Girolamo Frescobaldi
Cento partite sopra passacagli
100 Variations on Passacagli. 100 is not the only important number in this piece. The golden ratio, called also sectio aurea or proportia divina is considered to be an expression of beauty and balance in visual arts. But it also occurs as structural element in the form of musical pieces. In most cases it is not clear, whether it has been used consciously or instinctively by the composer. The golden ratio occurs when the ratio between a larger and a smaller part is the same as the ratio between their sum and the larger part. Mathematically expressed:
b/a = a+b/b = 1,61803….
Very often, at the very moment which divides a piece into the golden ratio, something special happens. In this piece, due to the meantone temperament, which was common during the 17th century, there are some places with notes that are somewhat out of tune. On a keyboard with 12 keys/octave and with meantone temperament, one could not have a good E flat and a good D sharp at the same time, nor a G sharp and also an A flat. But this piece features all these notes. And in bar 124 (of 326), we hear the most “dangerous” of all intervals: the “wolf”.
326-124=202
202/124=1,629
Not exactly 1,618. But very close.
Did Frescobaldi do exact calculations in order to know where to place the wolf?
Who knows…

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