A couple of scripts I wrote in C as tools for creating or discovering microtonal musical tunings. They include:
-
OPSL Finder: A script for finding EDO (equal divisions of the octave) tunings that consistently represent certain ranges of just (rational) frequency intervals. I’ll likely post an article in the future elaborating on what exactly OPSLs are.
-
SPIFE Finder: A script for finding a very specific type of interval. It’s maybe not very useful because less than 50 of these intervals are known to exist, I believe. In fact, I could probably list and categorize them by prime limit in less lines than the source file for this program. A SPIFE (or Superparticular Prime-Inclusive Fully Entangled) interval is a (positive) just ratio where (in simplest form) the numerator is one more than the denominator and where all prime numbers before the highest one in the prime factorizations of the numerator and denominator of the ratio are also in those prime factorizations. For example, 2080/2079 is a SPIFE because it’s 2^5 * 5 * 13 / (3^3 * 7 * 11), so all prime numbers less than 13 are present, but 10648/10647 is not, because its numerator and denominator do not have 5 as a factor, but do contain higher primes like 13.
Both of these scripts can be found here.