Ntiscifer

Ntiscifer is the temperament tempering out the Pythagorean double-augmented second, 43046721/33554432, or in other words, it equates 16 perfect fifths to the octave. This produces very flat fifths - specifically, assuming pure octaves, the fifths are 675c, 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 (assuming pure octaves).) In the Majestazic system for describing temperaments, it can be described as redefining the prime 3 to be equal to (2^25)^(1/16), or equivalently, redefining the prime 2 to be equal to (3^16)^(1/25).

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 equivalent to Western equal-tempered or well-tempered tuning, while mavila is the equivalent 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.

3-limit ntiscifer

Equivalent to 16edo, creating a circle of 16 fifths with the flat 675c fifths. This circle 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 375c, as in mavila temperament (and is actually the harmonic system used in the original setting). 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

Comma list: 43046721/33554432

Mapping: TBA

Optimal tuning: ~3/2 = 9\16, ~5/4 = TBA

Optimal ET sequence: TBA

Badness: TBA