Guitar Frets

I thought it would be interesting to show how to calculate the position of frets on the guitar fretboard. The same logic applies to any stringed instrument.

In the course of arriving at the final result we’ll cover some interesting physics – mainly the ideas behind standing waves, chromatic musical scales and the physics of vibrating strings. This isn’t a post about building musical instruments, it’s limited purely to understanding how the position of the frets are calculated.

There are many online fret position calculators that can be used to check the results that I’ll derive using the ideas developed in this article and if you’re building or maintaining a guitar I recommend using them because they provide many useful additional information e.g. the position and angle of the bridge on an acoustic, the position of the bridge on an electric.

There’s a good one on the StewMac site here

So, let’s make a start… Continue reading

Modelling Seashells

Introduction

I thought it would be fun to investigate the shapes of seashells and try to understand the factors that shape them.

In this post I’ve recorded what I’ve learned with examples for future reference. I’ve tried to make this post sufficiently complete that it could be used in the future as a reasonably comprehensive refresher in case I decide to come back to the subject and try playing with it further. In the course of thinking about this topic other ideas become important and the first part of this post summarises them (e.g. parametric surfaces, polar co-ordinates, ideas from Euclidean geometry). Where a particular subject requires it I’ve added a separate post to go into more detail and included a link to it in this post. Continue reading