Hyperpent and hypopent

Hyperpent or hyperpental edo is an equal division of the octave which has a just fifth that is less than a syntonic comma sharp. It is juxtaposed by hypopent or hypopental edo tuning systems, which have a just fifth that is less than a syntonic comma flat. In particular, a hyperpent edo has a fifth ranging from 3/2 to 243/160 and a hypopent edo has a fifth ranging from 40/27 to 3/2.

Background

"Hyperpental" is loosely associated with "superpyth," but specifically refers to equal division of the octave that result in any fifth tempered sharp, while "hypopental" is loosely associated with "meantone," but specifically refers to equal division of the octave that result in any fifth tempered flat.

Some edos may contain no intervals in the span of a just fifth plus or minus a syntonic comma, and thus are neither hyperpent nor hypopent, and are refered to as "anpent."

Partial List

Anpent (neither hypopent nor hyperpent)

2edo, 3edo, 4edo, 6edo, 8edo, 9edo, 11edo, 13edo, 16edo, 18edo, 23edo

Hyperpent

5edo, 10edo, 15edo, 17edo, 20edo, 22edo, 25edo, 27edo, 29edo, 30edo, 32edo, 34edo, 39edo, 41edo, 46edo

Hypopent

7edo, 12edo, 14edo, 19edo, 21edo, 24edo, 26edo, 28edo, 31edo, 33edo, 36edo, 38edo, 43edo