Bach Day #2: Left-handed Complement

So I've made it to Day 2 of my 2020 Bach-a-thon, just under the wire again.

Today's subject is: ME! Or rather, to discuss a bit more what it is I've done to Bach in the video I posted yesterday. To review quickly, this arrangement (minus a few 2020 tweaks) was originally made last March, inspired by a differently mischievous left hand part added by composer David Bruce. Bruce's basic goal was to bring out some of the inherent metrical ambiguities hidden in Bach's original work for solo violin. [Again, here is a really fun playlist, beginning with Bach's original, and continuing through many varied re-interpretations.]

The original Bach is composed almost entirely of running 16th notes in 3/4 time, but there are several passages in which the note groupings can be interpreted as something other than steady groups of 4 (which is the main topic that drew Bruce to his project). I know this well, because I've heard this piece hundreds and hundreds of times (my two daughters have each learned it), and I regularly experience cognitive/metrical dissonance because I lose track of the downbeat.

Here's an example of a passage in which my ear/brain almost always shifts the barline over by one 16th. Starting around m. 20, as the lowest note in each group of four gets lower and thus stands out from the three preceding, it just starts to feel like a downbeat. I've tried to illustrate what happens with this little video. It first shows (with aggressively accented beats) where the groupings actually fall. The second version shows one of the places where my ear will experience a shift and start hearing the downbeat one 16th note early. What's interesting is that I rarely experience this as if I've been cheated. It's only when the end of the passage comes, going into m.29 that I'm aware of an extra 16th note - almost like a record skipping. That's a lot of words, but maybe this makes sense:


David Bruce claims that most of his compositional choices are based on possible implied groupings in Bach's original. When listening to his version, I found myself skeptical in many places - but I also liked the places where the Bach seemed to be twisted beyond its own internal logic! So, the point of my own project was to be continuously disruptive, with all sorts of metrical tricks along the way. There are triplets that start on off-beats, downbeats shifted into odd places, rhythmic groupings of 3, 4, 7  16ths notes, etc. The process was honestly rather casual and improvisational ("hmm, let's try this") and took a LOT less time than it has for me to engrave the results. Rather than try to write about all of the choices, I made an annotated version that over-explains much of what is going on here:


There's a lot more that can be said about all of this, but I've got nine more days of Bach blogging to go. I will say for now that my "arrangement" is not necessarily intended to be performed by a human pianist, though I don't doubt there are those who could manage just about all of this. I might try to learn it at some point (I've managed the first 30 bars or so before), but part of what I love best about this is the absolute steadiness of Bach's right hand as essayed by my computer. When I listen, it's especially fun to try to keep the original 3/4 meter in mind - kind of like trying to organize an image fractured by a trick mirror.

Also worth noting that one of the most enjoyable things about this project is getting the notes to look right on the page (including for the "rhythmic feeling" demo above). There are choices I've made that would make this harder for a pianist to read - but that make it easier to see what's going on. That's an interesting tension in itself. More tomorrow...

I'll be Bach

Well, this day has almost completely gotten away from me, so the bigger post I'd had planned for Bach's birthday will have to wait. But, good news. Whereas I've spent most of my life thinking of March 21 as Bach's birthday, I guess there is also reason to celebrate on March 31. I mentioned this on Facebook, and a friend said he and his family had taken to celebrating eleven days of Bach, from the 21st to the 31st. Brilliant!

So, I'm gonna try to Bach-blog every day to the end of the month (giving me a flimsy excuse for my post title), beginning today with a new little reveal.

This "adaptation" of a famous Bach work actually debuted last March with not so much fanfare. In short (with more explanation to follow tomorrow?), I simply added an intentionally disruptive left hand part to a solo line originally written for one violin. I really liked the way it came out, and have listened to it happily many times, but had posted a version that only shows the original violin part. Because my left handed addition plays lots of metrical tricks, it's not so easy to notate, and it was only on March 1 of this year that I set out to make it look right. There were lots of interesting and unusual decisions I made along the way, and what you see below combines my interests in arranging, deranging, engraving, and score animating.


As I'll discuss more, it's not necessarily intended to be performed by a person which is one of its disruptive features. But it makes my brain dance in satisfying ways, and though it is not pure Bach, it definitely flows from a love for what his music does to my mind. Happy Birthday, Bach!

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J.S.P.S. Might as well include this as well:

Oh, and a playlist that shows the many, many ways this music has been re-imagined.

Notes that float

As the Internet, social media, and blogs have evolved over the years, it's likely that more people now see this blog (if they see it at all) on a mobile device than in its true webpage form. This is a little sad for me since I once spent a lot of time tweaking the Blogger templates to create a look I really liked. A typical mobile trip to MMmusing won't even show cool things like my should-be-patented "Multimedia Musing Machine," nor will it show my homemade Bachground wallpaper.

I also recently remembered that the web version of the blog has long featured a link to one of my favorite recordings of my own playing. I opened a 2012 recital (wow, so long ago!) with the Allemande from Bach's Partita No. 4 in D Major. I'd fallen in love with this piece after reading Jeremy Denk's wonderful 7-part blog series about it back in Aught-Seven. (Denk's series begins here.) 

I continue to find it unique among Bach's works for its meandering qualities, melodic but not in a particularly memorable way (meaning there's not really a singable tune). Rather, the highly ornamented right hand rolls along with a wide variety of rhythmic figurations and a sense of harmony that seems more free-floating than "typical" Bach. It manages to be improvisatory and intricate. And inspired.There's nothing else quite like it.

I have nothing against the other six movements of this suite, but this Allemande definitely stands on its own. (It is not as out-of-scale as the mighty Chaconne is in the D Minor violin partita, but it is unusually long and winding for an Allemande.) I also have nothing in particular against other recordings of this piece, but my own performance happens to say just what I would want this deeply personal music to say, so I figured it was time I posted it on YouTube. As it is a live performance played in front of an audience from memory, it is certainly not perfect, but it's really not the kind of thing that needs to be perfect.

To accompany the recording, I prepared my own engraving of this ornate score in Lilypond, a rewarding creative challenge in its own right. Because this music has such a linear quality, as if Bach is inventing each new melodic diversion on the spot, I liked the idea of a continuously scrolling visual. Lilypond has a function which makes it easy to create a score that extends horizontally for exactly as long as needed. Imagine a short sheet of paper (only needs to accommodate the height of two staves) which stretches out across the room. 

I also allowed Lilypond to let the music spacing breath a bit more than I did when preparing a companion "normal-sized" copy. When printing to paper, all of the elaborate rhythms (some measures include as many as 24 notes across) have to be made to fit within orderly staff systems and with some degree of logic across multiple pages. For a long scrolling video score, it's actually better if the measures are relatively uniform in length so that the scrolling speed doesn't have to vary too much, whereas normal engraving will usually take more advantage of less dense bars by compressing their spacing.

In some respects this is a work-in-progress, but I was happy to develop some more techniques both working with Lilypond and in creating scrolling animation. I have some other projects up my sleeve that will require more of the latter. 

But for now, I'll end this rather discursive post with this sublimely discursive bit of Bach:

A few postscripts:

• I am aware that the notes in the video are rather small. This is in part because using bigger notes would mean faster scrolling which can get a little dizzying, but also because I'm more interested in the visual than in the specific details. As I've written many times before, although there are plenty of nice ways to accompany music with visuals, I don't think anything beats the beauty of a musical score. Obviously, it provides a very close analog to the sounds being heard, but I find that listening while watching notes often helps to sharpen the ears. [To be totally honest, I wish the notes were a little bigger, so I might re-do this, but it takes time since quite a few synch points need to be entered manually to make the music flow properly.]
• Though still a work-in-progress, you can see what my engraving looks like on paper via this download.

Thirteen

Today just happens to mark the 13th anniversary of this blog. (MMmusing is a teenager!) And 13 just happens to be a Fibonacci number! So what better way to mark this occasion (and finish up this little blog series) than with a bit of Fibonacci fun?

In my last two posts, I talked about encounters I had with the Golden Ratio and the Fibonacci Sequence while preparing to lead some musical sessions as part of a broader academic day focused on those topics. I've already written about looking for the Golden Ratio in Beethoven and about writing a little vocal warm-up using Fibonacci numbers.

The latter is based on a simple diatonic pattern in which the primary notes of a scale (the "white notes" in C Major) are used as stepping tones for scalar ascents of 1, 2, 3, 5, and 8. Naturally, I was also interested in exploring larger numbers in the series, and though it's not practical to sing a range covering 55 notes, the piano keyboard can easily accommodate that. EXCEPT, I was actually a little surprised to realize that the 88 notes of a piano include only 52 white notes.

So, although I like the way the diatonic Fibonacci patterns emphasize the 3rd, 5th, and octave of a major scale, I set to work organizing the full chromatic complement of white AND black notes, which easily accommodates the Fibonacci 55. Sadly, the next number in the series is 89, and that's one note too far, but I also feel there might be diminishing returns if the number stretches out too far. (See postscript #1 to test this out.) It becomes difficult beyond 55 (or maybe beyond 21 or 34?) to feel the relationship to the groups preceding.

Anyway, the skeleton of my piece-in-progress is this very simple expression of Fibonacci numbers through expanding meters (Remember, the Fibonacci Sequence begins: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55):



There's not a lot of real "composing" going on there, but I then added a right hand part to emphasize some of those metrical tricks, build suspense, and also help support a vibrant ending in which a big C Major chord settles out into longer and longer notes values based on...well, you can figure it out. This little etude is called "Fibonacci Frenzy." (Yeah, yeah, yeah, I should record it like a real pianist and not subject you to this robo-performance, but I am appreciating the way Noteflight allows for the embedding of scrolling notation.)



 Since there are only a couple of hours left on this blogday, I'll just add two quick postscripts.

• In response to my Fibonacci vocal warm-up, Twitter friend Dan introduced me to a very entertaining and ever-expanding piece based on a Fibonacci-esque sequence: Narayana's Cows. This music definitely pushes the limits of how far out we can perceive these expanding connections.
• Rather coincidentally, this Sound Field video crossed my path a couple of days ago. Early on [0:21-0:40], one of the hosts indulges in some of that mystical "some music sounds right yada yada because...well...Golden Ratio!" As often happens with such discussions, there's not much substantive probing of what's going on and how valid this is aesthetically, though I appreciated some acknowledgement [3:28 - ] that Golden Ratios might just be the kind of thing you can always find if you look in the right place. But, most notably for me, the same host, Nahre Sol, ends the video with a little composition she wrote using both the Golden Ratio to govern the structure and some Fibonacci numbers to generate some riffs. (Oddly enough, the complete composition is not played in this video, so we don't get a chance to experience the Golden Ratio!) If you like hearing numbers dance, you might enjoy this.
  
  Happy MMmusing Day!

Warming up with math

In our last episode, I recounted some experiences thinking about the use of the Golden Ratio and the Fibonacci Sequence in musical structures. I focused in that post on the question of finding a mathematically "golden moment" in a work like Beethoven's Symphony No. 5, but for the teaching task that inspired all of this, I never even got around to Beethoven. (My students will get to hear me talk about the Golden Ratio in the Beethoven later in the semester.)

On the special "Golden Ratio" day in question, I was more focused on providing some direct musical encounters with the ratio that students could feel for themselves. We actually first experimented with seating the students in Fibonacci rows as follows:

X

X

X    X

X    X    X

X    X    X    X    X

X    X    X    X    X    X    X    X

Then we tried some counting-off games to help them feel how each row was the sum of the two rows in front. 

But I had also started playing around with composing some music that used these relationships, specifically: 1, 1, 2, 3, 5, 8, 13, etc. It wasn't too long before I'd come up with the following:

It actually had begun with just numbers as lyrics (1, 1, 1 2, 1 2 3, 1 2 3 4 5, 1 2 3 4 5 6 7 8), but I soon realized it might make an interesting vocal warm-up, so there you go. Of course, in real life, I probably would just notate the first three bars as one 3/8 bar, but these meters and the beaming patterns help to reinforce the additive process that's going on. Here's what it might sound like sung by creepy robots (but I have found it to be a fun and useful choral warm-up with humans):

And here's what it looks like notated fully. (If the embedded score doesn't work well, go here.)

One of the surprisingly rewarding things about doing this was realizing that the last three measures ascend to the 3rd, the 5th, and the octave, and of course, a major triad is constructed from root, 3rd, and 5th. That is pretty cool, although if you include the 2/8 bar, that one ascends to the 2nd scale degree which doesn't fit so nicely into the triad. 

Notice that, unlike the subtler principle of putting a structurally important musical moment 55/89 (61.8%) of the way into a piece, this use of the Fibonacci Sequence is right there on the surface. For better or for worse, the performer and listener can directly feel the asymmetry caused by the additive process. When a composer, intentionally or not, puts a surprisingly subdued oboe cadenza 254 seconds into a fiery 411-second movement (see end of previous post), it's highly unlikely that anyone could experience that golden relationship so consciously, though we may at some level feel its rightness. Of course, some would say that is part of the magic.

I have one more composition that came out of this whole experimenterience...and I'll reveal that soon.

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UPDATE: See follow-up post HERE.