22 equal temperament

These discrepancies arise because, unlike 12-ET, 22-ET does not temper out the syntonic comma of 81/80, but instead exaggerates its size by mapping it to one step.

The enharmonic structure is also reversed: sharps are sharper than flats, similar to Pythagorean tuning (and by extension 53 equal temperament), but to a greater degree.

Finally, 22-ET has a good approximation of the 11th harmonic, and is in fact the smallest equal temperament to be consistent in the 11-limit.

The net effect is that 22-ET allows (and to some extent even forces) the exploration of new musical territory, while still having excellent approximations of common practice consonances.

The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth-century music theorist RHM Bosanquet.

[2] Contemporary advocates of 22 equal temperament include music theorist Paul Erlich.

The third, Porcupine Notation, introduces no new accidentals, but significantly changes chord spellings (e.g. the 5-limit major triad is now C–E♯–G♯).