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. Small EDFs that support halftone include 5edf, 6edf, 7edf (not in the patent val), 11edf, 16edf, 17edf (not in the patent val), and 23edf (not in the patent val).

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 instead of a minor third. 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 instead of a minor third. These chords generally sound more consonant than a standard diminished triad but not as much as a major or minor triad. Both these are well approximated in halftone because it equates 4 7/5 with 10/9.

16edf is ay