For over thirty years I’ve been disturbed by the location of the downbeat in the Talking Heads song “Once in a Lifetime”. I listened to it dozens of times without paying a ton of attention to the meter, and naturally heard the verses like this:
Once I paid attention, though, I realized that there were two things kind of funny about this way of hearing it. One was that the bass line was exactly the same throughout the whole song, but was shifted by half a bar when you compared the verse and the chorus. The other was that there was a half-bar hitch both going into and coming out of the chorus.
Of course you can resolve both of these issues simultaneously by just shifting your perception of the chorus by half a measure; then the bass lines up and you don’t have to throw in any 2/4 measures:
But this really isn’t the way I want to hear the chorus! I can hear it this way if I have to, but it feels artificial, like in reality the band has shifted the beat and I’m just hearing it this way for intellectual reasons.
So how did the band hear it? Did they really hear the chorus the second way and were playing in 4/4 the whole way through, or did they hear the downbeat shift and thought that it was cool that the bass line went in and out of phase throughout the song? For decades I’ve wondered what the “correct” way to hear it is.
Until now, that is, when I read Sasha Frere-Jones’s profile of the song’s producer Brian Eno in the New Yorker. From the end of the article:
Eno’s production of this transparent, polyrhythmic light box, it turns out, is based on a mistake—his own. “That song was a very good case of people not agreeing about the one,” he told me, referring to the first beat of each measure. “I always heard it in a different place from everyone else, so I just kept sort of building things onto my one.”
The song as originally conceived by the band is in 4/4 throughout with a consistent bass groove, as in the second version of the chorus above. At this point it’s probably very natural to hear it that way.
However, Eno hears it in the other way, with the chorus displaced by two beats, and starts pushing the arrangement in a direction that emphasizes that hearing.
We end up with a rabbit-duck situation that has been specifically engineered to be confusing, and which was based explicitly on the producer’s confusion.
Over a year ago I started transcribing Henry Threadgill’s “To Undertake My Corners Open”. I got to the 90% point a long time ago, but as with many projects, it’s the last 10% that takes the most calendar time. One thing that slowed me down is that Threadgill’s flute is super sharp, especially in the high registers, approaching 50 cents by the end of the piece, playing havoc with my ability to match pitches as well as my motivation. I finally got out of that rut when I realized that he was consistently sharp and not just all over the place from one phrase to the next. Once again I could never have finished this project without the great software Transcribe!.
Here’s the PDF of the score; I won’t reproduce it here because it runs to 14 pages. Some analysis is coming up, but this has been so long in coming that I didn’t want to slow it down further by waiting until I had a complete essay written up about it. A few general points:
Each of the solo section has a different harmonic cycle. The trombone has 3 cycles of 95 beats, the guitar has 8 cycles of 22 beats, and the flute has 2 cycles of 96 beats. As far as I can tell they’re all completely independent.
The structure of each cycle definitely includes chords, or at least pitch collections, not just bass notes. They vary a bit each time around but in general the “changes” for each cycle are pretty consistent.
Just as the trombone cycle (mm. 18—41) is the head (mm. 1—15) slowed down,, the guitar cycle (mm. 90—95) is the little bit between the recap and coda (mm. 183—191) slowed down, and the flute cycle (mm. 130—150) is the coda (mm. 193—217) slowed down. I was particularly happy to discover this last one, since I was having trouble making sense of the coda before; I couldn’t even figure out how to bar it. If it seems a little over-barred now, it’s because I matched it to the meters of the flute cycle, and the rhythms don’t make any less sense than they would with any other barring.
Maybe it’s just me, but I feel like the cycles get further out harmonically as the piece progresses. The trombone solo feels very tonal in a lot of places, the guitar solo is a bit less consonant, and the flute solo feels really abstract (although perhaps the fact that he is 40 cents sharp doesn’t help).
Compare to other recorded performances of the same piece to see how much is kept consistent. For example, I assume that the entire coda is through-composed, but perhaps there’s some room for variation there.
This is a book about music cognition: attempting to understand how people understand the music they hear. Temperley’s main thesis throughout the book is that a profitable way to study music perception is to pretend that the listener is doing a Bayesian analysis to determine the structure (e.g., time signature and key) behind the musical surface (the audio signal being heard).
Bayes’ Theorem seems to be pretty hot these days. It’s a statement about probabilities, the main point of which is that the a priori likelihood of certain states is useful information when trying to figure out what state actually exists. A standard example is that if a certain disease is incredibly rare, then even if you test positive for it with an only slightly fallible test, it’s still quite unlikely that you really have it.
The whole idea that musical perception is largely about creating models in your head about what’s going on, with associated expectations about the future that can either be met or thwarted, and that composers are constantly playing with those expectations, is associated in my mind with the late Leonard Meyer, who is definitely worth reading. I recommend in particular Emotion and Meaning in Music.
Temperley uses Bayesian analysis to simulate how listeners create a presumptive model for a given musical signal; for example, if a note arrives a little later than expected, the listener has to make an on-the-fly guess whether that is due to a syncopation (the tempo remains constant and the note is offset from its expected location relative to it) or rubato (the tempo has slowed down slightly and the note is exactly where you’d expect in the slowed-down tempo). If you have a model for the relative probability of the two cases, you have good grounds for guessing which is actually going on. (Note that the model can change according to what kind of music you’re listening to: the answer to the above question is much more likely to be rubato if it’s a classical performance and syncopation if it’s a rock performance).
Temperley creates these sorts of models to generate proposed probability distributions in varied domains, from time signatures to key determination to modulation detection. There are some good standard corpora of analyzed musical examples so he’s able to evaluate his models to existing ones fairly accurately, and they perform well though not groundbreakingly so. One nice thing is that the models tend to be fairly simple compared to many other ones in the field, which tend to be rather special-cased and apparently a bit fragile.
I was very pleased, by the way, to find that a scale-determination system that I had come up with independently in the late 90s for use in creating automatic accompaniment for MIDI renditions of karaoke songs was basically exactly the same as one of the standard systems that the academic world came up with. (The short version is that for a given timespan you take the total duration of each pitch class and take the dot-product of that 12-dimensional vector with a vector representing a signature for each hypothetical scale, then take the maximum. Not rocket science but it was nice to come up with a simple quantitative algorithm that performed well in practice.)
Even though there’s no silver bullet here, the ideas in it are quite interesting. I particularly like that the models end up being fairly straightforward and don’t require a ton of specialized tweaks, which is a promising feature. The math involved is real, but if all you care about is the music you can probably gloss over most of it if you trust the author. Worth reading if you’re interested in how people perceive music, either for its own sake or because you want to exploit it as a composer or performer.
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