In 1987 I conceived a theoretical improvement on the quarter-comma meantone scale: the generators are 2−5/4 31/4 57/16 (a ‘tone’, 194.501 cents) and 27/2 3−1/2 5−9/8 (a ‘semitone’, 114.420 cents). I previously showed a guitar concept fretted accordingly; see that post for my motives.
Next, can I extend the concept to higher primes? One difficulty is that, while the lower primes have well-defined notation (2 is five tones and two semitones, 3 is eight tones and three semitones, 5 is twelve tones and four semitones), it is not so clear where to put higher primes: should a factor of 7 be approximated by 12 tones and 9 semitones, or 15 tones and 4 semitones, or some other combination? This choice, which must be done again for every prime to be added to the scheme, affects the optimization.
So I attacked a simpler problem: local optima – minimax temperaments – with a single generator.
The world mostly yawned.