Keemic chords

A magical seventh is an 11-limit essentially tempered dyadic chord consisting of three sharp classical minor thirds and a septimal whole tone, which closes at the octave since both 100/99 and 385/384 (and therefore 875/864) are tempered out. This means that in the 11-limit supermagic planar temperament tempering these out, the chord is the tempering of

• 1–6/5–16/11–7/4, with steps 6/5, 6/5, 6/5, 8/7.

In an optimized tuning for the supermagic temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val (104edo). Hence magic (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a Graham complexity of 12, so it does not appear that often.

Other temperaments that feature this chord prominently include 11-limit keemun, superkleismic, porcupine and doublewide.