Diary of an OCW Music Student, Week 5: Building a Diatonic Set

Education Insider talks a lot about OpenCourseWare (OCW), so maybe it's time we put some to the test. Therefore, over ten weeks this fall we'll be taking a course from the University of California - Irvine ourselves. In this installment, a semi-professional musician learns what it means to build a diatonic set of pitches, but what can we do with that knowledge?

By Eric Garneau


Coming to Terms

At the beginning of his fifth installment in 'Introduction to Pitch Systems in Tonal Music', lecturer John Crooks promises an 'especially exciting' lesson as he teaches us how to build a major scale using basic mathematics. Perhaps Crooks and I have different definitions of 'exciting,' because this lesson didn't really do it for me. Basically, this was one of the first weeks since the beginning of the course where I didn't feel like there was anything too helpful for a working musician like me. Academic trivia aside, I can't be sure I'll ever really need anything I picked up in this week's class.

I also felt that, much like week two, the vocabulary/technical terms came flying pretty hard and fast here, especially at the beginning of Crooks' presentation. But again, one of the great things about OCW is that its students can take all the time they need to soak up any new words or concepts. As such, I found myself pausing the first few minutes of this video a couple times to take notes. Here are a couple of the new terms introduced:

Diatonic set: The set of seven pitches that can be formed into any mode, like a major scale (N.B.: I don't really know what a 'mode' is, either, but the concept of a major scale should be recognizable to pretty much every musician).

Pythagorean scale/tuning: The organization of tones with which us Western musicians are used to working. I was hoping Crooks would explain the history of the term, which he didn't, although when I looked it up I shouldn't have been surprised: the tuning is attributed to the ancient Greek mathematician and philosopher Pythagoras who, it's said, discovered that simple ratios like 4:3, 3:2 and 2:1 were the basis of harmonious music (true, Crooks has been telling us for the last month, but it might have been nice to know its historical context).

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Built to Scale

Besides these concepts (which, admittedly, are cool to know), most of Crooks' presentation focuses on the major scale and how we can construct it using the mathematical ratios/relationships between tones we've explored in the past few classes. This strikes me as another fact that's interesting to know because of its historical context, but in practice it's very Byzantine and frankly kind of impractical. I have no doubt it's important we learn this stuff, and later lessons in the course will probably build off it, but while, for instance, I found the circle of fifths explored in Crooks' last two classes a really cool shorthand tool for practiced musicians like myself, I can't yet imagine any such application for this lesson.

Here's the short of it: we can construct a major scale by taking the frequency value of its root tone (or 'tonic,' as we learned last week) and multiplying it by 3/2, thus getting its perfect fifth tone. That tone will also be the fifth note in our scale. Once we have that fifth, we multiply its frequency value by 3/2 to get another tone in the scale, ad naseum, until we have seven tones (although for the last note in the scale we actually have to multiply the tonic's frequency by 2/3 instead). Then, because most of the resulting tones won't be in the same octave (they exceed the 2:1 octave ratio), we have to divide or multiply their frequencies by powers of two to make sure they align. Sound needlessly complicated? Well, it is. And although that's how Pythagoras may have done it (WHY DIDN'T YOU TELL US, PROFESSOR CROOKS?!), I know how to build a scale much more easily - I can go to my keyboard and starting with C play seven white keys in a row. Bam. Instant scale.

Of course I'm being facetious, so please forgive me. It's just that this whole exercise struck me as kind of running in place, which stands in contrast to Crooks' excitement for the lesson. If this were a typical undergraduate class, I'd temper my dissatisfaction, since some of this material could be on the final!!… but, after all, this is OCW. There are no finals, and each learner will take away from it what he or she wishes with no fear of bad grades. And aside from some trivia, what I took away from this lesson remains to be seen.

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