The Calkin-Wilf sequence contains every positive rational number exactly once:
1/1, 1/2, 2/1, 1/3, 3/2, 2/3, 3/1, 1/4, 4/3, 3/5, 5/2, 2/5, 5/3, 3/4, ….
I'd consider 5/1 to be a "simpler" ratio than 8/5, but it appears later in the series.
Is there a mathematical term for the "simpleness" of a ratio? It might be something like the numerator times the denominator, or maybe there are other ways to measure.
Is there a sequence that contains all the positive rational numbers, but with the "simpleness" of the ratios monotonically increasing?
(Small integer ratios are found in Just intonation, polyrhythm, orbital resonance, etc.)
If you use the Calkin-Wilf sequence with the num*den measure, for instance, it looks like this: