Pele

Pele is a rank-3 temperament generated by a perfect fifth of ~3/2 and a step for the syntonic~septimal comma to reach the interval classes of 5, 7, and higher primes. Using an arrow to represent this comma step, we have 5/4 at the down major third (C–vE), 7/4 at the down minor seventh (C–vBb), and 11/8 at the down diminished fifth (C–vGb), tempering out 441/440 and 896/891, which makes it a member of both werckismic temperaments and pentacircle clan.

The canonical extension to the 13-limit finds 13/8 at the double-down diminished seventh (C–vBbb), tempering out 196/195, 352/351 and 847/845, and a 17-limit extension is available by recognizing 17/16 at the minor second (C–Db), tempering out 256/255.

Another way to view this temperament is to look at it relative to parapyth, for which it is an extension that addresses the missing prime 5. If we use an arrow to represent the quartertone spacer of parapyth, we have 5/4 at the up augmented second (C–^D#).

See Hemifamity family #Pele for technical details.