The Golden Section and Music

Golden sections in Violin construction

The section on "The Violin" in The New Oxford Companion to Music, Volume 2, shows how Stradivari was aware of the golden section and used it to place the f-holes in his famous violins.

Baginsky's method of constructing violins is also based on golden sections.

Did Mozart use the Golden mean?

This is the title of an article in the American Scientist of March/April 1996 by Mike Kay. He reports on the analysis of many of Mozart's sonatas and finds they divide into two parts exactly at the golden section point in almost all cases. Was this a conscious choice (his sister said he was always playing with numbers and was fascinated by mathematics) or did he do this intuitively?

Article:The Mathematics Magazine Vol 68 No. 4, pages 275-282, October 1995 has an article by Putz on Mozart and the Golden section in his music.

Beethoven's Fifth

Article:In an interesting little article in Mathematics Teaching volume 84 in 1978, Derek Haylock writes about The Golden Section in Beethoven's Fifth on pages 56-57.
He finds that the famous opening "motto" appears not only in the first and last bars (bar 601 before the Coda) but also exactly at the golden mean point 0·618 of the way through the symphony (bar 372) and also at the start of the recapitulation which is phi or 0·382 of the way through the piece! He poses the question:

Was this by design or accident?

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