Distorted sounds: unlocking the physics of modern music

Abstract In the production of modern music, the musical characteristics of the guitar or keyboard amplifier play an integral role in the creative process. This article explores the physics of music with an emphasis on the role of distortion in amplification. In particular, we derive and illustrate how a distorted amplifier creates new musical notes that are not played by the musician, greatly simplifying the playing technique. In providing a comprehensive understanding, we commence with a discussion of the physics of music, highlighting the harmonic series and its relation to pleasing harmonies. This is placed in the context of the standard music notation of intervals and their relation to note frequency ratios. We then discuss the problems of tuning an instrument and why the equal temperament of standard guitar tuners is incompatible with good sounding music when amplifier distortion is involved. Drawing on the basic trigonometric identities for angle sums and differences, we show how the nonlinear amplification of a distorted amplifier generates new notes not played by the musician. Here the importance of setting your guitar tuner aside and using your ear to tune is emphasised. We close with a discussion of how humans decipher musical notes and why some highly distorted guitar chords give the impression of low notes that are not physically there. This article will be of assistance to students interested in the physics of music and lecturers seeking fascinating and relevant applications of mathematical trigonometric relations and physics to capture the attention of their students.