The rainbow effect on composing chaotic algorithmic music

The effect of rainbow color sequence on composing chaotic algorithmic music is examined. The mathematical range of the chaotic algorithm is mapped onto musical notes whose sequence follows the sequence of the seven main rainbow colors and their in-between five auxiliary colors. Each musical note is identified with the frequency of a color by a frequency shift. As a result, for a single rainbow, the scale of the chaotic music comprises an ascending chromatic F major scale without the thirteenth note, followed by its corresponding descending chromatic scale, for a total of twenty four notes. For aesthetic purposes, a note can be placed in any octave at the composer's will. The effect of a double rainbow on composing chaotic music is also studied. It is known from nature that the outer bow has its color sequence reversed. Thus, in this case, the double rainbow musical scale comprises forty eight notes on a repeated reversed full chromatic F major scale without the thirteenth note in the ascent or the first note in the descent, resembling in shape the letter w. Colorless regions in the rainbow or dark (Alexander's bands) regions in a supernumerary rainbow are included in the musical range as rests. With the musical scale based on the described rainbow mapping, chaotic music is composed from an algorithm defined by a semi-elliptical first order iterative map. The minor axis of the ellipse is defined by the range of the mathematical pitch from 0 to 1 while the semi-major axis by that of the succeeding pitch from 0 to r/2; r is a free parameter that varies from 1 to 2 to be chosen by the composer. The lower limiting value of the free parameter r corresponds to a circle of radius 1/2 yielding steady state music whereas all the other values of r correspond to ellipses. Chaotic compositions result from r values between 1.95 and 2, the latter value yielding full chaos from an ellipse with its major axis double its minor axis. Fixed notes are obtained for all r's, i.e., notes to be avoided for a prematurely ending composition. Chaotic musical scores are composed from the semi-elliptical iterative map with different initial pitches, on a single or a double rainbow musical scale.