The Guitar – Now With Geometry

Guitar Fretboard Graph

Read Time 3 Minutes

How the Idea for This Article Formed

So I was sitting at work the other day, staring down at my ginormous clown shoes, waiting to jump out of my barrel the moment the angry bull parading around threw off the cowboy sitting on him who was flailing around like a rag doll hanging out of a window flying down the highway.

Bunch of Ugly Shapes
The picture that started the idea for this article.

While this was all going on around me I was staring at a blank sheet of papering the desk I happened to have inside my barrel (my barrel is also a Tardis) and I was repeatedly tapping an ink pen onto the paper making several little dots. I then decided to draw a line from dot to dot until all had a line connecting them together. And do you know what I noticed?

I noticed that while the overall shape was an amorphous blob of a decagon it was filled with triangles. And as I looked at the beautiful mess my first thought was “there has to be a way to apply this to the guitar”.

The Guitar Graph

After looking at the poorly free-handed geometry I turned over my paper and drew a fretboard. It was then that I started to see a certain familiarity to the design. No, not because I play the guitar and know what the neck of a guitar looks like. Because my crude sketch had a striking resemblance to a sheet of graph paper.

Really when you break it down that’s exactly what not just the guitar but all fretboard instruments are. Graphs. Frets mark the vertical lines and strings mark the horizontal (or vice versa depending on your perspective). So that means that turning the guitar into the canvas for geometry is wonderfully accessible.

This worked to my advantage as each string intersected with a fret making nice and specific points to mark.

Guitar Triangles

Guitar Fretboard Graph
This is the basic shape I came up with. Its design was completely random.

Of course triangles have been applied to the guitar before, but it’s usually in the context of chord progressions. Things like the old I-IV-V or the ii-V-I progressions which are naturally triangular on the fretboard.

However I want to venture somewhere new with this. Geometrical melodies.

From here there are a few readily evident approaches. First thing to do is decide how many points the overall shape is going to have. I recommend five. It’s simple enough to control but advanced enough to offer pretty much unlimited options. Four points and fewer is quite limiting, but much easier to work with.

The next step is to decide whether you want to pick tones out or just randomly put dots on the neck and see what happens. The former offers control over the emotion conveyed by what you end up with while the latter liberates you from habit, (and of Nicholas has shown us anything it’s that habits are made to be broken).

I’m hardcore so I went with five randomly chosen points and ended up with two A’s, F, Bb, and E. I did a bit of line drawing and made some new points offering me G and Ab as well. I decided to stop there.

The Music of Triangles

What I did here was I took the letters that surfaced and I mostly played them in one position, though I did move out of it to welcome the same tones in higher octaves.  I got damn lazy with the drums.  I just wanted something to keep the rhythm while I improvised for what few minutes of spare time I ever have, so I just used a stock loop from EZ Drummer then smiled as a sensation of true accomplishment swept me over.
Graph Song by The Smitchens

Things I’ve Learned from Doing This

This could easily pass as an excellent way to learn the notes on the neck. Because you become so limited in the number of notes you’re after you really see the pattern of their positions from one to the others quickly. As you move up and down the neck you get a feel of where to find the others pretty quickly.

It’s also an excellent way to keep yourself from resorting to the same routine as usual. When you relinquish your ability to choose for yourself what notes you’re using you welcome the opportunity to play in keys and use intervals not necessarily indigenous to your style.

I learned that there are so many possibilities to this approach. Parallelograms, triangles, pentagons, any shape you can think of can be easily graphed out on the fretboard and by default can give you unlimited options. In fact why not try it the other way around? Try connecting the dots of your melodies and see what kinds of shapes they make?

I also learned that when a cowboy is thrown off a bull I’m not supposed to just sit in my barrel drawing shapes. He was rushed to the hospital to mend a brand new orifice and now I need to find a new job.

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Kyle Smitchens

Kyle Smitchens is the Guitar-Muse Managing Editor, super hero extraordinaire, and all around great guy. He has been playing guitar since his late teens and writing personal biographies almost as long. An appreciator of all music, his biggest influences include Tchaikovsky, Bach, Mozart, Beethoven, Steve Vai, Therion, and Jon Levasseur of Cryptopsy.

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Nicholas Tozier
9 years ago

There’s an amazing little book that illustrates a few music theory concepts as geometric shapes; I bet it’d be right up your alley, Smitch.

Scott Collins
9 years ago

Hey Smitch! Really cool article! A lot of my approach to fretboard visualization is pattern and shape oriented so this made me smile.

I was actually thinking about writing an article about a guy named Randy Bird who had an entire methodology called Chaostics he developed that’s completely based on geometrical fretboard manipulations.

Your chess game idea was particularly brilliant as well.

Keep on keepin’ on!


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