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I found a little discussion of the issue in Russell (2000), where he summarises some of the views of the scientific literature:

Recent reviews of the empirical literature bearing on the claim of special aesthetic significance for this ratio in the context of the perception of simple figures include Green (1995), Hoge (1995), and contributors to a dedicated edition of Empirical Studies of the Arts (Hoge 1997). Some investigators doubt that the golden section has any aesthetic significance, even suggesting that research on it be abandoned (Boselie 1992, 1997; Davis and Jahnke 1991). Others prefer to leave the question open, especially in view of the methodological difficulties associated with testing the significance of the golden section (Green 1995).

Green (1995) argues that "[t]here seems to be, in fact, real psychological effects associated with the golden section, but they are relatively sensitive to careless methodological practices."

Russel (2000) explored the height to width ratio of a large database of famous paintings and did not find any particular support for a preference for the golden-section. Russel suggests that in the real world functional factors tend to constrain ratios.

McManus (1980, PDF) provides an interesting discussion of the methodological issues and the findings of research that has empirically studied aesthetic judgements of simple figures. McManus advocates the use of the paired-comparison method whereby participants make aesthetic judgements on which of series of pairs of objects is more aesthetically attractive. McManus observed that there were substantial individual differences in such preferences. McManus felt that existing empirical research was unable to adequately differentiate preference for the golden-section versus other similar ratios such as 1.5, 1.6 or 1.75.

References