Wolf tones

A friend of mine and I were recently discussing music, and I happened to mention something I had heard about how on a piano keyboard you can determine which sharps are in each key by using something called the “circle of fifths.” The gist of the idea is that in each key (musical key) the black piano key just below the fifth is the sharp for that key, and also that starting with the fifth spanning C to G the number of sharps in a key increases by one with each successive musical key because it includes the one below the fifth plus all the sharps in the previous key.

I have no training in musical theory, and I was only barely able to blurt out some approximation of the above, which had all been new to me when I heard it, but my interlocuter, John, was familiar with the phenomenon and in fact went on to enthuse about a book he’d been reading called Temperament, by Stuart Isacoff. This book dealt with the fact that if you start on a properly tuned C note and rise in perfect (Pythagorian or “just”) fifths until you land on C again, that higher C will not match the tone you would hit if you had risen by perfect octaves. Some bizarre moebius of nature is responsible for this that I still don’t quite understand.

Apparently, this wasn’t a big deal in Pythagoras’ time (though it seems he was aware of it), because early music was simple and largely monophonic, but it became a big deal in the 14th century when composers started making more complex music with more thirds and fifths in it. If you tuned so that certain chords sounded pure, others sounded unpleasant or even harsh, and there was even something called a “wolf”, which was an interval that you did not dare play because it positively howled with dissonance.

The wild ride behind the modern keyboard we take for granted

The wild ride behind the modern keyboard we take for granted

An argument began during the Renaissance about how to tune keyboards to deal with this phenomenon — even how many keys an octave should have (12? 17? 32?) — that really wasn’t settled until the 19th century, and in some ways rages still, as we’ll see. Modern keyboards almost without exception use a tuning called equal temperament, which is a way of fudging a little bit on each string in the piano so that the chords sound okay in every part of the piano. The story of the long slog to equal temperament is the subject of this book, and it sounded like it was right up my alley. When John was finished with it I borrowed it, and I’ve enjoyed it (all except the math parts).

John also lent me another book, almost a companion volume, How Equal Temperament Ruined Harmony (and why you should care) by Ross Duffin. While Isacoff claims to champion no particular tuning and says it was the history of how we arrived at equal temperament that he found interesting, Duffin is very keen to convince you that much has been lost in tempering the keyboard the way we do, that in fact the very difficulty of reconciling the thirds and fourths and fifths in the various keys is what gives music for fixed-string instruments such great expressive potential.

I sometimes will read several books in a row on a topic if it captures my fancy, and I sailed right into this second book with plenty of momentum. Duffin is more fun, which surprised me because the title of his book made me not want to read it — some hothead with a bone to pick with the entirety of Western musical culture wants to get up in my grill about something I’m not even really smart enough to understand. But it’s clipping right along, and he explains the musical phenomena a bit more clearly — uses more diagrams, too, which is useful for me.

So the thing I wanted to say about all this: Duffin’s book quotes William Gardiner, writing to us from the 19th century, as saying:

“but when we come to tune a pianoforte, and raise the fifths one upon another, to our surprise we find the last note C, too sharp for the C we set out with…the Deity seems to have left music in an unfinished state, to show his inscrutible power.” 

I don’t claim to know much about what God thinks, but it strikes me that this is exactly the kind of monkey wrench God would leave lying around in his creation for us to stumble over, be incommoded by, argue about, and finally have to find a tuning for. And we can’t agree on a tuning. And that’s okay. How many aspects of my daily life are just like these dread wolf tones, howling and dissonant, and how will I ever tame them? How can I make other people hear the opus of my life the way I intended it to sound? But I guess that’s the point. We can tug on the strings all we want, but the compromise is always there somewhere. That’s life on earth. 


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