines various levels of expertise in writing, rhyming, piano playing, composing, arranging, animating, music engraving, video and graphic design, audio editing, and programming," I felt compelled to add the following parenthetical (bold added for emphasis here):
(I’m a novice programmer but intrigued by the ways in which programming and composition both magically transform bland symbols into entire worlds.)
I didn't want anyone to think I was claiming anything like real expertise as a programmer, which is why I added the first four parenthetical words. The other words just sort of magically followed - which is sort of like how this post has been magically generated by these previous bits of word-generated magic. Sort of.

The two contrasting points I'd want to make about my experiences as a programmer are:
  1. I really am mostly a self-taught novice, with perhaps a creative flair for getting things done, but with all sorts of faults I can't really even articulate - because my faultiness recursively includes not understanding fully what I don't understand - but having to do with writing inefficiently and struggling with more abstract principles of recursion and multi-dimensional thinking. 
  2. I LOVE programming. Maybe in part because I often don't quite know what I'm doing and am not working from familiar internal scripts, it's just always amazing to me when things work. Partly, the speed with which modern processors work and the remarkably flexible, powerful languages available mean that a lot can be accomplished with seemingly little. Paradoxically, there are many things that seems like they should be simple (because our own brains have so many sub-conscious algorithms) which can be a tricky to "explain" to a processor. And confronting that reality, while frustrating, is also fascinating.
The main reason I'm writing about this now is that I've been hard at work on a couple of code-oriented projects the last 2-3 days. One of them is still in process, but it's a music engraving challenge using Lilypond which has required a few deeper-than-normal dives into the program's text-based commands - commands that somehow produce really beautiful-looking music notes.

Unlike a more typical program such as Finale or Sibelius, you generally don't see results in real time in Lilypond. You type out commands and then update the output as needed. Finale and Sibelius will certainly take time to re-format a major layout change, but in Lilypond (using the Frescobaldi environment), even adding an articulation or accidental won't show up immediately in the notation. Although this might sound odd, my favorite part of this process is when I try out some solution, hit the "engrave" button and wait to see what happens. This can take 2-10 seconds depending on the complexity. A lot of times, it's back to the drawing board, but that makes the moments when things work that much more satisfying. 

My other recent project has to do with my day job, which I haven't written about much here. I have mentioned before that this blog got its start when I first started teaching a big arts lecture class to non-music majors. Grappling with "outsiders" who didn't necessarily think like musicians was a big disruption to my own way of thinking, and that's basically why I started blogging. I now teach at a boys prep school, work which includes general music classes for middle schoolers. This has pushed me yet further outside my comfort zone as the need to see things from a different perspective has shifted again. 

Currently, my 7th graders are learning about Beethoven's 5th - a handy topic in this Beethoven year - and I'm always searching for multimodal ways to get the boys into Beethoven's world. (We've done some simple composing using the primary motif, and one mad scientist student put this together in just fifteen minutes of class time after being provided only with the drums and once instance of the motif.) We've conducted the Exposition section of the first movement many times; conducting together is one thing that actually kind of works in this brave new Zoom world. Conducting has the advantage of being physical, without being as intimidating as dance, and it invites a range of ways to feel the music in the body and to pay attention to moments where the pulse is paused and where the character changes. It's also a fun excuse to show videos like this.

Earlier this week, I had each student submit a video of himself conducting the Exposition, and I was impressed by how well they were anticipating what was coming and responding to various style changes. (Was also fun to see the wide variety of conducting styles, from Bernstein-esque melodrama - one even donned a Beethovenesque wig -  to the most serious, sober-minded, technical focus.) So I thought it would be fun to put together a little puzzle game which would require re-assembling musical segments that are out of order. I'm sure that to some degree, something like this Google Doodle from Beethoven's 245th was in the back of my mind, though I wasn't thinking consciously about it.

Anyway, I dove into Scratch, MIT's amazing programming environment for "children" (which I've written about many times before) and after a few hours, I'd roughed out a little game. After a trial version with one class, I put some hours into refining it and adding fun graphics, and here you go:

I think it's pretty cool. It was a challenge for many students, though I had one solve it in less than three minutes. However, after their first attempt, for which they had no previous information about how the music was divided, we talked about what to listen for in each segment - not only what to recognize, but how to think about where it fits into the 8-part structure. (We had already spent a good bit of time learning to identify various themes, using my Beethoven listening map.) I think it was a very successful exercise.

If you don't feel like playing right now, you can watch this demo of the game in action.

Returning now to my parenthetical comment with which I began:
I’m a novice programmer but intrigued by the ways in which programming and composition both magically transform bland symbols into entire worlds.
I'm not saying that musical composition and programming are the same thing, although it is well-known now that computers can compose. My point is that the satisfactions both offer me feel similar. Of course, the situation is muddied by the fact that I do most of my composing and arranging on a computer, and most of my programming involves producing or manipulating music. (Here's a rare game I created which has nothing to do with music.)

But both do feel like a kind of magic. I'm proud to say I built my little Beethoven game in Scratch from scratch - meaning it's not based on another Scratch project. (One of the cool teaching features of Scratch is that anyone can look inside any other published project and copy the code to build something new. Programmers beware - the "code" inside my projects is typically sloppy, uncommented, and certainly inefficient). But even though I basically understand the logic of what's going on, it's still a little miracle when things work.

Here's a little summary of what it's like to do something like this: I conceived the basics of what I wanted the game to do, then put together a series of commands to get it to do what I wanted. This included such basic tasks as creating a function that puts 8 numbers in order by comparing them a pair a time. (A more advanced programming language would have this sort functionality built in, but part of the point of Scratch is to learn this kind of process.) There were multiple ways in which I could've written the instructions, but what matters most is the output. Also, as I worked and confronted challenges and successes, I added many elements to my original concept.

All of the above is pretty similar to what one does when composing, with music notation instead of code. (Yes, it is possible to compose without using notation.) It's also similar in some ways to writing (which also uses "codes") and other creative pursuits, but composition and programming feel a bit more closely connected to me. I find for example that when composing/arranging or programming, once my mind is switched into that mode, it's very difficult to come down from it. (I told my wife that, like drinking coffee, I should really try to stop programming by 6pm or I'll find it impossible to go to sleep.)

As I admitted parenthetically above, my code can be overlong and inefficient, and this is also true of my writing, so in final summary: GO PLAY.

Tuesday, April 28, 2020

Skip to my loop

This post might create a sort of strange loop for anyone visiting via the Boston Musical Intelligencer, which was kind enough to run an article of mine promoting this very blog. Read the article there, come here, follow the links back there, etc. Anyway, thanks to the Intelligencer for giving me this platform.

I've admired this site since it debuted more than a decade ago, inspired by the legendary Dwight's Journal of Music, a 19th century Boston institution. In a time when major newspapers are not really able (for mostly good reasons) to cover a town's musical scene, the Intelligencer provides a remarkable number of reviews (mostly written by volunteers, I believe) of local events as well as an indispensable concert listings page, various feature stories, and a lively reader commentariat. One can find a wide variety of viewpoints which provide a fascinating and reasonably broad picture of our local musical life. Some of the reviews display high levels of expertise and allow more room for digressions and personal commentary than a newspaper would. The commenter perspective can seem analogous at times to how sports radio gives voice to more than just the newspaper columnists. Although ill-mannered banter sometimes is a result, in general the Symphony Hall gang has a lot to offer, especially in showing how passionately people care about the music that comes to life on our stages.

I've always had an interesting relationship to music reviewers in that 1) I love reading reviews of concerts and recordings, 2) I don't feel like I would ever want to write such reviews. This is somewhat paradoxical because I do enjoy encountering strong opinions, and I sometimes have strong opinions; but I tend to feel like my own opinions about a given performance are too hopelessly subjective to be given the weight of print, virtual or otherwise.

There's also the fact that I don't actually get out to that many live concerts for various life reasons. As I wrote back in 2008, I sometimes feel like Tom Townsend from Whit Stillman's Metropolitan, who would argue passionately about the strengths and weaknesses of Jane Austen novels, only to admit that he'd never actually read the books - just the literary criticism. It's probably fair to say that I enjoy living on the periphery of the music world, diving in every now and then but often viewing from a distance, and the work I do on this blog has a similar relationship to actual performing. What I'm doing here is often articulating around the edges of what's going on in performance of a given musical work, rather than just performing the music and letting it speak for itself.

Anyway, as the Intelligencer concert listings page is a bit more dispensable during the pandemic, I figured this was a good time to promote access to the mostly online musical diversions I've been creating here. It does perhaps feel a little dissonant to promote my own "play" in a time of suffering and loss, but of course all artists are grappling with what it means to make art in such times. And I do intentionally use the word "play" to suggest something more substantive than it might first appear. I have definitely found that I'm listening to music and thinking about music more during the past two months, and though there may be some element of escapism there, it's also about connecting more deeply with music's expressive and spiritual power.

As for promoting the blog, I am always hopeful that my strange creations will find their audience, however spread out around the world that audience might be. And I've also always wanted to resist the idea that a blog is just an ephemeral collection of passing thoughts. Packaging a lot of those thoughts together is a way to affirm that something more lasting is happening here. As I wrote way back in 2008 when I debuted my "Multimedia Musing Machine":
George Costanza once said, while trying to impress a NYC tour guide who thought he'd just moved in from Arkansas, "You know if you take everything I've ever done in my entire life and condense it down into one day... it looks decent." To paraphrase, "if you take everything I've ever done in my entire blogging career and condense it down into one looks decent."