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 at least 7-limit 72 & 77, but may more broadly be interpreted as a 2.3.7.{5.13.17} temperament (meaning it has a good 13/5, 17/5, and 17/13) also called Island Slendric. It it notable for being present in most edos containing generators for both Island (~15/13) and Slendric (~8/7).

Hexamech superset

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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 sharp fifth be used as the Hemiseven generator. This splits 7/4 into six parts, making it hexamech in ploidacot using the proposed -mech suffix for 7/4.

Vengeance is easy to add by making this temperament half-octave.