Along their musical education, most piano students learn the circle of fifths. They probably develop some fuzzy connection between the circle of fifths and keys: G Major has one sharp and its tonic is a perfect fifth above C; D Major has two sharps and its tonic is a perfect fifth above G; etc. Perhaps they will learn that the order of sharps is an ascending circle of fifths, and the order of flats is a descending circle of fifths. If they are very lucky, they will begin to understand the human ear’s affinity for the circle of fifths and its implications on tonal harmony (think ii V I).
But, for all the glory that the circle of fifths deserves, I believe that the circle of thirds should be taught to our music students long before the circle of fifths, because the circle of thirds is the foundation of reading music and building harmony.
Consider how many students are introduced to the treble staff. Most of us began to read by learning some crutch phrase, like “Every Good Boy Does Fine.” We then learned that the first (bottom) line of the treble clef staff was an E (Every), the next line up was a G (Good), and so forth. The problem with “Every Good Boy Does Fine” (what about girls? or bad boys?) is that it does nothing to teach the structure of a staff or an understanding of the staff. The student is left with nothing to help them read ledger lines or staves with different clefs. To read the bass clef, students must learn another crutch phrase (I learned “Good Boys Deserve Fudge Always” … how come I didn’t always get fudge?). And to learn ledgers? I don’t recall receiving much help for that. And forget C clefs. I had to navigate that one completely on my own.
With the circle of thirds memorized, deciphering a staff uses the same skill no matter what clef is used: Identify the anchor note (G for treble clef, F for bass clef, and C for C clef), and then count up or down the lines to find the note along the circle of thirds. It doesn’t matter if the lines are on the staff or if they are ledger lines. The counting is the same.
(I’ve always wondered how most European countries teach reading, since they use solfege instead of letter names. I wouldn’t be surprised if they used the circle of thirds.)
Knowing the circle of thirds also facilitates identifying and creating triads. Creating a triad from the circle of thirds is trivially simple. What’s the tonic? F. Walk up the circle of thirds, and name the triad F A C.
I want all of my students to be able to look at any three notes of a triad on a staff and easily identify the root of that triad. In the early stages of learning this skill, the circle of thirds can be very helpful.
Consider the D minor chord shown to the right. A student who is trying to decipher this chord might start by reading the notes from the top down. The top note is an F. With knowledge of the circle of thirds, the notes possible to fit within a triad that has an F are:
B D F A C
The next note down is an A. That removes the B as an option, leaving these as the possible notes in the chord:
D F A C
The next note down is a D. At this point, the student can identify the root of the triad:
When we teach in letter names, the circle of thirds going up is an easy mnemonic:
GBD FACE (pronounced Gee-Bee-Dee Face).
Students who repeat GBD FACE repeatedly (Gee-Bee-Dee Face Gee-Bee-Dee Face …) for a whole week can easily remember the ascending circle of thirds. Going in descending order takes a bit more thinking. Unfortunately, I know of no other way to learn to navigate fluently up and down the circle of thirds in solfege than to employ lots of verbal repetition. (Do Mi Sol Si Re Fa La Do Mi … and Do La Fa Re Si Sol Mi Do La …)
Becoming fluent in reading and in chord recognition takes practice. [Ideally these skills are developed on many levels: analytical understanding (do you understand how it is constructed?), visual understanding (do you see it on the keyboard?), and aural understanding (can you hear it?).] However, without knowing how to fully decipher the staff or triad, a student attempting to become fluent in these skills is easily frustrated. They do not understand the logic behind what they are attempting to memorize, and hence they cannot self correct during the process. In my next post, I will talk about how to use fingers to help students navigate the circle of thirds.