Hofstadter, Monroe and Bulatov: The Eternal Shepard

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.

For those that enjoy this illusion, Daniel Repasky has produced a 10 hour version matched to a fractal video by Vladimer Bulatov derived from ‘Circle Limit III’ by M.C.Escher.

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.

Index: There are indices for the TAWOP site here and here Twitter: You can follow ‘The Amazing World of Psychiatry’ Twitter by clicking on this link. Podcast: You can listen to this post on Odiogo by clicking on this link (there may be a small delay between publishing of the blog article and the availability of the podcast). It is available for a limited period. TAWOP Channel: You can follow the TAWOP Channel on YouTube by clicking on this link. Responses: If you have any comments, you can leave them below or alternatively e-mail justinmarley17@yahoo.co.uk. Disclaimer: The comments made here represent the opinions of the author and do not represent the profession or any body/organisation. The comments made here are not meant as a source of medical advice and those seeking medical advice are advised to consult with their own doctor. The author is not responsible for the contents of any external sites that are linked to in this blog.


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