218edo - Revision history

ArrowHead294 at 14:17, 20 February 2025

2025-02-20T14:17:26Z

← Older revision		Revision as of 14:17, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	218edo is in[[consistent]] to the [[5-odd-limit]], with [[harmonic]] [[3/1\|3]] falling about halfway between its steps. However, it contains very accurate ratios, such as [[7/4]], [[9/7]], [[9/8]], [[10/9]], [[11/10]], [[17/16]], and [[19/16]], which are approximated within 0.55-cent deviation (10% the step size). The suggested [[subgroup]]s are therefore 2.9.7.17.19 and 2.9.5.7.11.17.19.23.		218edo is in[[consistent]] to the [[5-odd-limit]], with [[harmonic]] [[3/1\|3]] falling about halfway between its steps. However, it contains very accurate ratios, such as [[7/4]], [[9/7]], [[9/8]], [[10/9]], [[11/10]], [[17/16]], and [[19/16]], which are approximated within 0.55-cent deviation (10% the step size). The suggested [[subgroup]]s are therefore 2.9.7.17.19 and 2.9.5.7.11.17.19.23.

FloraC: Rework

2024-04-02T07:27:05Z

Rework

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''218edo''', having a step size of 5.50458715596 [[cent]]s, contains very accurate ratios, such as [[7/4]], [[9/7]], [[8/7]], [[9/8]], [[10/9]], [[11/10]] and [[17/16]] which are approximated within 0.55&cent; deviation (10% the step size).
+{{EDO intro}}
-The following table shows the nearest matches for the interval, not the matches from the [[patent val]]. '''Bold''' numbers are off within less than 0.1 (10%) of the step size.
+edo is in[[consistent]] to the [[5-odd-limit]], with [[harmonic]] [[3/1|3]] falling about halfway between its steps. However, it contains very accurate ratios, such as [[7/4]], [[9/7]], [[9/8]], [[10/9]], [[11/10]], [[17/16]], and [[19/16]], which are approximated within 0.55-cent deviation (10% the step size). The suggested [[subgroup]]s are therefore 2.9.7.17.19 and 2.9.5.7.11.17.19.23.
 Commas using the [[13-limit]] patent val:
@@ Line 49: / Line 14: @@
 ; [[13-limit]]: 28672/28561, 86240/85683, 20480/20449, 5600/5577, 16807/16731, 25000/24843, 6125/6084, 86625/86528, 68992/68445, 58080/57967, 96800/95823, 847/845, 41503/41067, 33275/33124, 65219/64896, 29575/29403, 4225/4224, 21632/21609, 676/675, 33124/32805, 9295/9261, 46475/45927, 13013/12960, 28561/28512
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+=== Odd harmonics ===

Plumtree: Infobox ET added

2022-10-04T21:23:31Z

Infobox ET added

← Older revision		Revision as of 21:23, 4 October 2022
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			{{Infobox ET}}
	'''218edo''', having a step size of 5.50458715596 [[cent]]s, contains very accurate ratios, such as [[7/4]], [[9/7]], [[8/7]], [[9/8]], [[10/9]], [[11/10]] and [[17/16]] which are approximated within 0.55¢ deviation (10% the step size).		'''218edo''', having a step size of 5.50458715596 [[cent]]s, contains very accurate ratios, such as [[7/4]], [[9/7]], [[8/7]], [[9/8]], [[10/9]], [[11/10]] and [[17/16]] which are approximated within 0.55¢ deviation (10% the step size).

Fredg999 category edits: Sort key

2022-07-03T18:34:11Z

Sort key

← Older revision		Revision as of 18:34, 3 July 2022
Line 48:		Line 48:
	; [[13-limit]]: 28672/28561, 86240/85683, 20480/20449, 5600/5577, 16807/16731, 25000/24843, 6125/6084, 86625/86528, 68992/68445, 58080/57967, 96800/95823, 847/845, 41503/41067, 33275/33124, 65219/64896, 29575/29403, 4225/4224, 21632/21609, 676/675, 33124/32805, 9295/9261, 46475/45927, 13013/12960, 28561/28512		; [[13-limit]]: 28672/28561, 86240/85683, 20480/20449, 5600/5577, 16807/16731, 25000/24843, 6125/6084, 86625/86528, 68992/68445, 58080/57967, 96800/95823, 847/845, 41503/41067, 33275/33124, 65219/64896, 29575/29403, 4225/4224, 21632/21609, 676/675, 33124/32805, 9295/9261, 46475/45927, 13013/12960, 28561/28512

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Keenan Pepper category edits: Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

2020-12-04T23:13:18Z

Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

← Older revision		Revision as of 23:13, 4 December 2020
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	; [[13-limit]]: 28672/28561, 86240/85683, 20480/20449, 5600/5577, 16807/16731, 25000/24843, 6125/6084, 86625/86528, 68992/68445, 58080/57967, 96800/95823, 847/845, 41503/41067, 33275/33124, 65219/64896, 29575/29403, 4225/4224, 21632/21609, 676/675, 33124/32805, 9295/9261, 46475/45927, 13013/12960, 28561/28512		; [[13-limit]]: 28672/28561, 86240/85683, 20480/20449, 5600/5577, 16807/16731, 25000/24843, 6125/6084, 86625/86528, 68992/68445, 58080/57967, 96800/95823, 847/845, 41503/41067, 33275/33124, 65219/64896, 29575/29403, 4225/4224, 21632/21609, 676/675, 33124/32805, 9295/9261, 46475/45927, 13013/12960, 28561/28512

	[[Category:~~Edo~~]]		[[Category:Equal divisions of the octave]]

Xenllium at 02:49, 23 March 2019

2019-03-23T02:49:44Z

← Older revision		Revision as of 02:49, 23 March 2019
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	Commas using the [[13-limit]] patent val:		Commas using the [[13-limit]] patent val:

	; [[3-limit]]: 1/1		; [[5-limit]]: 20000/19683, 1220703125/1207959552

	; [[5-limit]]: ~~20000~~/~~19683~~		; [[7-limit]]: 4000/3969, 65625/65536, 245/243, 2401/2400 117649/116640

	; [[7-limit]]: 4000/~~3969 65625~~/~~65536 245~~/~~243 2401~~/~~2400 60025~~/~~59049~~		; [[11-limit]]: 4000/3993, 12005/11979, 16384/16335, 4375/4356, 78125/77616, 896/891, 67228/66825, 1375/1372, 6875/6804, 5632/5625, 385/384, 94325/93312, 15488/15435, 75625/75264, 15488/15309, 3388/3375, 1331/1323, 6655/6561, 65219/64800, 43923/43904, 73205/72576,

	; [[11-limit]]: ~~4000~~/~~3993 12005~~/~~11979 16384~~/~~16335 4375~~/~~4356 78125~~/~~77616 896~~/~~891 67228~~/~~66825 1375~~/~~1372 6875~~/~~6804 5632~~/~~5625 385~~/~~384 94325~~/~~93312 15488~~/~~15435 75625~~/~~75264 15488~~/~~15309 3388~~/~~3375 1331~~/~~1323 6655~~/~~6561 65219~~/~~64800 43923~~/~~43904 73205~~/~~72576~~		; [[13-limit]]: 28672/28561, 86240/85683, 20480/20449, 5600/5577, 16807/16731, 25000/24843, 6125/6084, 86625/86528, 68992/68445, 58080/57967, 96800/95823, 847/845, 41503/41067, 33275/33124, 65219/64896, 29575/29403, 4225/4224, 21632/21609, 676/675, 33124/32805, 9295/9261, 46475/45927, 13013/12960, 28561/28512

	; [[13-limit]]: 28672/28561 86240/85683 20480/20449 5600/5577 16807/16731 25000/24843 6125/6084 86625/86528 68992/68445 58080/57967 96800/95823 847/845 41503/41067 33275/33124 65219/64896 29575/29403 4225/4224 21632/21609 676/675 33124/32805 9295/9261 46475/45927 13013/12960 28561/28512

	~~[[Category:Stub]]~~
	[[Category:Edo]]		[[Category:Edo]]

Xenwolf: Corrected synopsis. To talk of a deviation limit of 5.5 cents is pointless in this edo.

2018-10-02T10:56:42Z

Corrected synopsis. To talk of a deviation limit of 5.5 cents is pointless in this edo.

← Older revision		Revision as of 10:56, 2 October 2018
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	'''218edo''', having a step size of 5.50458715596 [[cent]]s, contains very accurate ratios, such as [[7/4~~]], [[11/8~~]], [[9/7]], [[8/7]], [[9/8]], [[10/9]], [[11/10]] and [[17/16]] ~~(sizes~~ are approximated within 5.~~5 cents~~).		'''218edo''', having a step size of 5.50458715596 [[cent]]s, contains very accurate ratios, such as [[7/4]], [[9/7]], [[8/7]], [[9/8]], [[10/9]], [[11/10]] and [[17/16]] which are approximated within 0.55¢ deviation (10% the step size).

	The following table shows the nearest matches for the interval, not the matches from the [[patent val]]. '''Bold''' numbers are off within less than 0.1 (10%) of the step size.		The following table shows the nearest matches for the interval, not the matches from the [[patent val]]. '''Bold''' numbers are off within less than 0.1 (10%) of the step size.

Xenwolf: added links, todo: expand table, add deltas (absolute in cents, relative in % of step size)

2018-10-02T07:16:05Z

added links, todo: expand table, add deltas (absolute in cents, relative in % of step size)

← Older revision		Revision as of 07:16, 2 October 2018
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	'''218edo''', having a step size of 5.50458715596 [[cent]]s, contains very accurate ratios, such as 7/4, 11/8, 9/7, 8/7, 9/8, 10/9, 11/10 and 17/16~~, and its step size can be~~ approximated as 5.5 cents.		'''218edo''', having a step size of 5.50458715596 [[cent]]s, contains very accurate ratios, such as [[7/4]], [[11/8]], [[9/7]], [[8/7]], [[9/8]], [[10/9]], [[11/10]] and [[17/16]] (sizes are approximated within 5.5 cents).

	'''Bold numbers are off within less than 0.1 step size~~'''~~		The following table shows the nearest matches for the interval, not the matches from the [[patent val]]. '''Bold''' numbers are off within less than 0.1 (10%) of the step size.

	{\| class="wikitable"		{\| class="wikitable"
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	\| '''181'''		\| '''181'''
	\|}		\|}

	~~^ this table shows the nearest matches for the interval, not the matches from the [[patent val]]~~

	Suggested [[subgroup]]s: 2.9.7.17 and 2.9.5.7.11.17.		Suggested [[subgroup]]s: 2.9.7.17 and 2.9.5.7.11.17.

Xenwolf: reworked: table style (maybe better with delta values); definition list for p-limit presentation; added to edo category

2018-10-02T07:10:46Z

reworked: table style (maybe better with delta values); definition list for p-limit presentation; added to edo category

← Older revision		Revision as of 07:10, 2 October 2018
Line 1:		Line 1:
	'''218edo''', having a step size of 5.50458715596 ~~cents~~, contains very accurate ratios, such as 7/4, 11/8, 9/7, 8/7, 9/8, 10/9, 11/10 and 17/16, and its step size can be approximated as 5.5 cents.		'''218edo''', having a step size of 5.50458715596 [[cent]]s, contains very accurate ratios, such as 7/4, 11/8, 9/7, 8/7, 9/8, 10/9, 11/10 and 17/16, and its step size can be approximated as 5.5 cents.

	'''Bold numbers are off within less than 0.1 step size'''		'''Bold numbers are off within less than 0.1 step size'''
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	~~\| \|~~ fraction:		! Interval fraction
	\| \| 3/2		\| [[3/2]]
	\| \| 4/3		\| [[4/3]]
	\| \| 5/4		\| [[5/4]]
	\| \| 8/5		\| [[8/5]]
	\| \| 5/3		\| [[5/3]]
	\| \| 6/5		\| [[6/5]]
	\| \| '''7/4'''		\| '''[[7/4]]'''
	\| \| '''8/7'''		\| '''[[8/7]]'''
	\| \| 10/9		\| [[10/9]]
	\| \| 9/5		\| [[9/5]]
	\| \| '''9/8'''		\| '''[[9/8]]'''
	\| \| '''16/9'''		\| '''[[16/9]]'''
	\|-		\|-
	~~\| \| steps~~ in 218edo:		! Steps in 218edo
	\| \| 128		\| 128
	\| \| 90		\| 90
	\| \| 70		\| 70
	\| \| 148		\| 148
	\| \| 161		\| 161
	\| \| 57		\| 57
	\| \| '''176'''		\| '''176'''
	\| \| '''42'''		\| '''42'''
	\| \| 33		\| 33
	\| \| 185		\| 185
	\| \| '''37'''		\| '''37'''
	\| \| '''181'''		\| '''181'''
	\|}		\|}

	^ this table shows the nearest matches for the interval, not the matches from the patent val		^ this table shows the nearest matches for the interval, not the matches from the [[patent val]]

	Suggested ~~subgroups~~: 2.9.7.17 and 2.9.5.7.11.17.		Suggested [[subgroup]]s: 2.9.7.17 and 2.9.5.7.11.17.

	Also explore [[436edo]].		Also explore [[436edo]].

	Commas using the 13-limit patent val:		Commas using the [[13-limit]] patent val:

	3-limit: 1/1		; [[3-limit]]: 1/1

	5-limit: 20000/19683		; [[5-limit]]: 20000/19683

	7-limit: 4000/3969 65625/65536 245/243 2401/2400 60025/59049		; [[7-limit]]: 4000/3969 65625/65536 245/243 2401/2400 60025/59049

	11-limit: 4000/3993 12005/11979 16384/16335 4375/4356 78125/77616 896/891 67228/66825 1375/1372 6875/6804 5632/5625 385/384 94325/93312 15488/15435 75625/75264 15488/15309 3388/3375 1331/1323 6655/6561 65219/64800 43923/43904 73205/72576		; [[11-limit]]: 4000/3993 12005/11979 16384/16335 4375/4356 78125/77616 896/891 67228/66825 1375/1372 6875/6804 5632/5625 385/384 94325/93312 15488/15435 75625/75264 15488/15309 3388/3375 1331/1323 6655/6561 65219/64800 43923/43904 73205/72576

	13-limit: 28672/28561 86240/85683 20480/20449 5600/5577 16807/16731 25000/24843 6125/6084 86625/86528 68992/68445 58080/57967 96800/95823 847/845 41503/41067 33275/33124 65219/64896 29575/29403 4225/4224 21632/21609 676/675 33124/32805 9295/9261 46475/45927 13013/12960 28561/28512		; [[13-limit]]: 28672/28561 86240/85683 20480/20449 5600/5577 16807/16731 25000/24843 6125/6084 86625/86528 68992/68445 58080/57967 96800/95823 847/845 41503/41067 33275/33124 65219/64896 29575/29403 4225/4224 21632/21609 676/675 33124/32805 9295/9261 46475/45927 13013/12960 28561/28512

	[[Category:Stub]]		[[Category:Stub]]
			[[Category:Edo]]

PiotrGrochowski at 18:49, 23 September 2018

2018-09-23T18:49:46Z

← Older revision		Revision as of 18:49, 23 September 2018
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	\|}		\|}

			^ this table shows the nearest matches for the interval, not the matches from the patent val

	Suggested subgroups: 2.9.7.17 and 2.9.5.7.11.17.		Suggested subgroups: 2.9.7.17 and 2.9.5.7.11.17.