Hemiseven

Hemiseven is a temperament generated by a very sharp diatonic fifth, with 6 of them mapped to prime 3. This generator is very close to sqrt(16/7), equivalent to sqrt(7), hence the name. It is traditionally considered to be 7-limit or higher 72 & 77, but the more common interpretation covers a broader range including the 2.3.7.{5.13.17} temperament (2.3.7.13/5.17/5.17/13) also called Island Slendric. It is notable for being present in most edos containing generators for both Island (~15/13) and Slendric (~8/7).

Hexamech superset

g_

Some of my favorite rank-2 temperaments are alpha-dicot (semiquartal, including Island and its Intergan extension) and tricot (specifically Slendric). This makes anything in the Hemiseven range useful. There are two others, beta-tricot/omega-tricot (specifically Porcupine) and delta-triseph (like Vengeance and other antidiatonic tunings of Pentagoth).

The best way to add Porcupine to Hemiseven is to have the typical sharp 3/2 be used as the Hemiseven generator, making it a straddle-3 temperament. This splits 7/4 into six parts, making it hexamech in ploidacot using the proposed -mech suffix for 7/4. I propose that the most straightforward name is Sextanseventh because while it does not split 7/1 into six parts, 7/4 is the harmonic seventh. I cannot escape 6-7 jokes. It's even more obnoxious that 67edo is a great tuning of it.

The GTO string is 1200