I am on the road again this week. So as I cruise at 34,000 feet over Knoxville, Tennessee, let me share with you the long, circuitous history of my learning to play guitar. It’s a story which has lessons about mathematics as well as the importance of matching teaching styles to students.

A prominent feature in my house when I grew up was a baby grand piano. My mother, father, and sister all played. But not me. Like many a rebellious youth, I did not want to play the same instrument as everyone else in the house. So, after a short and rather pathetic attempt at playing the baritone, I started taking guitar lessons when I turned 10.

My first teacher was a woman in the neighborhood who was primarily a piano teacher. Her lessons consisted of teaching me to play the melodies of songs like She’ll be Coming ‘Round the Mountain. While there is some utility in this, the usual role of a guitar is to play the chords of a song in support of a vocalist or other instruments. Feeling dissatisfied, I switched to a new teacher who was a professional musician, and I was soon playing the chords for some of my favorite Eagles and Fleetwood Mac tunes of the late 1970s. However, even though I could now play Hotel California, every time I learned a new song, it was a unique, stand-alone challenge.

As my journey in learning the guitar continued, I found myself craving a deeper understanding of the instrument. It wasn’t until I stumbled upon a seasoned instructor who not only shared my passion for rock classics but also emphasized the fundamental building blocks of music theory. Under his guidance, I delved into the world of chords, discovering the rich texture they added to my repertoire. The introduction of 7th chords on guitar became a pivotal moment, unlocking a new dimension in my playing. These extended chords not only enhanced the harmonic complexity of songs but also provided a versatile toolkit for creative expression. Suddenly, each new song wasn’t just a standalone challenge, but a piece of a larger puzzle, where 7th chords seamlessly intertwined with the melodies, transforming my guitar journey into a more holistic and satisfying musical experience.

While I do not have much in way of innate musical talent, I do have persistence. I kept taking lessons until I was 18 years old and performed in a couple of high school talent shows. Unfortunately, despite practicing and playing diligently for 8 years, my guitar playing did not improve. When I left for college, I put the guitar in a closet and there it stayed for many years.

When I think back now about quitting guitar it makes me sad, especially since, had I been taught differently, things might have worked out so much better. Music in general, and guitar in particular, are very mathematical. I am an engineer; math I get. But the instruction I received as a child left the math out, and so I foundered.

Before proceeding, let’s review the key features of a guitar. A typical guitar has six strings which run down a long neck to the sound box. The neck has a series of small metal bars across it called frets. The mathematics for where the frets are placed were initially worked out by Pythagoras, he of the Pythagorean Theorem. Pressing your finger down between two of the frets changes the effective length of the string. The length, along with the thickness and tension of the string, determines the frequency at which the string will vibrate when plucked. The higher the frequency of the vibration the higher the pitch of the sound produced. Chords are made by playing several strings simultaneously. Alas, no one taught me this mathematical component as a child. It would be 28 years before I picked up my guitar again.

My return to the guitar was inspired by my friend, Greg Bell. Readers may know Greg from his performances in many local bands over the years, including the Chicken Wire Gang, or from his role in running the annual Eno River Festival. A visit to the Bell home, as often as not, will include a sing-along. After attending quite of few of these, I started to get the itch to play again.

Greg is a remarkably talented musician and has a particular gift that I would observe with utter amazement. We would be having a sing-along and someone would suggest a song. Often Greg would already know the guitar chords, but when he didn’t, he would ask someone to start singing and, after listening to just a couple of lines, Greg would play the chords to the whole song. It was like magic.  To a degree, watching Greg allowed me to let myself off the hook about what I perceived as my failure to become a good guitar player as a child. I do not possess anything close to Greg’s ear for music, so how could I possibly have been successful?

As his son entered his teen years, Greg began to teach him to play the guitar. And, as they played along together, rather than calling out the names of chords, like G or A minor, Greg called out numbers from 1 to 7. I was intrigued. If Greg’s magic had some math behind it, maybe there was a chance for me after all.

So I got my guitar back out of the closet and, at Greg’s recommendation, started taking lessons from Brian Dennis at the Music Loft in Carrboro. You may recognize Brian’s name from the local music scene as well. I explained to Brian my goals as a guitar player and my observations from Greg. He got out a piece of paper, told me it was all based on mathematical patterns, and taught me basic music theory in under an hour. I learned more from Brian in my first month of lessons than I had in eight years from my childhood teachers.

While I had long known that songs were written in different keys, I had never been taught what that meant in terms of guitar chord progressions, or how to convert a song from one key to another. I mentioned this to Brian and he got out another piece of paper and showed me that each key had seven chords that followed a simple pattern. This was mathematical information which was presented visually, perfect for me. Now I finally understood what Greg meant when he was calling out those numbers.

Allow me to let you in on the secret. The table below shows the chords for the keys of G and D by number. Note that the number 1 chord is what defines the key.

1

2

3

4

5

6

7

G

A minor

B minor

C

D

E minor

F

D

E minor

F# minor

G

A

B minor

C#

Let say you learned a song in the key of G and the chord progression for the verses was G, D, E minor, and C.  In numbers, this chord progression is 1, 5, 6, 4, a very typical progression in pop music. Now imagine you’ve learned the song in the key of G and head to the Bells’ preparing to strut your stuff at the next sing-along. You get started and the vocalist calls a halt, and instead wants to sing the song in the key of D. Pre-Brian, I would be completely stymied. But now that know the math, I can switch to the 1, 5, 6, and 4 chords in the key of D, which are D, A, B minor and G. And voila! The job is done.

I have been taking lessons from Brian for a little over two years now and am a far, far better guitar player than I have ever been. I plan to stick with it this time. But beyond my own personal satisfaction in becoming a better musician, there are some broader lessons here.

Everyone has different learning styles. I can remember almost everything that I see but only a modicum of what I hear. Further, I like information that occurs in patterns and is structured mathematically. Since my childhood teachers where not mathematical and presented the information verbally, I struggled. When I finally found a teacher taught in the right style for me, I blossomed.

This is not intended as an indictment of my childhood teachers, but serves as a reminder of how to create a successful learning environment. Student achievement is maximized when we can create an environment with the capacity and flexibility to present information in a variety of ways to reach students with a variety of learning styles. If we were to reduce capacity and flexibility by doing things such as increasing class sizes and eliminating teaching assistants, then student achievement would necessarily decline. But no one would do that, would they?

Have a comment or question? Use the interface below or send me an email to commonscience@chapelboro.com. Think that this column includes important points that others should consider? Send out a link on Facebook or Twitter. Want more Common Science? Follow me on Twitter on @Commonscience.