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.
5-limit ntiscifer
Equivalent to the 16edo circle of fifths with an added dimension for 5/4. In 16edo, this maps 5/4 to 375 cents, as in mavila temperament. Tunings with a separate, more accurate third include 64edo, 80edo, and 96edo; 96edo is a particularly accurate tuning, though 64edo might be considered more practical.
Subgroup: 2.3.5
Mapping: [⟨16 25 0], ⟨0 0 1]]
- CTE: ~2048/2187 = 1\16, ~5/4 = 386.3137 (~135/128 = 11.3137)
- CWE: ~2048/2187 = 1\16, ~5/4 = 373.1508 (~128/135 = 1.8492)
Badness: 3.05