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Diary of an OCW Music Student, Week 7: The Minor Triad and a Circular System of Thirds

Education Insider talks a lot about OpenCourseWare (OCW), so maybe it's time we put some to the test. Over ten 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? This week we're making things a little more sinister with a look at minor triads.

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By Eric Garneau

dark side

On the Dark Side

In last week's installment of 'Introduction to Pitch Systems in Tonal Music', lecturer John Crooks promised to teach us how to tune an instrument using Pythagorean tonality. This week, like a spiteful parent (not really) he reneges on his promise a few minutes into his presentation to take us into darker territory. It's time for us to learn about minor chords.

For musicians who've been following along at home, you've probably been wondering when we'd get to this topic. So far most of our discussion has been spent building major triads, major scales, etc., with no discussion of a full half of the musical spectrum. Well, you can all rest easy, because in this lesson Crooks gives the same attention to minor tonalities that he's given to major ones over the past few weeks, teaching us the mathematic ratios by which we can create minor triads (10:12:15) and even showing us how to find i-iv-v minor progressions, the evil-sounding cousins of the I-IV-V major chords that we learned a few weeks ago to be the principle parts of so much music.

I'm going to argue that perhaps musicians in popular music don't exploit those minor progressions enough. To make my point, let's return again to the circle of fifths, which has probably been my favorite thing I've learned in all these lessons. I mentioned way back in week three that you can find the relative minor of the major key you're playing in by moving three stops to the right on the circle. What I didn't say then (because I didn't know it) is that the relative minor of a major chord also has dominant and subdominant triads in a i-iv-v relationship with itself, and you can find those on the circle the same way you find the major I-IV-V relationships.

circle of fifths

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To use a concrete example: we already know that C makes a I-IV-V relationship with its two neighbors on the circle, the subdominant F (to its left) and the dominant G (to its right), and we know that A is the relative minor of C. Thanks to this week's lesson, we now can further tell that A minor has a relationship with D minor (to its immediate left on the circle) and E minor (to its immediate right), and that this relationship exists in the ratio i-iv-v like the C-F-G relationship does.

What are the practical applications of this knowledge? Access to a world of chords you might not have even considered! And as I said above, I think that musicians, at least in the pop/rock world, don't value this knowledge enough. Think about it - how many songs can you name with C-F-G or G-D-C progressions? There seems to be an endless supply. But how many of those G-D-C songs include Em-Bm-Am chords too? You'll almost definitely get the Em, because so many pop songs are built off a I-V-vi-IV progression (think 'Push' by Matchbox 20 or Journey's 'Don't Stop Believin' as simple examples), but so many of those songs never go past using one minor chord, or maybe two. Why is that? Think of the tonal depth you could get by making use of the full minor triad as you have the major one.

Of course that's just my personal opinion. I do, however, think it's really interesting and useful to know that the relationship between minor chords functions the same way the relationship between major chords does, and I love that using the circle of fifths we can see which minor chords will be harmonious with whatever song we're playing or writing. So even though I'm still waiting eagerly to see how Crooks will teach us to tune instruments, I'm glad he took this small diversion to the dark side.

How does Portland's Charles Lewis use music to better the lives of his students?

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