Microtemperament

A microtemperament is a very accurate and usually very complex temperament. Due to their complexity, microtemperaments are usually not particularly useful for composition, although they can be in some cases and are often related to comma theory. Additionally, they usually have extremely narrow tuning ranges.

Notable microtemperaments are schismic, alphatricot, and ennealimmal. Of these, schismic is the exception: while ennealimmal requires a 36-note scale in order to reach all of the prime harmonics in its target subgroup, consequently a 63-note scale if the prime subharmonics are to be included, and an 81-note scale to include 9/8 and 16/9, and while alphatricot reaches 5/4 after 29 generator steps leaving 53edo as the only reasonably small edo tuning, schismic finds 5/4 after only eight steps, and is viable as a 17-note scale in 29edo or 41edo, making it somewh