8188044

I wanted to arrange a small musical composition / experiment in which the frequencies of the tones were values in the Fibonacci Sequence (1,1,2,3,5,8,13,21,34,55,89,etc.). Then I came upon the question, "How long should these tones play for?" If each tone was played for one full second, it would be slow and not necessarily capture the essence of the divine proportion, so I created two other methods of integrating the sequence into time. One method was to use only one cycle of each tone, increasing in speed as it increases in pitch. The other was to extend the time by the same amount as the increase in hertz, playing higher tones longer and longer. The results are simply astounding: Let's compare them in terms of the constant time scenario. By the time we reach one minute (that's 60 total different tones, less that your average piano), 44 seconds of it is impossible to hear with the human ear. Using the same frequencies in the one cycle per frequency method, we reach a total time of just over 2.3 seconds and will, in fact, never even reach 2.4 seconds, regardless of how many more frequencies we add, and the amount of audible time is a mere 1/8 of a second or 124 milliseconds. Meanwhile, using the method by which the amount of time per frequency increases at the same rate as the cycles increase, we start with the first frequency only lasting for 1/1000 of a cycle and by our marked ending point, the last frequency reaches over 6.27 sextillion cycles and the whole sequence lasts for 207 years, 11 months, 6 days, 23 hours, 12 minutes, and 39 seconds. Of this time, 1 minute and 15 seconds is audible to the human ear.