1200edo - Revision history

FloraC: No need to remind readers of what a regular temperament is everywhere

2025-04-11T11:20:22Z

No need to remind readers of what a regular temperament is everywhere

← Older revision		Revision as of 11:20, 11 April 2025
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	The equal temperament [[tempering out\|tempers out]] 2460375/2458624 and 95703125/95551488 in the [[7-limit]], supporting the 171 & 1029 temperament, with a period of 1/3 octave and a generator which is an approximate [[225/224]] of 7\1200. It tempers out [[9801/9800]], 234375/234256 and 825000/823543 in the 11-limit, supporting the 494 & 706 temperament, with a half-octave period and an approximate 99/98 generator of 17\1200.		The equal temperament [[tempering out\|tempers out]] 2460375/2458624 and 95703125/95551488 in the [[7-limit]], supporting the 171 & 1029 temperament, with a period of 1/3 octave and a generator which is an approximate [[225/224]] of 7\1200. It tempers out [[9801/9800]], 234375/234256 and 825000/823543 in the 11-limit, supporting the 494 & 706 temperament, with a half-octave period and an approximate 99/98 generator of 17\1200.

	It also provides a 7-limit val, 1200ccd, which is extremely closely close to the 7-limit [[POTE tuning]] of [[quadritikleismic temperament]]: {{val\| 1200 1902 2785 3368 }}. It also provides the optimal patent val for the 224 & 976 temperament tempering out [[2200/2197]], [[4096/4095]], 9801/9800 and 35750/35721. ~~(''See [[regular temperament]] for more about what all this means and how to use it.'')~~		It also provides a 7-limit val, 1200ccd, which is extremely closely close to the 7-limit [[POTE tuning]] of [[quadritikleismic temperament]]: {{val\| 1200 1902 2785 3368 }}. It also provides the optimal patent val for the 224 & 976 temperament tempering out [[2200/2197]], [[4096/4095]], 9801/9800 and 35750/35721.

	Upwards to the 47-limit, 1200edo offers relatively accurate approximations for 2, 3, 7, 17, 31, 41, and 47, and in the 2.3.7.17.31.41.47 [[subgroup]] it tempers out 2304/2303, 3808/3807, 6273/6272, 506447/506268, 632056/632043, 10218313/10214416. The 47th harmonic is 6666 steps and 666 steps reduced – a mathematical coincidence in our decimal system.		Upwards to the 47-limit, 1200edo offers relatively accurate approximations for 2, 3, 7, 17, 31, 41, and 47, and in the 2.3.7.17.31.41.47 [[subgroup]] it tempers out 2304/2303, 3808/3807, 6273/6272, 506447/506268, 632056/632043, 10218313/10214416. The 47th harmonic is 6666 steps and 666 steps reduced – a mathematical coincidence in our decimal system.

BudjarnLambeth: /* Theory */ (''See regular temperament for more about what all this means and how to use it.'')

2025-04-11T07:52:33Z

Theory: (''See regular temperament for more about what all this means and how to use it.'')

← Older revision		Revision as of 07:52, 11 April 2025
Line 9:		Line 9:
	The equal temperament [[tempering out\|tempers out]] 2460375/2458624 and 95703125/95551488 in the [[7-limit]], supporting the 171 & 1029 temperament, with a period of 1/3 octave and a generator which is an approximate [[225/224]] of 7\1200. It tempers out [[9801/9800]], 234375/234256 and 825000/823543 in the 11-limit, supporting the 494 & 706 temperament, with a half-octave period and an approximate 99/98 generator of 17\1200.		The equal temperament [[tempering out\|tempers out]] 2460375/2458624 and 95703125/95551488 in the [[7-limit]], supporting the 171 & 1029 temperament, with a period of 1/3 octave and a generator which is an approximate [[225/224]] of 7\1200. It tempers out [[9801/9800]], 234375/234256 and 825000/823543 in the 11-limit, supporting the 494 & 706 temperament, with a half-octave period and an approximate 99/98 generator of 17\1200.

	It also provides a 7-limit val, 1200ccd, which is extremely closely close to the 7-limit [[POTE tuning]] of [[quadritikleismic temperament]]: {{val\| 1200 1902 2785 3368 }}. It also provides the optimal patent val for the 224 & 976 temperament tempering out [[2200/2197]], [[4096/4095]], 9801/9800 and 35750/35721.		It also provides a 7-limit val, 1200ccd, which is extremely closely close to the 7-limit [[POTE tuning]] of [[quadritikleismic temperament]]: {{val\| 1200 1902 2785 3368 }}. It also provides the optimal patent val for the 224 & 976 temperament tempering out [[2200/2197]], [[4096/4095]], 9801/9800 and 35750/35721. (''See [[regular temperament]] for more about what all this means and how to use it.'')

	Upwards to the 47-limit, 1200edo offers relatively accurate approximations for 2, 3, 7, 17, 31, 41, and 47, and in the 2.3.7.17.31.41.47 [[subgroup]] it tempers out 2304/2303, 3808/3807, 6273/6272, 506447/506268, 632056/632043, 10218313/10214416. The 47th harmonic is 6666 steps and 666 steps reduced – a mathematical coincidence in our decimal system.		Upwards to the 47-limit, 1200edo offers relatively accurate approximations for 2, 3, 7, 17, 31, 41, and 47, and in the 2.3.7.17.31.41.47 [[subgroup]] it tempers out 2304/2303, 3808/3807, 6273/6272, 506447/506268, 632056/632043, 10218313/10214416. The 47th harmonic is 6666 steps and 666 steps reduced – a mathematical coincidence in our decimal system.

ArrowHead294 at 16:55, 18 February 2025

2025-02-18T16:55:25Z

← Older revision		Revision as of 16:55, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1200~~}}		{{ED intro}}

	1200edo is notable for being the equal division of the octave whose step size corresponds to exactly 1 [[cent]].		1200edo is notable for being the equal division of the octave whose step size corresponds to exactly 1 [[cent]].

Fredg999: Remove bold around "cent" (MOS:BOLD), rephrase

2024-09-04T01:19:09Z

Remove bold around "cent" (MOS:BOLD), rephrase

← Older revision		Revision as of 01:19, 4 September 2024
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	{{EDO intro\|1200}}		{{EDO intro\|1200}}

	1200edo is notable for being the equal division of the octave ~~corresponding~~ to ~~'''~~[[cent]]~~s'''~~.		1200edo is notable for being the equal division of the octave whose step size corresponds to exactly 1 [[cent]].

	== Theory ==		== Theory ==
	1200edo is [[consistency\|distinctly consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val\| 1200 1902 2786 3369 4151 }}. It is [[enfactoring\|enfactored]] in the [[5-limit]], having the same tuning as [[600edo]].		1200edo is [[consistency\|distinctly consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val\| 1200 1902 2786 3369 4151 }}. It is [[enfactoring\|enfactored]] in the [[5-limit]], having the same tuning as [[600edo]].

Francium: /* Music */ +music

2024-05-28T12:56:19Z

Music: +music

← Older revision		Revision as of 12:56, 28 May 2024
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	== Music ==		== Music ==
			; [[Hideya]]
			* [https://www.youtube.com/watch?v=FJhmgbuoRHA ''Like scattered blue light''] (2024)

	; [[Sevish]]		; [[Sevish]]
	* [https://www.youtube.com/watch?v=lTT3QGTngIs ''Dream Up''] (2021, demo version)		* [https://www.youtube.com/watch?v=lTT3QGTngIs ''Dream Up''] (2021, demo version)

	[[Category:Listen]]		[[Category:Listen]]

Francium: +categories

2024-02-13T18:25:04Z

+categories

← Older revision		Revision as of 18:25, 13 February 2024
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	; [[Sevish]]		; [[Sevish]]
	* [https://www.youtube.com/watch?v=lTT3QGTngIs ''Dream Up''] (2021, demo version)		* [https://www.youtube.com/watch?v=lTT3QGTngIs ''Dream Up''] (2021, demo version)

			[[Category:Listen]]

Eliora: adopt intro

2024-02-03T16:55:31Z

adopt intro

← Older revision		Revision as of 16:55, 3 February 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~1200 equal divisions of the octave''' ('''1200edo'''), or the '''1200(-tone) equal temperament''' ('''1200tet''', '''1200et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 1200 [[equal]] parts of exactly 1 [[cent]] each, and a size close to [[1729/1728]]. It is notable mostly because it is the equal division corresponding to cents.		{{EDO intro\|1200}}

			1200edo is notable for being the equal division of the octave corresponding to '''[[cent]]s'''.
	== Theory ==		== Theory ==
	1200edo is [[consistency\|distinctly consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val\| 1200 1902 2786 3369 4151 }}. It is [[enfactoring\|enfactored]] in the [[5-limit]], having the same tuning as [[600edo]].		1200edo is [[consistency\|distinctly consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val\| 1200 1902 2786 3369 4151 }}. It is [[enfactoring\|enfactored]] in the [[5-limit]], having the same tuning as [[600edo]].

Eliora: /* Theory */

2023-11-30T17:03:33Z

Theory

← Older revision		Revision as of 17:03, 30 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1200edo is [[consistency\|distinctly consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val\| 1200 1902 2786 3369 4151 }}. It is [[enfactored]] in the [[5-limit]], having the same tuning as [[600edo]].		1200edo is [[consistency\|distinctly consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val\| 1200 1902 2786 3369 4151 }}. It is [[enfactoring\|enfactored]] in the [[5-limit]], having the same tuning as [[600edo]].

	The equal temperament [[tempering out\|tempers out]] 2460375/2458624 and 95703125/95551488 in the [[7-limit]], supporting the 171 & 1029 temperament, with a period of 1/3 octave and a generator which is an approximate [[225/224]] of 7\1200. It tempers out [[9801/9800]], 234375/234256 and 825000/823543 in the 11-limit, supporting the 494 & 706 temperament, with a half-octave period and an approximate 99/98 generator of 17\1200.		The equal temperament [[tempering out\|tempers out]] 2460375/2458624 and 95703125/95551488 in the [[7-limit]], supporting the 171 & 1029 temperament, with a period of 1/3 octave and a generator which is an approximate [[225/224]] of 7\1200. It tempers out [[9801/9800]], 234375/234256 and 825000/823543 in the 11-limit, supporting the 494 & 706 temperament, with a half-octave period and an approximate 99/98 generator of 17\1200.

FloraC: Misc. cleanup

2023-10-31T10:08:18Z

Misc. cleanup

← Older revision		Revision as of 10:08, 31 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1200edo is ~~distinctly~~ [[consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val\| 1200 1902 2786 3369 4151 }}. It is [[enfactored]] in the [[5-limit]], having the same ~~mapping~~ as [[600edo]].		1200edo is [[consistency\|distinctly consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val\| 1200 1902 2786 3369 4151 }}. It is [[enfactored]] in the [[5-limit]], having the same tuning as [[600edo]].

	~~1200et~~ tempers out 2460375/2458624 and 95703125/95551488 in the [[7-limit]], supporting the 171 & 1029 temperament, with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200. It tempers out [[9801/9800]], 234375/234256 and 825000/823543 in the 11-limit, supporting the 494 & 706 temperament, with a half-octave period and an approximate 99/98 generator of 17\1200.		The equal temperament [[tempering out\|tempers out]] 2460375/2458624 and 95703125/95551488 in the [[7-limit]], supporting the 171 & 1029 temperament, with a period of 1/3 octave and a generator which is an approximate [[225/224]] of 7\1200. It tempers out [[9801/9800]], 234375/234256 and 825000/823543 in the 11-limit, supporting the 494 & 706 temperament, with a half-octave period and an approximate 99/98 generator of 17\1200.

	It also provides a 7-limit val, 1200ccd, which is extremely closely close to the 7-limit [[POTE tuning]] of [[quadritikleismic temperament]]: {{val\| 1200 1902 2785 3368 }}. It also provides the optimal patent val for the 224&~~752~~ temperament tempering out 2200/2197, 4096/4095, 9801/9800 and 35750/35721.		It also provides a 7-limit val, 1200ccd, which is extremely closely close to the 7-limit [[POTE tuning]] of [[quadritikleismic temperament]]: {{val\| 1200 1902 2785 3368 }}. It also provides the optimal patent val for the 224 & 976 temperament tempering out [[2200/2197]], [[4096/4095]], 9801/9800 and 35750/35721.

	Upwards to the 47-limit, 1200edo offers relatively accurate approximations for 2, 3, 7, 17, 31, 41, and 47, and in the 2.3.7.17.31.41.47 subgroup it tempers out 2304/2303, 3808/3807, 6273/6272, 506447/506268, 632056/632043, 10218313/10214416. The 47th harmonic is 6666 steps and 666 steps reduced – a mathematical coincidence in our decimal system.		Upwards to the 47-limit, 1200edo offers relatively accurate approximations for 2, 3, 7, 17, 31, 41, and 47, and in the 2.3.7.17.31.41.47 [[subgroup]] it tempers out 2304/2303, 3808/3807, 6273/6272, 506447/506268, 632056/632043, 10218313/10214416. The 47th harmonic is 6666 steps and 666 steps reduced – a mathematical coincidence in our decimal system.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	The divisors of 1200 are {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, and 600 }}. These are all the edos whose step size is an integer amount of cents, and thus can be played exactly on any digital audio workstation that offers detuning by cents.		The nontrivial divisors of 1200 are {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, and 600 }}. These are all the edos whose step size is an integer amount of cents, and thus can be played exactly on any digital audio workstation that offers detuning by cents.

	== Regular temperament properties ==		== Regular temperament properties ==
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	\| 2.3.5.7		\| 2.3.5.7
	\| 2460375/2458624, 95703125/95551488, {{monzo\| 36 -5 0 -10 }}		\| 2460375/2458624, 95703125/95551488, {{monzo\| 36 -5 0 -10 }}
	\| [{{~~val~~\| 1200 1902 2786 3369 }}]		\| {{mapping\| 1200 1902 2786 3369 }}
	\| +0.0112		\| +0.0112
	\| 0.0748		\| 0.0748
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 9801/9800, 234375/234256, 825000/823543, 1771561/1769472		\| 9801/9800, 234375/234256, 825000/823543, 1771561/1769472
	\| [{{~~val~~\| 1200 1902 2786 3369 4151 }}]		\| {{mapping\| 1200 1902 2786 3369 4151 }}
	\| +0.0273		\| +0.0273
	\| 0.0743		\| 0.0743
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	== Music ==		== Music ==
	* [https://www.youtube.com/watch?v=lTT3QGTngIs Dream Up (~~Demo Version~~)~~] by [[Sevish]]~~		; [[Sevish]]
			* [https://www.youtube.com/watch?v=lTT3QGTngIs ''Dream Up''] (2021, demo version)

BudjarnLambeth at 06:51, 9 July 2023

2023-07-09T06:51:20Z

← Older revision		Revision as of 06:51, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	The '''1200 equal divisions of the octave''' ('''1200edo'''), or the '''1200(-tone) equal temperament''' ('''1200tet''', '''1200et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 1200 [[equal]] parts of exactly 1 [[cent]] each, and a size close to [[1729/1728]]. It is notable mostly because it is the equal division corresponding to cents.		The '''1200 equal divisions of the octave''' ('''1200edo'''), or the '''1200(-tone) equal temperament''' ('''1200tet''', '''1200et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 1200 [[equal]] parts of exactly 1 [[cent]] each, and a size close to [[1729/1728]]. It is notable mostly because it is the equal division corresponding to cents.