Fibonacci Loops

for an indefinite set of instruments (1993)

This abstract and minimalistic work of the experimental kind is based on the famous Fibonacci sequence, a mathematical series of numbers in which each term is the sum of the two previous ones, starting with two terms equal to 1:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, ...

This sequence has a lot of remarkable properties, the most famous being that the ratio of two consecutive terms gets closer and closer to the Golden Section Number equal to 1.6180339887...

The melodic patterns of Fibonacci Loops have been obtained by recalculating the numbers of the Fibonacci sequence using modular arithmetic, what yields periodic sequences. For instance :

• mod 2 : 1, 1, 0, 1, 1, 0, 1, 1, 0, ... (period 3)
• mod 3 : 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, ... (period 8)
• mod 4 : 1, 1, 2, 3, 1, 0, 1, 1, 2, 3, 1, 0, ... (period 6)
• ...

Calculating until the mod 25 operation, the numbers obtained (from 0 to 24) are then matched to the notes of a 2-octava chromatic scale (starting from C3) in order to obtain patterns used as loops in the piece. For instance the mod 12 pattern (of period 24) sounds as follows :

The inversion of the patterns are also used in the piece. The work is "scored" for any set of instruments able to play this kind of pattern and having a range that encompasses the notes from C3 to C5, the most suitable being keyboard or mallet instruments.

The piece unfolds as follows: the first instrument plays the first pattern in a loop, then the second starts some time after with the second pattern, and so on until the last instrument is entered. At this point, the first instrument switches to the next pattern that remains to play, and so on until all patterns have been used. Then, the instruments stop playing one by one.

The material includes also an optional percussion part derived from the decimal writing of the Golden Section Number.

Score

Score available at Geyser Music Edition