Dirt

Dirt is the temperament which tempers out the dirt comma, 1342177280/1162261467, in the 5-limit. The optimal pure-octave tuning of this temperament has a very sharp ~3/2 generator at about 715 cents and a somewhat sharp ~5/4 at about 391 cents which is 19 generators up. The source of the temperament's name is unknown. 5edo appears to have the optimal patent val for this temperament.

This temperament could serve as a full 7-limit extension to archy near 1/2-comma superpyth, where even ultrapyth maps 5/4 too sharp (to 418.2 cents). By this point, the error on the perfect fifth may become a serious issue, so most people who use archy use a flatter fifth that works for 7-limit superpyth instead.

See Syntonic–diatonic equivalence continuum #Dirt for technical data.