It Might Get Messy

The musical scale is more twisted than you think. I learned to play music in a way that handicapped me severely. As a clarinetist, even one who play the enlarged alto version of the instrument, I never learned to read in bass clef. Which is the low notes, played with the left hand on the piano, that are annotated completely differently from the right hand, which is in treble clef. 

But that’s not the issue here. The real problem is that those of us who learned music in “modern” times (roughly since the mid-1800s) learn that sharps and flats in the same interval (say, like A sharp and B flat) are “enharmonic”—they are the same note. You can see this on a fretted guitar—A sharp and B flat are sounded at the same fret, between the A fret and the B fret. But, from the perspective of the physics of sound—the wave forms generated by vibrating strings or reeds—this is not strictly true. If you run up musical octaves (like middle C to high C, a reach of several octaves) and divide by intervals of perfect thirds, vs. intervals of perfect 5ths, you don’t come out to exactly the same place. In other words, between the notes that define the octave, the intervals you play determine how close you are to being in tune at the end. 

This is very weird. And discomfiting to modern musicians. It turns out that modern pianos are tuned to a scale called “equal temperament”. Basically, the unequal intervals are averaged over the length of the piano keyboard. But there are many alternatives to equal temperament. And many of them were used, for hundreds of years. The thing is, you can tune a piano so that certain ranges of keys yield very close to perfect harmony whether you play by thirds or fifths. But this pushes the “error” in vibrations off to the ends of the keyboard. Which then sound out of tune.

Quirky, no? The simplest (and, in the past, most popular) alternative to equal temperament was to play sharps (say, A sharp) as 5/9 of the distance to the next full tone (B in this case). And to play the corresponding flat (in this case, B flat) as 4/9 of the distance. In this tuning, your sharps are a little sharper than the corresponding flat, which is flatter than in equal temperament. 

None of this would matter much if it didn’t have serious implications for musicians playing orchestral string instruments—violins, violas, cellos, basses—which are not fretted. Good string players, when not constrained by playing with fixed-tuning instruments (like pianos), instinctively play such that their sharps and flats are NOT truly enharmonic. They play them more or less by 5/9 vs. 4/9 system [1]. Then, when they are playing with fixed-tuned instruments (pianos, organs, most woodwinds) they default to playing true enharmonics—with the sharps and flats identical.

Think of the incredible feat of memory this is. It seems (from [1]) that the musicians don’t necessarily do this consciously. Their muscles and their ears are so attuned, from countless hours of practice, that they can make this switch subconsciously. Their brains, ears, and fingers form a memory system that is almost unbelievable. 

I bring this bit of esoterica to your attention because memory, just simple brute-force memory, is important when doctors are attempting to diagnose post-cancer-treatment physiological difficulties. You have to be able to recall what you did for the past week when the doctor is trying, say, to understand why last weekend you were sick for 3 days, pouring thick, ropey mucous from mouth and throat.

I took ill late on Friday, and was sick all weekend, especially Monday. On Monday my throat hurt all day, and I was generating mucous like a hagfish on a whale carcass. So I emailed the doctors. Dr. H was back in town from vacation, and instructed me to get squeezed into his Wednesday schedule. By Wednesday, I was feeling fine. Dr. H scoped me, said everything not only looked good, it looked better than when I was there a couple weeks before. He asked about things I might have done to precipitate the weekend’s throat crisis. He asked specifically about eating ice cream. Told him I hadn’t had any for a couple of weeks. He shrugged his shoulders and sent me on my way, since I was no longer ill.

But I had forgotten something (I hate to say my brain is getting old, but…). On the prior Friday, I had been in to see the dieticians for a “swallowing test”. The technician fed me little scoops of an ice cream substitute, then peered into my throat with a flashlight. Where she could see the little bolus of ice cream perched on my dysfunctional epiglottis. Sips of water didn’t help push the ice cream into the proper channel. Everything felt good, though. I thought I was getting the stuff into my gastrointestinal system.

But apparently I wasn’t. I was aspirating at least some of the ice cream, and coating my airway with thick goo. My airway responded by manufacturing substantially more goo on its own. Leading me to be ill for 3 days in a row.

Duh. If only I had musician’s memory. I emailed Dr. H as soon as I remembered I’d been swallow-tested right before my throat came apart.

Dr. H suggested I give my throat a rest, and don’t eat ice cream for a while. To which, given how sick I was last weekend, I readily agreed. Dr. H had no advice for my faulty memory. Not his problem… . 

This and a new piece over at www.aehsfoundation.org, will be the only entry in the weblog empire this weekend. Don’t forget Dr. Crossley’s wild west blog at http://www.daccrossley.typepad.com . Yesterday we spent a pleasant day out on the Eastern Shore with Dan and Liz, Lance, Phoebe and Jen, Jeff and Jenny, and Mike and Laura. My first outing since visiting Antietam with my sister a number of weeks ago. I really AM recovering. 

Thanks for being here, everyone. You’re a huge chunk of the reason I’m getting better. Love to all!!!

Notes

[1] A wonderfully readable little book on this topic is “How Equal Temperament Ruined Harmony (And Why You Should Care) by Ross W. Duffin, published in 2007 by W.W. Norton & Company. This book makes the complexities of acoustic physics understandable and interesting. Not an easy task, given the esoteric nature of the subject and the hellishly convoluted nature of the underlying physical reality.