“The Use and Abuse of Fibonacci Numbers and the Golden Section in Musicology Today”

• The numbers in the so-called Fibonacci Sequence express Euclid’s division in extreme and mean ratio (DEMR), popularly known as the Golden Section. Since the manuscript describing the sequence, Fibonacci’s Liber abbaci, was written in 1202 and since Euclid described DEMR c. 300 BCE, many musicologists have naïvely assumed that composers since 1202 consciously used Fibonacci numbers to express the Golden Section. This is historically misguided. For example, although Euclid’s DEMR was widely-published and discussed throughout maths history, Fibonacci's Liber abbaci (1202) was not. After a brief transmission in manuscript form, Liber abbaci was lost until the mid-eighteenth century and forgotten for a further hundred years until Prince Baldassarre Boncompagni rediscovered it and published it in two volumes in 1857 and 1862. Although there were a few sporadic appearances of a numerical expression for DEMR in the 17th and 18th centuries (unrelated to Fibonacci), real interest in the Golden Section and its aesthetic properties was first awakened in the late 19th century with the golden numberism movement. This paper will examine the historical facts and set out clear principles to guide the analyst.

Keyword

Musikvetenskap

Musicology

Konstvetenskap

History of Art

Idé- och lärdomshistoria

History of Sciences and Ideas

Fibonacci Euclid DEMR Musicology Numbers

Publication and Content Type

ref (subject category)

art (subject category)