How to Play the Guitar by Ear (for Mathematicians and Physicists)

This essay presents the theory of music associated with the guitar. It is intended to provide a technically oriented person an understanding of how musical chords are constructed and which chords “go together” in a musical piece. It is useful background in learning to play the guitar by ear (i.e., to play any song, in any key, by ear (i.e., without reference to musical notation)). From the Introduction… I like to understand the reason behind what I do, and just accepting the rote pronouncements of the music theory that I read was very unsatisfying. Recently, I spent some time figuring out the “whys” of music theory. There are very good reasons for the tenets of music theory, and it is very satisfying to know why things are the way they are. Before explaining how to accompany songs with chords, I will explain this theory. I have not seen this theory anywhere else, but I have not researched the topic and this material is probably available from somewhere (but not in music stores!). (I do not have ready access to specialized reference materials here in Botswana, so I have not checked this out.) The explanation is not difficult to someone who has some basic knowledge of physics (sound, wave motion, harmonics) and mathematics (the exponential and logarithmic functions). It is because of this mathematical/physical description of music theory that I refer to this method as one directed to mathematicians and physicists. If you have no interest in understanding music theory, you can still learn to play the guitar by ear – you will just not understand why it works.