Ntiscifer

Ntiscifer is the temperament tempering out the Pythagorean double-augmented second, 43046721/33554432, or in other words, it equates an octave-reduced stack of sixteen perfect fifth's to the octave. This produces very flat fifths – specifically, assuming pure octaves, the fifths are 675 cents, or in other words, flattened by 1/16 of the "comma". This is the tuning of 16edo, though like the compton family, the tuning of the primes larger than 3 is more flexible. 16edo is the unique ntiscifer temperament in the 5-limit that is also a mavila temperament.

Ntiscifer is part of an attempt by Vector to define a system of antidiatonic music theory analogous to Western diatonic music theory. In that context, it is the analog to Western equal-tempered or well-tempered tuning, while mavila is the analog to meantone tuning.

The name comes from the planet Ntiscifer in Vector's science fiction setting, which has an alien species that uses a 16edo scale, and is pronounced "nn-ti-shi-fer" – this name ultimately derives from a randomly generated name in Universe Sandbox that appears frequently due to a glitch.

The circle of 16 fifths with the flat 675-cent fifths shares some properties with the 12edo circle of fifths, namely that the note a tritone from any given note can be found by going halfway around it (8 steps), and that adjacent to that (9 and 7 steps) are the sharpened and flattened version of that note, respectively.

See 16th-octave temperaments #Ntiscifer for technical data.