from The Century Dictionary and Cyclopedia
- n. In ancient Greek music, the next to the lowest tone of either the lowest or the middle tetrachord: so called because it lay next (above) the tone hypate. Its pitch was probably about that of either middle C or the F next above it. See tetrachord.
Sorry, no etymologies found.
Thus, parhypate, which in the enharmonic is at the interval of half a semitone from hypate, has a semitone interval when transferred to the chromatic.