Ntiscifer: Difference between revisions

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Ntiscifer is the temperament tempering out the Pythagorean double-augmented second, [[43046721/33554432]], or in other words, it equates 16 [[3/2|perfect fifth]]<nowiki/>s 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|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 the temperament tempering out the Pythagorean double-augmented second, [[43046721/33554432]], or in other words, it equates 16 [[3/2|perfect fifth]]<nowiki/>s 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|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).

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.

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	Ntiscifer is the temperament tempering out the Pythagorean double-augmented second, [[43046721/33554432]], or in other words, it equates 16 [[3/2\|perfect fifth]]<nowiki/>s 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\|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 the temperament tempering out the Pythagorean double-augmented second, [[43046721/33554432]], or in other words, it equates 16 [[3/2\|perfect fifth]]<nowiki/>s 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\|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).

	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.		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.