Halftone

Halftone is a nonoctave (fifth-repeating) regular temperament in the 3/2.5/2.7/2 fractional subgroup that tempers out 9604/9375. It could be used as a harmonic basis for "1/2 prime" (3/2.5/2.7/2.11/2.13/2 etc.) systems with the equivalence as 3/2, similar to meantone for full prime-limit systems with the equivalence as 2/1 and Bohlen-Pierce-Stearns for no-twos systems with the equivalence as 3/1. If tone clusters with intervals of supraminor seconds or less are ignored, the most fundamental 3/2.5/2.7/2 chord that can fit inside a perfect fifth is 45:50:63 (1-10/9-7/5), essentially a diminished triad with a major second. There is also a more "major-sounding" counterpart of it 50:63:70 (1-63/50-7/5), a diminished triad with a major third. Both of these are well approximated in halftone because it equates 4 7/5 with 10/9.