Ntiscifer - Revision history

FloraC: - parent category

2025-04-28T14:29:02Z

- parent category

← Older revision		Revision as of 14:29, 28 April 2025
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	See [[16th-octave temperaments #Ntiscifer]] for technical data.		See [[16th-octave temperaments #Ntiscifer]] for technical data.

	[[Category:~~Temperaments~~]]		[[Category:Ntiscifer\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	~~[[Category:Ntiscifer\| ]] <!-- main article -->~~

Lériendil at 23:30, 19 April 2025

2025-04-19T23:30:47Z

← Older revision		Revision as of 23:30, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]
	[[Category:Ntiscifer\| ]] <!-- main article -->		[[Category:Ntiscifer\| ]] <!-- main article -->

FloraC: Data moved to 16th-octave temperaments page. +categories

2024-07-04T05:38:58Z

Data moved to 16th-octave temperaments page. +categories

← Older revision		Revision as of 05:38, 4 July 2024
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	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.		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 ===~~		See [[16th-octave temperaments #Ntiscifer]] for technical data.
	~~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~~		[[Category:Temperaments]]
			[[Category:Ntiscifer\| ]] <!-- main article -->
	~~[[Comma list]]~~: ~~[[43046721/33554432~~]]

	~~{{Mapping\|legend=1\| 16 25 0 \| 0 0 1 }}~~

	[[~~Optimal tuning]]s~~:
	* [[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)

	~~{{Optimal ET sequence~~\|~~legend=1\| 16 }}~~

	~~[[Badness~~]]~~: 3.05~~

FloraC: Complete the data

2024-07-04T05:35:41Z

Complete the data

← Older revision		Revision as of 05:35, 4 July 2024
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	[[Comma list]]: [[43046721/33554432]]		[[Comma list]]: [[43046721/33554432]]

	Mapping~~: TBA~~		{{Mapping\|legend=1\| 16 25 0 \| 0 0 1 }}

	Optimal tuning: ~3/2 = 9\16, ~5/4 = ~~TBA~~		[[Optimal tuning]]s:
			* [[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)

	Optimal ET sequence~~: TBA~~		{{Optimal ET sequence\|legend=1\| 16 }}

	Badness: ~~TBA~~		[[Badness]]: 3.05

FloraC: General cleanup, linking, and style improvements. Remove the 3-limit version (you're not supposed to name an edo).

2024-07-04T05:26:27Z

General cleanup, linking, and style improvements. Remove the 3-limit version (you're not supposed to name an edo).

← Older revision		Revision as of 05:26, 4 July 2024
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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)~~.		'''Ntiscifer''' is the [[regular temperament\|temperament]] [[tempering out]] the Pythagorean double-augmented second, [[43046721/33554432]], or in other words, it equates an [[octave reduction\|octave-reduced]] stack of sixteen [[3/2\|perfect fifth]]'s to the [[octave]]. This produces very flat fifths – specifically, assuming pure octaves, the fifths are 675 [[cent]]s, 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 ~~equivalent~~ to Western equal-tempered or well-tempered tuning, while mavila is the ~~equivalent~~ to meantone tuning.		Ntiscifer is part of an attempt by [[User:VectorGraphics\|Vector]] to define a system of [[antidiatonic]] music theory analogous to Western [[5L 2s\|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 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 ===~~		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.
	~~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 ===		=== 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.		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		[[Subgroup]]: 2.3.5

VectorGraphics at 06:07, 3 July 2024

2024-07-03T06:07:28Z

← Older revision		Revision as of 06:07, 3 July 2024
Line 1:		Line 1:
	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.

VectorGraphics: uyjgt

2024-07-03T03:52:23Z

uyjgt

New page

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 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