216edo - Revision history

Squib at 19:10, 2 March 2026

2026-03-02T19:10:57Z

← Older revision		Revision as of 19:10, 2 March 2026
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	216edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with many mappings possible for the 13-limit. The following four will be discussed here: {{val\| 216 342 502 606 747 799 }} ([[patent val]]), {{val\| 216 '''343''' 502 '''607''' '''748''' '''800''' }} (216bdef), {{val\| 216 342 '''501''' 606 747 799 }} (216c), and {{val\| 216 342 502 '''607''' 747 799 }} (216d).		216edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with many mappings possible for the 13-limit. The following four will be discussed here: {{val\| 216 342 502 606 747 799 }} ([[patent val]]), {{val\| 216 '''343''' 502 '''607''' '''748''' '''800''' }} (216bdef), {{val\| 216 342 '''501''' 606 747 799 }} (216c), and {{val\| 216 342 502 '''607''' 747 799 }} (216d).

	The 216c val is [[Enfactoring\|enfactored]] in the 11-limit, and it happens to be of the best accuracy. Like 72, it [[Tempering out\|tempers out]] [[15625/15552]] and [[531441/524288]] in the 5-limit; [[225/224]], [[1029/1024]], and [[4375/4374]] in the 7-limit; [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]] in the 11-limit. However, it tempers out [[2200/2197]] and 2205/2197 in the 13-limit, and ~~practically corrects the approximate~~ [[13/1\|13th harmonic]] ~~to as fit as it can be~~.		The 216c val is [[Enfactoring\|enfactored]] in the 11-limit, and it happens to be of the best accuracy. Like [[72edo\|72]], it [[Tempering out\|tempers out]] [[15625/15552]] and [[531441/524288]] in the 5-limit; [[225/224]], [[1029/1024]], and [[4375/4374]] in the 7-limit; [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]] in the 11-limit. However, unlike 72, it tempers out [[2200/2197]] and 2205/2197 in the 13-limit, and is an good correction from 72edo's flat [[13/1\|13th harmonic]]. This val supports [[phicordial]], a [[weak extension]] of [[miracle]].

	The 216bdef val chooses the sharp mapping for each of the harmonics, so it is the opposite of 216c in terms of tuning. It tempers out [[2048/2025]] and {{monzo\| 1 -46 31 }} in the 5-limit; [[3136/3125]], [[4000/3969]], and 40353607/39858075 in the 7-limit; [[2560/2541]], [[3025/3024]], [[3388/3375]], and 12005/11979 in the 11-limit; [[325/324]], [[364/363]], [[640/637]], and [[1716/1715]] in the 13-limit.		The 216bdef val chooses the sharp mapping for each of the harmonics, so it is the opposite of 216c in terms of tuning. It tempers out [[2048/2025]] and {{monzo\| 1 -46 31 }} in the 5-limit; [[3136/3125]], [[4000/3969]], and 40353607/39858075 in the 7-limit; [[2560/2541]], [[3025/3024]], [[3388/3375]], and 12005/11979 in the 11-limit; [[325/324]], [[364/363]], [[640/637]], and [[1716/1715]] in the 13-limit.

ArrowHead294 at 19:28, 20 February 2025

2025-02-20T19:28:21Z

← Older revision		Revision as of 19:28, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|216~~}}		{{ED intro}}

	216edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with many mappings possible for the 13-limit. The following four will be discussed here: {{val\| 216 342 502 606 747 799 }} ([[patent val]]), {{val\| 216 '''343''' 502 '''607''' '''748''' '''800''' }} (216bdef), {{val\| 216 342 '''501''' 606 747 799 }} (216c), and {{val\| 216 342 502 '''607''' 747 799 }} (216d).		216edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with many mappings possible for the 13-limit. The following four will be discussed here: {{val\| 216 342 502 606 747 799 }} ([[patent val]]), {{val\| 216 '''343''' 502 '''607''' '''748''' '''800''' }} (216bdef), {{val\| 216 342 '''501''' 606 747 799 }} (216c), and {{val\| 216 342 502 '''607''' 747 799 }} (216d).

FloraC: Rework

2023-10-10T07:17:29Z

Rework

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''216edo''' is the [[EDO|equal division of the octave]] into 216 parts of 5.5556 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 13-limit: &lt;216 342 502 606 747 799| (patent val), &lt;216 343 502 607 748 800| (216bdef), &lt;216 342 501 606 747 799| (216c), and &lt;216 342 502 607 747 799| (216d). Using the patent val, it tempers out 531441/524288 and 1990656/1953125 in the 5-limit; 126/125, 1029/1024, and 118098/117649 in the 7-limit; 243/242, 3388/3375, 41503/41472, and 43923/43904 in the 11-limit; 676/675, 847/845, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 216bdef val, it tempers out 2048/2025 and |1 -46 31&gt; in the 5-limit; 3136/3125, 4000/3969, and 40353607/39858075 in the 7-limit; 2560/2541, 3025/3024, 3388/3375, and 12005/11979 in the 11-limit; 325/324, 364/363, 640/637, and 1716/1715 in the 13-limit. Using the 216c val, it tempers out 15625/15552 and 531441/524288 in the 5-limit; 225/224, 1029/1024, and 4375/4374 in the 7-limit; 243/242, 385/384, 441/440, and 4000/3993 in the 11-limit; 2200/2197 and 2205/2197 in the 13-limit. Using the 216d val, it tempers out 2430/2401, 3136/3125, and 531441/524288 in the 7-limit; 176/175, 243/242, 1375/1372, and 131769/131072 in the 11-limit; 676/675, 1188/1183, 1287/1280, and 3042/3025 in the 13-limit.
+{{EDO intro|216}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with many mappings possible for the 13-limit. The following four will be discussed here: {{val| 216 342 502 606 747 799 }} ([[patent val]]), {{val| 216 '''343''' 502 '''607''' '''748''' '''800''' }} (216bdef), {{val| 216 342 '''501''' 606 747 799 }} (216c), and {{val| 216 342 502 '''607''' 747 799 }} (216d).

Plumtree: Infobox ET added

2022-10-04T21:23:14Z

Infobox ET added

← Older revision		Revision as of 21:23, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''216edo''' is the [[EDO\|equal division of the octave]] into 216 parts of 5.5556 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 13-limit: <216 342 502 606 747 799\| (patent val), <216 343 502 607 748 800\| (216bdef), <216 342 501 606 747 799\| (216c), and <216 342 502 607 747 799\| (216d). Using the patent val, it tempers out 531441/524288 and 1990656/1953125 in the 5-limit; 126/125, 1029/1024, and 118098/117649 in the 7-limit; 243/242, 3388/3375, 41503/41472, and 43923/43904 in the 11-limit; 676/675, 847/845, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 216bdef val, it tempers out 2048/2025 and \|1 -46 31> in the 5-limit; 3136/3125, 4000/3969, and 40353607/39858075 in the 7-limit; 2560/2541, 3025/3024, 3388/3375, and 12005/11979 in the 11-limit; 325/324, 364/363, 640/637, and 1716/1715 in the 13-limit. Using the 216c val, it tempers out 15625/15552 and 531441/524288 in the 5-limit; 225/224, 1029/1024, and 4375/4374 in the 7-limit; 243/242, 385/384, 441/440, and 4000/3993 in the 11-limit; 2200/2197 and 2205/2197 in the 13-limit. Using the 216d val, it tempers out 2430/2401, 3136/3125, and 531441/524288 in the 7-limit; 176/175, 243/242, 1375/1372, and 131769/131072 in the 11-limit; 676/675, 1188/1183, 1287/1280, and 3042/3025 in the 13-limit.		'''216edo''' is the [[EDO\|equal division of the octave]] into 216 parts of 5.5556 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 13-limit: <216 342 502 606 747 799\| (patent val), <216 343 502 607 748 800\| (216bdef), <216 342 501 606 747 799\| (216c), and <216 342 502 607 747 799\| (216d). Using the patent val, it tempers out 531441/524288 and 1990656/1953125 in the 5-limit; 126/125, 1029/1024, and 118098/117649 in the 7-limit; 243/242, 3388/3375, 41503/41472, and 43923/43904 in the 11-limit; 676/675, 847/845, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 216bdef val, it tempers out 2048/2025 and \|1 -46 31> in the 5-limit; 3136/3125, 4000/3969, and 40353607/39858075 in the 7-limit; 2560/2541, 3025/3024, 3388/3375, and 12005/11979 in the 11-limit; 325/324, 364/363, 640/637, and 1716/1715 in the 13-limit. Using the 216c val, it tempers out 15625/15552 and 531441/524288 in the 5-limit; 225/224, 1029/1024, and 4375/4374 in the 7-limit; 243/242, 385/384, 441/440, and 4000/3993 in the 11-limit; 2200/2197 and 2205/2197 in the 13-limit. Using the 216d val, it tempers out 2430/2401, 3136/3125, and 531441/524288 in the 7-limit; 176/175, 243/242, 1375/1372, and 131769/131072 in the 11-limit; 676/675, 1188/1183, 1287/1280, and 3042/3025 in the 13-limit.

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

Fredg999 category edits: Sort key

2022-07-03T18:33:51Z

Sort key

← Older revision		Revision as of 18:33, 3 July 2022
Line 1:		Line 1:
	'''216edo''' is the [[EDO\|equal division of the octave]] into 216 parts of 5.5556 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 13-limit: <216 342 502 606 747 799\| (patent val), <216 343 502 607 748 800\| (216bdef), <216 342 501 606 747 799\| (216c), and <216 342 502 607 747 799\| (216d). Using the patent val, it tempers out 531441/524288 and 1990656/1953125 in the 5-limit; 126/125, 1029/1024, and 118098/117649 in the 7-limit; 243/242, 3388/3375, 41503/41472, and 43923/43904 in the 11-limit; 676/675, 847/845, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 216bdef val, it tempers out 2048/2025 and \|1 -46 31> in the 5-limit; 3136/3125, 4000/3969, and 40353607/39858075 in the 7-limit; 2560/2541, 3025/3024, 3388/3375, and 12005/11979 in the 11-limit; 325/324, 364/363, 640/637, and 1716/1715 in the 13-limit. Using the 216c val, it tempers out 15625/15552 and 531441/524288 in the 5-limit; 225/224, 1029/1024, and 4375/4374 in the 7-limit; 243/242, 385/384, 441/440, and 4000/3993 in the 11-limit; 2200/2197 and 2205/2197 in the 13-limit. Using the 216d val, it tempers out 2430/2401, 3136/3125, and 531441/524288 in the 7-limit; 176/175, 243/242, 1375/1372, and 131769/131072 in the 11-limit; 676/675, 1188/1183, 1287/1280, and 3042/3025 in the 13-limit.		'''216edo''' is the [[EDO\|equal division of the octave]] into 216 parts of 5.5556 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 13-limit: <216 342 502 606 747 799\| (patent val), <216 343 502 607 748 800\| (216bdef), <216 342 501 606 747 799\| (216c), and <216 342 502 607 747 799\| (216d). Using the patent val, it tempers out 531441/524288 and 1990656/1953125 in the 5-limit; 126/125, 1029/1024, and 118098/117649 in the 7-limit; 243/242, 3388/3375, 41503/41472, and 43923/43904 in the 11-limit; 676/675, 847/845, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 216bdef val, it tempers out 2048/2025 and \|1 -46 31> in the 5-limit; 3136/3125, 4000/3969, and 40353607/39858075 in the 7-limit; 2560/2541, 3025/3024, 3388/3375, and 12005/11979 in the 11-limit; 325/324, 364/363, 640/637, and 1716/1715 in the 13-limit. Using the 216c val, it tempers out 15625/15552 and 531441/524288 in the 5-limit; 225/224, 1029/1024, and 4375/4374 in the 7-limit; 243/242, 385/384, 441/440, and 4000/3993 in the 11-limit; 2200/2197 and 2205/2197 in the 13-limit. Using the 216d val, it tempers out 2430/2401, 3136/3125, and 531441/524288 in the 7-limit; 176/175, 243/242, 1375/1372, and 131769/131072 in the 11-limit; 676/675, 1188/1183, 1287/1280, and 3042/3025 in the 13-limit.

	[[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
Line 1:		Line 1:
	'''216edo''' is the [[EDO\|equal division of the octave]] into 216 parts of 5.5556 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 13-limit: <216 342 502 606 747 799\| (patent val), <216 343 502 607 748 800\| (216bdef), <216 342 501 606 747 799\| (216c), and <216 342 502 607 747 799\| (216d). Using the patent val, it tempers out 531441/524288 and 1990656/1953125 in the 5-limit; 126/125, 1029/1024, and 118098/117649 in the 7-limit; 243/242, 3388/3375, 41503/41472, and 43923/43904 in the 11-limit; 676/675, 847/845, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 216bdef val, it tempers out 2048/2025 and \|1 -46 31> in the 5-limit; 3136/3125, 4000/3969, and 40353607/39858075 in the 7-limit; 2560/2541, 3025/3024, 3388/3375, and 12005/11979 in the 11-limit; 325/324, 364/363, 640/637, and 1716/1715 in the 13-limit. Using the 216c val, it tempers out 15625/15552 and 531441/524288 in the 5-limit; 225/224, 1029/1024, and 4375/4374 in the 7-limit; 243/242, 385/384, 441/440, and 4000/3993 in the 11-limit; 2200/2197 and 2205/2197 in the 13-limit. Using the 216d val, it tempers out 2430/2401, 3136/3125, and 531441/524288 in the 7-limit; 176/175, 243/242, 1375/1372, and 131769/131072 in the 11-limit; 676/675, 1188/1183, 1287/1280, and 3042/3025 in the 13-limit.		'''216edo''' is the [[EDO\|equal division of the octave]] into 216 parts of 5.5556 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 13-limit: <216 342 502 606 747 799\| (patent val), <216 343 502 607 748 800\| (216bdef), <216 342 501 606 747 799\| (216c), and <216 342 502 607 747 799\| (216d). Using the patent val, it tempers out 531441/524288 and 1990656/1953125 in the 5-limit; 126/125, 1029/1024, and 118098/117649 in the 7-limit; 243/242, 3388/3375, 41503/41472, and 43923/43904 in the 11-limit; 676/675, 847/845, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 216bdef val, it tempers out 2048/2025 and \|1 -46 31> in the 5-limit; 3136/3125, 4000/3969, and 40353607/39858075 in the 7-limit; 2560/2541, 3025/3024, 3388/3375, and 12005/11979 in the 11-limit; 325/324, 364/363, 640/637, and 1716/1715 in the 13-limit. Using the 216c val, it tempers out 15625/15552 and 531441/524288 in the 5-limit; 225/224, 1029/1024, and 4375/4374 in the 7-limit; 243/242, 385/384, 441/440, and 4000/3993 in the 11-limit; 2200/2197 and 2205/2197 in the 13-limit. Using the 216d val, it tempers out 2430/2401, 3136/3125, and 531441/524288 in the 7-limit; 176/175, 243/242, 1375/1372, and 131769/131072 in the 11-limit; 676/675, 1188/1183, 1287/1280, and 3042/3025 in the 13-limit.

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

Xenllium: Created page with "'''216edo''' is the equal division of the octave into 216 parts of 5.5556 cents each. It is inconsistent to the 5-limit and higher limit, with four mappings possib..."

2019-03-11T00:24:58Z

Created page with "'''216edo''' is the equal division of the octave into 216 parts of 5.5556 cents each. It is inconsistent to the 5-limit and higher limit, with four mappings possib..."

New page

'''216edo''' is the [[EDO|equal division of the octave]] into 216 parts of 5.5556 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 13-limit: <216 342 502 606 747 799| (patent val), <216 343 502 607 748 800| (216bdef), <216 342 501 606 747 799| (216c), and <216 342 502 607 747 799| (216d). Using the patent val, it tempers out 531441/524288 and 1990656/1953125 in the 5-limit; 126/125, 1029/1024, and 118098/117649 in the 7-limit; 243/242, 3388/3375, 41503/41472, and 43923/43904 in the 11-limit; 676/675, 847/845, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 216bdef val, it tempers out 2048/2025 and |1 -46 31> in the 5-limit; 3136/3125, 4000/3969, and 40353607/39858075 in the 7-limit; 2560/2541, 3025/3024, 3388/3375, and 12005/11979 in the 11-limit; 325/324, 364/363, 640/637, and 1716/1715 in the 13-limit. Using the 216c val, it tempers out 15625/15552 and 531441/524288 in the 5-limit; 225/224, 1029/1024, and 4375/4374 in the 7-limit; 243/242, 385/384, 441/440, and 4000/3993 in the 11-limit; 2200/2197 and 2205/2197 in the 13-limit. Using the 216d val, it tempers out 2430/2401, 3136/3125, and 531441/524288 in the 7-limit; 176/175, 243/242, 1375/1372, and 131769/131072 in the 11-limit; 676/675, 1188/1183, 1287/1280, and 3042/3025 in the 13-limit.

[[Category:Edo]]

← Older revision		Revision as of 19:10, 2 March 2026
Line 4:		Line 4:
	216edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with many mappings possible for the 13-limit. The following four will be discussed here: {{val\| 216 342 502 606 747 799 }} ([[patent val]]), {{val\| 216 '''343''' 502 '''607''' '''748''' '''800''' }} (216bdef), {{val\| 216 342 '''501''' 606 747 799 }} (216c), and {{val\| 216 342 502 '''607''' 747 799 }} (216d).		216edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with many mappings possible for the 13-limit. The following four will be discussed here: {{val\| 216 342 502 606 747 799 }} ([[patent val]]), {{val\| 216 '''343''' 502 '''607''' '''748''' '''800''' }} (216bdef), {{val\| 216 342 '''501''' 606 747 799 }} (216c), and {{val\| 216 342 502 '''607''' 747 799 }} (216d).

	The 216c val is [[Enfactoring\|enfactored]] in the 11-limit, and it happens to be of the best accuracy. Like 72, it [[Tempering out\|tempers out]] [[15625/15552]] and [[531441/524288]] in the 5-limit; [[225/224]], [[1029/1024]], and [[4375/4374]] in the 7-limit; [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]] in the 11-limit. However, it tempers out [[2200/2197]] and 2205/2197 in the 13-limit, and ~~practically corrects the approximate~~ [[13/1\|13th harmonic]] ~~to as fit as it can be~~.		The 216c val is [[Enfactoring\|enfactored]] in the 11-limit, and it happens to be of the best accuracy. Like [[72edo\|72]], it [[Tempering out\|tempers out]] [[15625/15552]] and [[531441/524288]] in the 5-limit; [[225/224]], [[1029/1024]], and [[4375/4374]] in the 7-limit; [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]] in the 11-limit. However, unlike 72, it tempers out [[2200/2197]] and 2205/2197 in the 13-limit, and is an good correction from 72edo's flat [[13/1\|13th harmonic]]. This val supports [[phicordial]], a [[weak extension]] of [[miracle]].

	The 216bdef val chooses the sharp mapping for each of the harmonics, so it is the opposite of 216c in terms of tuning. It tempers out [[2048/2025]] and {{monzo\| 1 -46 31 }} in the 5-limit; [[3136/3125]], [[4000/3969]], and 40353607/39858075 in the 7-limit; [[2560/2541]], [[3025/3024]], [[3388/3375]], and 12005/11979 in the 11-limit; [[325/324]], [[364/363]], [[640/637]], and [[1716/1715]] in the 13-limit.		The 216bdef val chooses the sharp mapping for each of the harmonics, so it is the opposite of 216c in terms of tuning. It tempers out [[2048/2025]] and {{monzo\| 1 -46 31 }} in the 5-limit; [[3136/3125]], [[4000/3969]], and 40353607/39858075 in the 7-limit; [[2560/2541]], [[3025/3024]], [[3388/3375]], and 12005/11979 in the 11-limit; [[325/324]], [[364/363]], [[640/637]], and [[1716/1715]] in the 13-limit.