Auditory illusions cause a misperception of presented sounds in contrast with auditory hallucinations which occur in the absence of a presented sound. The Shepard Tone illusion consists of three tones played simultaneously. Two tones keep rising whilst one drops an octave. Then another drops an octave while the remaining two keep rising. The end result is that the listener thinks the sound is continuously rising.
In the seventeenth century, Frederick the Great asked Johann Sebastian Bach to write a musical piece based on a theme that he presented to Bach. The resulting piece ‘The Musical Offering‘ consists of several canons and fugues and one of these – ‘the Ricercar a 6’ is established as one of the most important pieces in music. Below is ‘Canon a 2, per tonos’ which is also known as the ‘Neverending Canon’.
Professor Michael Monroe has produced a variation on ‘Canon a 2, per tonos’ which uses a suggestion by Pulitzer prize winning author Professor Douglas Hofstadter in his work ‘Gödel, Escher, Bach: An Eternal Golden Braid’. This variation uses the Shepard tone concept to ensure that the piece ends on the octave that it started with.
There is an MIT open course on Hofstadter’s ‘Gödel, Escher, Bach: An Eternal Golden Braid’ here. What is really interesting is that auditory and visual illusions above have been created through an understanding of mathematics.
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