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The Research Page

Mathematical Model of a Guitar String

Back in 2014 I started developing a simple mathematical model of a guitar string. Why? Well, I had started making guitars, and wanted to make better ones. I am also interested in maths and physics, so it seemed like a good idea! I suppose I was primarily interested in trying to find a better way of ensuring that a guitar was as in tune with itself as it was possible to be. I wanted to try and answer questions like:

  • how do you know where to put the frets on a fingerboard?
  • how accurate do fret positions have to be?
  • how do you intonate a guitar?
  • why do guitars allow for adjustments to be made to bridge positions for each string?
  • why don't guitars allow for adjustments to be made to nut positions for each string?

So, here is the current state of my model. I've written a number of documents. This one is about fret theory in general. I haven't come up with this stuff. This is generally known.

Fret Theory

This is the main thrust of my model:

How to Intonate a Guitar

And these are consequences of my model:

How Accurate do Frets Have to Be?

Model Sensitivities

This model has not been tested. I could say the reason for this is that I'm a theoretical physicist, but the real reason is that I don't have the tools or the environment to do the job properly.

And here is the computer program based on my model. The zip file contains the program (written in Java), instructions, and sample string data.

Guitar Intonator Program


If you are interested in mathematical models of guitar strings, please check this out, and get back to me about all the mistakes that I've made.