Collection VII

Lucas and Fibonacci in White

Casey Mongoven

June 10, 2008

description of sequences: Lucas sequence; define a(0) = 2, a(1) = 1, for n > 1 a(n) = a(n - 1) + a(n - 2). Fibonacci sequence; define a(0) = 0, a(1) = 1, for n > 1 a(n) = a(n - 1) + a(n - 2).
description of piece: This piece is based on Fibonacci and Lucas harmonic partials. The fundamental frequency (1st partial) can be defined, but it must be 21.71 Hz or below. White noise is filtered an FFT-based bandpass filter (or a Butterworth bandpass filter in another version). The filter makes a linear sweep upward from the fundamental frequency; this means that everything below the fundamental frequency is cut off in the beginning. The two sequences are separated into two channels (definable). The bandwidth expands as the filter sweeps upward parallel on both speakers until the filter reaches the next Lucas or Fibonacci harmonic partial at which point everything below that partial is filtered out; if a Lucas or Fibonacci partial is reached, that only affects the speaker designated for that sequence. When the 610th partial on the channel playing the Fibonacci sequence is reached by the filter, that channel stops and the Lucas channel plays on. Once the 843rd partial is reached by the filter on the speaker designated for the Lucas sequence, the piece ends. An anti-click envelope is used - see Csound file.
optional: Using a long piano string with a base frequency at or below 21.71 Hz, attach a transducer to the string at one end and a piezoelectric microphone at the other. Set the fundamental frequency of the piece to the same frequency as the fundamental of the string and send both the Fibonacci and Lucas channels through the string separately with the transducer, using the microphone to record the result on the other end (individually recorded, one and then the other). Place both resulting sound files parallel on two channels (a stereo file) and play them back parallel to one another through two loudspeakers.
offset: 1 for Lucas sequence, 2 for Fibonacci
number of members used: 14
number of channels: 2
piece length: defined by base note value multipled by 2204
base note value: definable, .04138 seconds or greater (same for both sequences)
orientation: ascending
temperament: based on series of harmonic partials
lowest frequency: definable, 21.71 Hz or lower highest frequency: lowest frequency multiplied by 843
number of unique frequencies: infinite
synthesis technique: white noise filtered by bandpass filter
dynamic: definable, from ppppp to fff
synthesis language used: Csound