The theme of the Golden Ratio in music is also surrounded by mystery and debate. Several articles have claimed that Mozart (1756-1791) used the Golden Ratio in his piano sonatas. Since Mozart was interested in working with figures, according to his sister, in his school years - he is one of the better candidates to have had knowledge of and used the Golden Ratio in his works. John F. Putz at the Alma College in Michigan did a careful study of Mozart's sonatas. The sonatas are divided into two parts, the Exposition and the Development and Recapitulation. The Exposition is an introduction to the musical theme while the Development and Recapitulation further develop it. Putz examined the ratio of numbers of measures per section and came up with a ratio of 1.63 for Sonata #1 in Major C, but Putz examined all Mozart's sonatas quite carefully and concluded that the Golden Ratio was not used purposefully by Mozart (Livio, 2003).
There is evidence that there are other composers who may have used the Golden Ratio, and indeed if they did not do it intentionally, it apparently created music that was pleasing to the ear. Some of these composers were Bela Bartok (1881-1945) and Claude Debussy (1862-1918). The use of the Golden Ratio in music is not doubted however, in music made after the twentieth century (Livio, 2003).
The musical intervals that are generally considered most pleasing are close to the Golden Ratio. These are the major sixth and minor sixth. Of course this is subject to opinion and is a bit ambiguous, but it points to the inherent beauty of this proportion.
The Golden Ratio is not only used in music composition, but it has also been applied in developing musical instruments. The Golden Ratio is present in the violin several times over. The sound box usually has twelve plus arcs of curvature on each side, the flat arc at the base is often times centered at the Golden Section of the center line. Antonio Stradivari (1644-1737) was a well-known violin maker whose original drawings show that he used the Golden Section to place the eyes of the f-holes of the violin. Few believe that this is actually what makes his violins special, but nonetheless, he did use the ratio (Livio, 2003).
The piano is also cited as having a relationship with the Fibonacci numbers. This also is debated and although the black and white keys and the primary scale can be aligned with five consecutive Fibonacci numbers, that is the end of the tie. Also, this arrangement of piano keys dates back to before a good understanding of the Fibonacci numbers was prevalent (Livio, 2003).