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.
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