Usage: primeratiogen Scalename [PrimeCount] [SubsetSize]

Scalename the name of the scale to embed in the Scala file. PrimeCount the number of prime numbers starting with 2 to use SubsetSize the number of notes to choose from the generated set of ratios.

primeratiogen generates Scala tuning files according to a simple algorithm:

Take the first N primes, and make a set that permutes every combination of prime ratios. Sort them ascending by numeric value. Throw out any duplicates or fractions greater than 2 or less than 1 -- i.e. all that fit within a single octave.

Example:

The first 3 primes are 2, 3, and 5.

The permutations are 2/3, 3/2, 2/5, 5/2, 3/5, 5/3 In order by value: 2/5, 3/5, 2/3, 3/2, 5/3, 5/2

2/5 and 3/5 are less than one, and 5/2 is more than 2, so toss them.

You're left with 3 pitch ratios 3/2, 5/3, 2/1.

The SubsetSize argument says how many notes to include in the scale. The notes chosen are the most evenly spaced subset of the larger scale. This is done using the Bjorklund algorithm.

This is exactly how a Euclidean sequencer chooses note timing, but instead of choosing the most equidistant events in the time domain, the scale generator chooses the most equidistant N tones in an octave of M tones.