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Tuesday, October 11, 2016

Conjecture Explaining Downward Pitch Drift of A Cappella Singing Groups

I've been doing some barbershop singing lately, both in a chorus of about 30 men and also a quartet. I'm still learning the ropes so (fortunately) there are no recordings of me (yet) doing this particular form of music. But if you're curious about the sorts of things we sing, the following video shows Ringmasters, a really excellent quartet, performing one of the songs we're working on (both the chorus and the quartet I sing with) and is a good example of "modern" barbershop music.

Because there are no instruments to anchor the pitch, even a top notch group like Ringmasters will end the song at a slightly different pitch level than they start with. In this case, my "pitch pipe" tells me they end very slightly sharper than they started. They're so close that my ear couldn't tell and I needed an electronic tuner to discern that.

While a group can end either sharp or flat, the vast majority of a cappella groups end flat a majority of the time. This is especially true for bigger groups and often I can easily tell that with just my ear and without any sort of electronic help.

The question is why flat and not sharp? I've not found any of the answers to be compelling. Therefore, I've crafted my own conjecture, but I'm pretty confident that it's at least part of the explanation since it matches my experience recording music. On the other hand, it's so simple and obvious that I would've thought that it would be a common explanation, but I haven't seen it.

When we speak and sing, we usually mostly hear ourselves via internal pathways. In other words, our vocal cords flap about and the vibrations from that flapping are transmitted via our flesh and blood and bone up to our hearing apparatus. There's also reflected sound from the vibrations coming out our mouths (and noses to some extent) and then bouncing off of surfaces around us back to our ears. However, most of what we hear under typical conditions is received by our ears via the internal pathways.

Many of us who are past the half-century mark may have never heard ourselves speak or sing until we were teenagers or older. There simply wasn't all that much access to recording equipment and the early consumer recording devices had dismal accuracy when playing back a recording. I remember being SHOCKED when I first heard what I sounded like. It sounded nothing like I sound to me via my internal pathways.

In particular, I sound slightly sharper to myself via the internal pathways than I do via the external pathways. When singing along with instruments, I always sound very slightly flatter during playback than I expect given what it sounds like to me during recording.

It's very slight. So slight that it's hardly out of tune. The perception is more a matter of the other definition of "flat": dull; lifeless; low-energy. Whereas being very slightly sharp is perceived as alive, brilliant, and exciting! A somewhat related fact is that classical instrumental groups were tuned to ever higher pitch levels over the centuries:
During historical periods when instrumental music rose in prominence (relative to the voice), there was a continuous tendency for pitch levels to rise. This "pitch inflation" seemed largely a product of instrumentalists competing with each other, each attempting to produce a brighter, more "brilliant", sound than that of their rivals.
Another experiment that confirmed that I sound sharper internally than externally is what I call the "wall trick." To hear myself better from external reflections, instead of singing into a room, I'll stand facing a wall, about a foot away. It looks kinda silly, but instead of hearing myself mainly internally, I'm also able to hear the external reflections and it gives me an idea of what my pitch and tone sound like to the rest of the world. Recently, I sang a single note into a tuner while walking towards the wall. I maintained the same pitch the whole time. As I got closer to the wall, I sounded progressively flatter even though the tuner said I was singing the same pitch the whole time.

So both record/playback and external reflections confirm that I sound a tiny bit flatter externally than internally. I suspect, but haven't yet proven, that's true for most people. After all, people are similar physiologically, and I think the effect is due to our internal transmission filters being slightly more high-pass than the external transmission filters which probably are more affected by the resonating cavities that form our vowel sounds. Well, that's my conjecture anyway. I really don't know why. All I know is that internally I sound sharper than externally.

When we start a song in an a cappella group, someone blows the root of the key on a pitch pipe or electronic equivalent. If I sing my note and it sounds right to me internally, it will sound very slightly flat to those around me. Everybody around me will also do the same thing and sing very slightly flat. I'm going to sound flat to everyone else and everyone else will sound flat to me. But we want to align so we'll all adjust incrementally downwards a little tiny bit. And then we all sound flatter to each other so we adjust downward again. And again. And again. They're all tiny adjustments, minuscule really. But over the course of a whole song, all those increments add up and the group might end up noticeably flat, maybe even a half-step. Maybe even more. Even for very accomplished groups.


Clovis e Adri said...

Quite an interesting take, Bret.

You can actually design tests for your hypothesis. Make a lone person to make a choir with pre-recorded (or computer generated) singers. Then substitute the computer for another singer and repeat. Introduce yet another human and repeat. And so on.

The pattern of flattening must keep some correlation with greater human presence if your self-coordination theory is right (as an extreme example, we can discard yours if the flattening keeps happening with only one human singer). The other theories (humidity, people getting tired, etc) can get tested in such a setting too.

Needless to say, it ought to be an experiment with very many trials to take in account the large variations any single human singer can induce to the group - I take, for example, that the cases when the chorus end up sharper may be due to some particular inger inducing it somehow.

I will risk another explanation, not necessarily in contradiction with yours: I suppose it takes more energy to sustain sharper notes than flatter ones (does it?). Thinking like we do in statistical mechanics, that alone would be reason enough for the final effect, even if you do not pinpoint the particular path the system takes to do so (or the many possible particular paths).

Bret said...

Clovis wrote: "You can actually design tests for your hypothesis."

Yes. But it's a bit more work than I'm up for. It seems that someone, somewhere must have done similar experiments, but I can't seem to find them. My guess is that they were done before the Internet so google doesn't find them.

Clovis wrote: "...greater human presence..."

My overall experience is that the bigger the group, the more likely it is that they'll end up flat. Only anecdotal though.

Clovis wrote: "...chorus end up sharper..."

Quartets are interesting (and the most fun as far as I'm concerned) because each of the 4 people are constantly reacting to each other and one guy significantly missing a note in one direction or the other can trigger quite an unpredictable recovery sequence that can easily overwhelm the flatness thang.

However, a few things keep it from going unstable or spiraling down any flatter than it does. The first is absolute pitch. If I'm supposed to sing a C, I know reasonably closely what a C is supposed to sound like. As the group gets flatter from the correct notes, those with the absolute pitch capability (sometimes called "perfect" pitch even though nothing is ever quite perfect) are torn between trying to align with others and wanting to sing the perfect pitch (even if they'd sing a hair below it).

Also, because of my recording experience (and perhaps because I want to sound alive, excited, etc.) I try to always sound to myself a hair sharp because I know that will get me to the right pitch (or at least closer) externally. I don't know anybody else who does that though.

Clovis wrote: "I suppose it takes more energy to sustain sharper notes than flatter ones (does it?)."

It probably does on average, especially when singers are near the upper limit of a given register. And that is the most common put forth reason for flatness. It doesn't necessarily explain why (in my experience) that quartets don't go as flat as larger groups and indeed it's why I've offered my alternative explanation.