Saturday, March 28, 2020

Bach Day #8: Listening to Math

Today I spent a fair amount of time fixing a couple of mistakes that had been hidden (from me) in yesterday's 30-minute version of Bach's Canon per tonos from The Musical Offering. I noticed one mistake while listening to the WHOLE thing cooking breakfast, and a friend with a very good ear noticed the other. It's rather crazy that I tried to get that complicated project online so quickly, but it's the way I tend to work; if I didn't do it this way - I probably wouldn't do it. I'm sure other little things could use fixing as well, but hopefully nothing major. So, first of all, here again is the latest "corrected" version:


The main thing I wanted to add today is that, as much as I admire Bach's craftsmanship, I can't really say I think this is a great piece, which is one reason it has surprised me that my earlier version has been so popular on YouTube. And I doubt Bach would argue. It's more puzzle than art perhaps - not that the worlds are mutually exclusive.

Just look at how simple the original is on the page:


That's all there is to it, though the second canonic voice is not written out, nor are the modulations. Bach wants the user to figure out how the music goes. But as music, it's rather perplexing. Of course, it doesn't help that the whiny theme Frederick the Great presented to Bach is so unwieldy. The music of this canon is overindulgently chromatic, the cadence into the repetition is hardly satisfying (which means it never really feels resolved), the rhythm is odd, with lots of offbeat notes that sound less like syncopation and more like general disorientation, and the general tone is one of restless busyness.

I've always found it comical that Bach appended the following to this puzzle: "As the modulation rises, so may the King's glory rise." OK, but it does not sound very glorious. The fact that the top voice is mostly descending doesn't help. (As with the Shepard Tone principle, the descending melody helps camouflage the tonal motion upward.) Of course, paying tribute to the King's theme is a way of glorifying him, I suppose, and it's Frederick's own fault that the tone is so somber. (To be fair, the clumsiness of the theme was perhaps part of the challenge in the first place.)

But I DO like this canon! I like a lot of things that are odd, and the fact that this sounds kind of like someone working out a math problem isn't so bad. (I also like math.) One can hear a kinship with some of the harshly intellectual music of the 20th century from the likes of Babbitt and Boulez, music that is uncompromising in its commitment to its own logic. When I listened to the whole 30-minute version this morning, I found it soothing and stimulating, an interesting combination. Eventually, that sense of never arriving becomes its own strange comfort.

Unfortunately, I did have one more thought - which I only later realized I'd seen executed elsewhere. It occurred to me that another "solution" to the ever-rising problem is to slide downwards continuously over each 8-bar group. By sliding down a whole step over this time, we end up magically where we started. Since Bach called his piece a "Canon per tonos" ('tonos' referring to movement by a whole tone), I'm calling this "Canon per microtonos." I did NOT spend a lot of time on it, but imagine an instrument in such bad shape that the strings are constantly loosening. Wait, you don't have to imagine!



I'll admit that I had a vague sense of déjà vu that I'd thought or heard of this concept before. I finally did a search and remembered that the remarkable Stephen Malinowski had done much the same thing, though using synth strings, with his Musical Animation Machine. That version is arguably more successful at disguising the pitch drop, though I like the clattering harpsichord - and everyone's already used to harpsichords being out of tune!

Maybe you'll need something to cleanse the ear after that, so here's one last possibility. Just let the music rise until it disappears. It turns out that using the basic synth built into Finale, it can go pretty far up using the piano sound, and it becomes quite charming and ethereal. (WARNING: I also found my head hurt a bit after listening to this...]

Friday, March 27, 2020

Bach Day #7: Bring out the Canons!

So I've been blogging and posting multimedia for more than thirteen years, and honestly there were a few times that I thought I would hit the big time. Not yet! However, my two steadiest performers over the years (the "big guns," one might say) have been two relatively simple animations I created of canons from Bach's The Musical Offering, so I knew they'd figure into these eleven days of Bach.

In fact, of the almost 900,000 YouTube views I have as of today, more than a third of them are for a video of the endlessly rising canon, the "Canon per tonos." (The title "per tonos" refers to the fact that this canon rises by a whole tone each time through.) To my great surprise, this video has amassed more than 340,000 views. My version of the crab canon has just over 200,000 views, so together, that's well over half of my YouTube audience.

Both videos are, from my point-of-view, more notable for audio tricks I played than for the animations, adorable crabs aside. For the crab canon, a single melody played against itself backwards, I actually recorded the melody only once and then reversed the audio to create the second voice. A YouTube commenter alerted me not too long after I'd posted it in 2008 that it had a wrong note in the score and recording. Ugh. Fortunately, that only took me a little over ten years to fix. That wrong note has been seen and heard many times!

As for the endlessly rising canon, I used a technique suggested by the great Douglas Hofstadter in Gödel, Escher, Bach. Because the basic structure is that the 8-bar canon modulates up a whole step each time through, a performance taken to its logical conclusion would actually run out of playable/audible pitches. Hofstadter's idea was to use the Shepard Tone technique by which the constant, gradual introduction of a lower octave occurs while the original octave fades out above. If executed correctly, the listener doesn't really notice the switch, but finds that the music, having risen an octave, is right back where it started. Here's a version of a Shepard Tone illusion created by a Wikipedia contributor:



Notice that the tones seem to be descending continuously, but they never run out of space. The effect is often compared to a barber's shop pole. Of course, applying this effect to a musical composition is something quite different.

My first attempt "to Shepard" Bach was posted more than twelve years ago, and though I'm pleased with it, I've always intended to fix some things. Among the problems with the original are a few misspelled enharmonics, the stubborn refusal to change clefs (resulting in some wacky ledger lines, although it makes the overall "rising" effect clear), and most importantly, the failure to go beyond two full times through the sequence. In the decade that has passed, there are far more novelty YouTube videos that go on for hours, and this was an obvious candidate for that approach (though I stopped at half an hour).

So, the truth is I had all these thoughts three or four days ago and figured it wouldn't take long to make a new version. As with so many projects, I mapped it out in my head and thought, "just do this, this, and this" and I'll be good to go. But I've realized that, though it's a straightforward project in many respects, the details, details, details kept multiplying. I also had to make choices about how much I wanted to copy things I'd done in the first video and where I wanted to do something different.

The two biggests tasks were recreating the score (in my beloved Lilypond) and making a new recording. I actually thought about sticking with the original acoustic guitar version, as it has a nice mellow quality that's suitable for endless listening. But I thought it would be more fun to try something new, since that video is still available. After a lot of experimenting, I felt the virtual harpsichord provided the most authentic and satisfying effect, though the sound is perhaps a little more annoying. I mean, it's a harpsichord sound. (I'll leave the Beecham jokes out of this.)

Creating the cross-fade effect is trickier than it sounds, and after much tinkering, I was also reminded how different the results can sound depending on the dynamic range of the speakers being used. But I think I've settled on something that basically does the job. It really does keep rising without going anywhere, though it's not so hard to hear why that's happening.

As for the score, I struggled over many decisions. Unlike the previous version, I finally decided NOT to use key signatures. Bach's version only shows 8 bars, which clearly start in C Minor, but with no signature. He doesn't even include the middle voice! The performers are supposed to add in the canonic voice, which follows the lower voice by one bar and a fifth above, and then work out the transpotions for each repetition.


Although key signatures are a nice way to signal change of tonality, the music is so chromatic that it actually reads a little more smoothly without key signatures since so many notes end up changed anyway, especially as the modulation is prepared for the next key. Also, after flirting with the elegance of alto clef, which mostly works beautifully for the middle voice, I finally decided to stay with treble and bass clefs only, with discreet changes along the way, simply because more people read each fluently. I did keep a couple of quirky features from before: the barlines do not connect the staves (it just looks cleaner this way) and I kept the little cue note at the end to show the new tonic that is coming.

Well, that's surely more than anyone wants to know about the endless hours I put in this week creating this endless video, so perhaps I should just finish with the video. Tomorrow, I'll write a bit more about the work itself. If the last two days focused on Bach at his most jovial, this is surely Bach at his most austere and cerebral. And, spoiler alert: Frederick the Great's theme (on which all of The Musical Offering is based) is....not that great. But we know Bach liked a challenge....



UPDATE: The morning after posting this I listened to the whole thing while making a big breakfast - and discovered a mistake (a volume irregularity in the middle) ! It has now been fixed.

UPDATE #2: There was another mistake, but thanks to the great ears of a great friend, it has been fixed as well, along with a few other minor stylistic tweaks. Putting something this complicated out so quickly is kind of insane, but it's how I roll.

Thursday, March 26, 2020

Bach Day #6: Pass the Popcorn

To continue with some of the levity from Day #5 (there is more "serious" Bach ahead), I'll just do a quick re-share today. I mentioned the C-sharp Major fugue from Book of The Well-tempered Clavier yesterday. It's a piece I "discovered" a few years back when I was looking for a church postlude in D-flat Major, and I turned from the Book I fugue I'd known well to this delightfully compact, intricate romp, which is full of surprises.

When I wrote about it several years back, I quoted my blogger pianist friend Erica Sipes' vivid description: "The fugue reminds me of popcorn popping...starting with a kernel or two as the oil heats up and then speeding up as they all start popping." This image ended up playing a big role in one of my most elaborate Scratch projects, a little program that plays and plays with this fugue. You can change the tempo, change "instrument," put in temporary ritards and accelarandi, invert the whole thing, make it play with all three voices in different keys, play microtonally, etc.

The whole time it plays, popcorn kernels are randomly popping, which is a nice analogue for how little outbursts of fast notes pop up all over the score. And speaking of the score, you can switch back and forth between score view and popcorn view and, yes, when the music inverts, the score inverts as well. Honestly, I'd forgotten how much this silly little program does, which is a nice analogue for how much Bach does in this silly little fugue.

Here's a straightforward "performance" of the fugue by my program:



...and you can go to this fancy page in which the program is embedded with lots of instructions to let you create mayhem.


P.S. Bach's wig in the Scratch program is one of my better creations, by the way.

Wednesday, March 25, 2020

Bach Day #5: LOL

A couple of my Bach projects are dragging along more slowly than expected - music is hard! - so I'm going to lighten my own spirits on Day #5 of 11 with the silliest, most humorous music by Bach that I know. Yes, he wrote plenty of jaunty gigues and other dances which have lighthearted qualities, and his counterpoint can be effervescent. For some reason, for example, he seemed amused by C-sharp Major and wrote two of his giddiest fugues in that key:



[By the way, though I like Glenn Gould's approach to the Book I fugue, he plays the Book II fugue at a slower tempo than I could've imagined. It's SO slow, it's still kinda funny.]

Anyway, this is a lighthearted post about some music by Bach that is not just light or fun. No, this duet from the Cantata No. 78 "Jesu, der du meine Seele" is really laugh-out-loud silly, especially in this fantastic recording by the American Bach Soloists.



The text in English is as follows (translation by Pamela Dellal from the amazing Emmanuel Music archive):
We hasten with weak, yet eager steps,
O Jesus, O Master, to You for help.
You faithfully seek the ill and erring.
Ah, hear, how we lift up our voices to beg for help!
Let Your gracious countenance be joyful to us!
The way the two soloists chase each other around is clearly a whimsical take on the idea of following weakly in Jesus's steps. Perhaps not every recording/performance is quite on the same Goofy Greats level as the one above (and I mean that with all respect and admiration - just listen to their way with "zu dir"), but I do find the tone and bounciness of this music to be an outlier for Bach. That's not necessarily a bad thing, because I love his more typical fare, but it's nice to hear him letting his powdered wig down a bit.

The combination of that non-stop bouncing bass line and those twirling vocal lines makes the music seem a bit simpler and sunnier than so much Bach, even though there is still lots of cleverness in the construction.


I suppose maybe there's a certain kinship with the wonderful Brandenburg Concerto No. 6 (Desert Island material for sure) with its follow-the-leader soloists and simple bass line [listen starting at 48.12 here].



But as joyful and cheerful as that music is, it's just a little too dignified to be ridiculous. I'm glad Bach left behind at least one bit of music that cheerfully crosses that line!

Tuesday, March 24, 2020

Bach Day #4: Orpheus in the Underworld?

Well, life definitely caught up with me today, and although I did get some work done on something new, it's not quite ready yet.

So, we return to the winter of 2009 and a Bach recording I've always been pleased with. As described in this post, the recording was made pretty informally, with a few tidying-up edits made later. It was originally posted without score, which I added in 2011. The video only shows the orchestral score, from which I more or less made up a version (it helps that the keyboard part covers much of the material). Someday I should create an honest-to-goodness notated piano version, but that will have to wait.


The music is better-known as the slow movement of the composer's Violin Concerto in A Minor, but there is a harpsichord version of this concerto in G Minor. As so often happens with Bach, music that seems perfect on one instrument can turn out to be pretty satisfying on another as well. Here's what I wrote about this back in Aught Nine:
I hear the slow movement of this concerto as a sort of "Orpheus Taming the Furies" dialogue. True, the orchestra isn't as gruff as in the famous "Orpheus" movement of Beethoven's 4th piano concerto, but there's a stubbornness in Bach's bass ritornello that the solo passages seem intent on melting. The final solo statement is a miracle of sweetness and simplicity, so perfect that there is no concluding ritornello. It's less a victory than it is a unification of opposing forces. Honestly, I can't really put into words what happens in this musical dialogue, so I figured I'd just play it.
There are many compromises at play here. First of all, all those long, suspended notes the violin sings can really only be imagined as sustaining that way in a piano version. Second of all, I didn't have an orchestra available when I slipped into the recital hall early this morning, so it's just a dialogue between my two hands, not a violin (or piano) vs. orchestra. I did my best to incorporate the orchestral violin parts, but I'm inconsistent about that. Third, I only had about 15 minutes, so I just sat and played, and when I had a couple of slips, I backtracked a little and then stitched things together later this afternoon. It's far from perfect. But, whatever. I really love the way it sounds this way, and in some respects the fragility of the piano sonority just adds to the impossibly beautiful writing.
In 2011, when I added the video, I also added this comment:
I remember that when I first heard this music years ago, I found the repetitiveness of the bass line to be a bit annoying; but perhaps it's supposed to be that way, and I think it's quite telling that the R.H. melody gets the last word.
I've also always been puzzled by that rhythm in the bass - the stubborn "Furies" rhythm. Although I believe it should basically be played as written, the fast notes always somehow feel more like triplets. I think I'd thought that's what they were from a recording I'd heard before I ever saw the score.


I can't really put my finger on what I mean exactly. I actually tried having a synth record this with a rhythm halfway between the "16th + 2 32nds" and a triplet, and I also tried just adding a tiny bit extra to the triplet (so that each measure ends up being a tiny bit longer), but I couldn't generate what I was hearing. So you're just stuck with my performance! Perhaps after three days of me bragging about robo-performances, it was about time the computers lost one.