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Diary of an OCW Music Student, Week 3: Octave Equivalence, Circular Pitch Systems and the Major Triad

Study.com is a huge supporter of the open education movement, and want to educate you, our readers, on how these great, free online educational resources can improve your lives. Follow the journey of one writer as he completes an open music course through UC Irvine OpenCourseWare.

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By Eric Garneau

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Where Theory Meets Practice

Last week I detected a bit of a learning curve in the second segment of UC Irvine's 'Introduction to Pitch Systems in Tonal Music' course. Through a dense, math-filled discussion of octaves, pitch systems and harmonics, I found myself a bit confused by the implications of everything lecturer John Crooks was laying down. Though it was an interesting, useful lesson, parts of it stumped this semi-seasoned musician.

This week, things have changed. We're back to a 10-minute lesson after last week's 20-minute outing, and the contents here strike me as both comprehensible and totally practical. Crooks uses the third of his video lectures/presentations to focus on two major topics: the circle of fifths and major thirds, another tonal interval like the octaves, fifths and perfect fourths we discussed last week.

When introducing the circle of fifths, Crooks notes that it's 'probably familiar to anyone who's studied any music theory.' I mentioned back in my first column that I never officially learned any theory; as a result, this circle was totally new to me, which is too bad, because this thing is super helpful. It's a purely visual representation of how music notes and keys relate to each other mathematically and tonally.

Crooks uses the circle to express the relationship between tones as a mathematical ratio from which we can build and understand other relationships, but from a DIY musician standpoint this circle has other immediate, practical uses. Have you ever wanted a quick way to figure out the relative minor of whatever major key you're playing in (FYI, relative minors make solos sound cool)? Just travel three stops clockwise on the circle. Are you a harmonica player who wants to get some interesting tones by playing cross-harp on a tune? Look to the immediate right of whatever key your song's in and you'll know in a snap what harmonica you need to grab. This is such a helpful tool for understanding musical relationships that you might want to print out a picture of it and keep it in your gig bag - it couldn't hurt!

circle of fifths

As a side-effect of Crooks' lesson, live musicians who need to be versatile (which should be all of us) can understand why the principle of key transposition works. Music is about ratios and interval relationships moreso than tones, so if you're wondering why you can put a song in a different key and it still basically sounds like the same piece of music, it's because as long as you keep the mathematical relationship between notes the same, you're essentially playing the same piece regardless of its key. Transposition has all sorts of benefits; in the world of rock and roll, it's especially useful for cover musicians who work with many different singers, not all of whom have the exact right range needed to replicate a song in its original key. Instead of forcing a singer out of his or her comfort zone, why not transpose the song? The power of math tells you how.

Find A-Chord

Crooks also instructs us on how mathematic relationships allow us to build the interval of the major third, which, when joined with the perfect fifth we learned last week, gives us our first major chord. These are the basic units which comprise much music, and with Crooks' lesson we now understand how and why they work. And although it may seem too academic for rock and roll, being able to speak in the language of thirds and fifths might have some surprising benefits. For instance, if you ever find yourself in the position of needing to sing backup harmonies in a song, you'll have an easier time communicating with your lead singer if you can articulate just what harmony you think he or she wants you to produce. It's my experience that most vocal harmonies in rock (at least most cool-sounding ones) are sung at a third above the melody, so keep that in mind if you're looking for an interesting way to add some vocal panache to your latest composition.

As I make my way through Crooks' course, it strikes me just how mathematical music is. Far from taking the magic out of a highly creative art form, though, I think that actually makes the process of creating and understanding music all the more interesting. If you grasp the basic, formulaic building blocks through which most music works, that puts you in a better position to manipulate them for your own purposes. If nothing else, you'll probably have a serious advantage over others in your scene if you can confidently talk about major thirds and pure intervals.

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