Microtempering

Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a microtemperament. There is no agreed on value for the threshold to microtempering, and here we will use less than a cent in error as our line of demarcation, which some people would call a nanotemperament. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 236, 270 ... are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 ... are 7-limit microtemperaments; 764, 836, 1084, 1106 ... are 11-limit microtemperaments, and that 1171, 1178, 1186 ... are 13-limit microtemperaments.

Putting 118 and 171 together, we see that the 5-limit schismatic temperament, which tempers out the schisma of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that ennealimmal temperament, which tempers out the breedsma 2401/2400 and the ragisma 4375/4374 is also a microtemperament.