Dissonance in b-Smooth

Inspired by Adi Shamir's TWINKLE optical device for finding smooth numbers, which works at GHz, I wrote an audio device for finding smooth numbers, which works at low kHz. In absence of a good, screeching acronym, I'd call it Dysphony in b-Smooth.

The idea is to convert the smaller prime factors of numbers into sound. The code does this by keeping n counters, each of which is increased modulo its individual prime. At the moment, these are the first 1000 primes. After every increment the counters that contain a zero are collected and a sine wave is constructed from the associated frequencies (index*(2000/n) + 40 Hz) at an amplitude proportional to the logarithm of the prime (so that the frequent divisors 2,3,5,etc have a low impact). Each sound lasts a small fraction of a second. If a loud noise is audible, it is the representation of a number with many different and/or larger prime factors.

The scientific value of this is approaching zero from the left, but it was a nice exercise to have the computer produce sound after my last attempts in 1987 on an Atari ST.

Thu, 08 Mar 2012
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