Diary of an OCW Music Student, Week 6: Pythagorean Tuning and the Pure Triad

Education Insider talks a lot about OpenCourseWare (OCW), so maybe it's time we put some to the test. Over nine weeks this fall we'll be taking a course from the University of California - Irvine ourselves. What does a semi-professional musician stand to learn from an OCW course in music theory? It's time we went back to school.

By Eric Garneau


In Which I Admit I Was Wrong

Last week I found myself underwhelmed by the fifth installment of Professor John Crooks' 'Introduction to Pitch Systems in Tonal Music' course. That lesson was all about building a major scale in Pythagorean tuning using mathematics, and I wondered what its practical application was. Yes, it's interesting to know the mathematics behind Western music, but does it actually matter to working musicians?

Fortunately, I left myself a tiny out by saying 'I'm sure the value of this lesson will become apparent later,' because this week that's exactly what happened. Though I didn't detect any serious mention of it last week, it turns out that what Professor Crooks has been preparing us for is a discussion of how to tune an instrument and, perhaps more importantly, why they're tuned the way they are. You wouldn't necessarily think that the frequency values and mathematic relationships of notes in a scale could help you much with that (at least in a practical sense), but it sure seems that they do.

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Tune Up

And what more practical matter is there for a gigging musician than the issue of tuning? If you've ever played live without being in tune, you probably know how awful/embarrassing/uncool it can be (although I have scored major points with audiences by doing a 5-second retune in the middle of a song). And if you're a guitar player who's been at it for a little while, chances are you've probably experimented with alternate tunings before - Eb, dropped D, open D, etc. What Professor Crooks is promising to show us is why those tunings work for us with stringed instruments - not just guitars but pianos, violins and the like.

But not quite yet. First, Crooks has to illustrate that tuning instruments may not be quite as simple as we think. To do so, he pulls on a few of his past lessons, including last week's instruction on Pythagorean tuning, as well as his presentation from a few weeks ago about just or pure triads in a 4:5:6 ratio. You'll remember that last week we were able to calculate the frequency of every note in a scale basically by multiplying our starting frequency by 3/2 ad naseum and then aligning the resulting notes so they sat in the same octave by dividing their frequencies by powers of two as required.

As it turns out, arriving at pitches that way produces frequencies that are slightly off from what they'd be by calculating them using only ratios like 3:2, 4:3, 5:4, etc. Though the frequency difference is only a few hertz in each example, it's enough to produce a bit of a discordant effect. It's also enough, Crooks says, to prevent any difficulties that would arise from tuning an instrument using only just/pure intervals. What does he mean by that? Who knows?! We've got to come back next week to find out. But he presents enough of a puzzle here to make me want to return for more right away, so I think that's 'mission accomplished.'

Tune up your instruments and your brain with the power of music.

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