Möbius Strip Bach

Posted by John Farrier in Music, Video Clips on September 11, 2009 at 4:00 pm


(YouTube Link)

This video shows a selection from Johann Sebastian Bach’s Musical Offering (1747) played forwards, then backwards, then both forwards and backwards at the same time. It was created by mathematical illustrator Jos Leys and science/philosophy blogger Xantox. This Bach piece has long intrigued mathematicians:

In each of these canons a musical line is played twice (or four times in Canon 10). The second version is always transformed with respect to the first by shifting in time, but it may also be shifted in pitch, turned upside-down, stretched, or played backwards. Each of these transformations occurs in the mathematics of elementary functions; they are examples of how new functions can be made out of old and of how a function can be tailored to fit a new situation.

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Bach's Forgotten Horn

Posted by John Farrier in Music, Science & Tech on July 13, 2009 at 8:18 am

Musicians and scientists have re-created a lost musical instrument known as the ‘lituus’:

In 1737-8, Johann Sebastian Bach composed and performed a cantata, “O Jesu Christ, meins lebens licht” (”O Jesus Christ, light of my life”). Among the instruments called for in the score are “two Litui.” However, the Lituus is a forgotten instrument. No one has played or heard the instrument in modern times; there aren’t even illustrations of one.

Musicians at a Swiss conservatory, the Schola Cantorum Basiliensis (SCB), had heard of a computer program developed by a University of Edinburgh Ph.D. student to help in the design of modern brass instruments. The SCB provided a group of Edinburgh scientists with design requirements, such as notes that would have been played with the Lituus, how it sounded and how it might have been played. (Though likely made of wood, the Lituus qualifies as a brass instrument.) The result: a two-and-a-half-meter-long horn made of pine with a flared bell at one end and a mouthpiece made of cow horn at the other. And they built two.

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