196edo - Revision history

ArrowHead294 at 19:30, 20 February 2025

2025-02-20T19:30:41Z

← Older revision		Revision as of 19:30, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

BudjarnLambeth: Moved table to seperate page because it slowed loading time a fair amount

2024-10-02T07:04:48Z

Moved table to seperate page because it slowed loading time a fair amount

← Older revision		Revision as of 07:04, 2 October 2024
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	== Intervals ==		== Intervals ==
	~~{{Interval table}}~~		See: [[Table of 196edo intervals]]

FloraC: +subsets and supersets

2024-04-15T13:37:03Z

+subsets and supersets

← Older revision		Revision as of 13:37, 15 April 2024
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|196}}		{{Harmonics in equal\|196}}

			=== Subsets and supersets ===
			Since 196 factors into {{factorization\|196}}, 196edo has subset edos {{EDOs\| 2, 4, 7, 14, 28, 49, and 98 }}.

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

FloraC: Review

2024-04-15T13:35:30Z

Review

← Older revision		Revision as of 13:35, 15 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''196edo''' is the [[~~EDO\|equal division of the octave]] into 196 parts of 6.1224 cents each. It tempers out 9765625/9565938 (fifive comma) and 4294967296/4271484375 (escapade comma) in the 5-limit. Using the patent val, it tempers out 245/243, 65625/65536, and 235298/234375 in the 7-limit; 385/384, 896/891, 3388/3375, and 117649/117128 in the 11-limit; 352/351, 364/363, 625/624, 1001/1000, and 9295/9261 in the 13-limit; 289/288, 442/441, 715/714, and 1156/1155 in the 17-limit.		{{EDO intro}}

	~~196edo can also treated as a 2.5.~~7.9~~.11.13.17 subgroup temperament~~ (~~with~~ the ~~patent 9), providing a distinct flat tendency for harmonics~~ 5~~, 7, 9, 11, 13, and 17~~. ~~With~~ the patent 9, it tempers out ~~321489~~/~~320000~~, ~~420175~~/~~419904~~, and ~~703125~~/~~702464~~ in the ~~2.5.~~7~~.9 subgroup~~; ~~441~~/~~440~~, ~~8019~~/~~8000~~, ~~41503~~/~~41472~~, and ~~9453125~~/~~9437184~~ in the ~~2.5.7.9.~~11 ~~subgroup~~; ~~729~~/~~728~~, ~~1001~~/~~1000~~, ~~1575~~/~~1573~~, ~~6656~~/~~6655~~, and ~~10985~~/~~10976~~ in the ~~2.5.7.9.11.~~13 ~~subgroup~~; ~~833~~/~~832~~, ~~936~~/~~935, 1089/1088~~, ~~1225~~/~~1224, 2025/2023~~, and ~~14365~~/~~14336~~ in the ~~2.5.7.9.11.13.~~17 ~~subgroup~~.		== Theory ==
			The equal temperament [[tempering out\|tempers out]] 9765625/9565938 (fifive comma) and {{monzo\| 32 -7 -9 }} ([[escapade comma]]) in the 5-limit. Using the [[patent val]], it tempers out [[245/243]], [[65625/65536]], and 235298/234375 in the 7-limit; [[385/384]], [[896/891]], [[3388/3375]], and 117649/117128 in the 11-limit; [[352/351]], [[364/363]], [[625/624]], [[1001/1000]], and 9295/9261 in the 13-limit; [[289/288]], [[442/441]], [[715/714]], and [[1156/1155]] in the 17-limit.

	~~Since~~ it~~'s part of~~ the ~~Fibonacci sequence beginning with~~ 5 and 12, ~~it closely approximates~~ [[~~peppermint~~]] ~~temperament~~.		196edo can also treated as a 2.9.5.7.11.13.17 [[subgroup]] temperament (with the patent 9), providing a distinct flat tendency for [[harmonic]]s [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[13/1\|13]], and [[17/1\|17]]. With the patent 9, it tempers out 321489/320000, [[420175/419904]], and [[703125/702464]] in the 2.9.5.7 subgroup; [[441/440]], [[8019/8000]], [[41503/41472]], and 9453125/9437184 in the 2.9.5.7.11 subgroup; [[729/728]], [[1001/1000]], [[1575/1573]], [[6656/6655]], and [[10985/10976]] in the 2.9.5.7.11.13 subgroup; [[833/832]], [[936/935]], [[1089/1088]], [[1225/1224]], [[2025/2023]], and 14365/14336 in the 2.9.5.7.11.13.17 subgroup.

	== ~~Harmonics~~ ==		Since it is part of the Fibonacci sequence beginning with 5 and 12, it closely approximates [[peppermint]] temperament.

			=== Odd harmonics ===
	{{Harmonics in equal\|196}}		{{Harmonics in equal\|196}}

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

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

BudjarnLambeth: Added link to “peppermint”, added harmonics table, added interval table

2024-01-21T07:37:55Z

Added link to “peppermint”, added harmonics table, added interval table

← Older revision		Revision as of 07:37, 21 January 2024
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	196edo can also treated as a 2.5.7.9.11.13.17 subgroup temperament (with the patent 9), providing a distinct flat tendency for harmonics 5, 7, 9, 11, 13, and 17. With the patent 9, it tempers out 321489/320000, 420175/419904, and 703125/702464 in the 2.5.7.9 subgroup; 441/440, 8019/8000, 41503/41472, and 9453125/9437184 in the 2.5.7.9.11 subgroup; 729/728, 1001/1000, 1575/1573, 6656/6655, and 10985/10976 in the 2.5.7.9.11.13 subgroup; 833/832, 936/935, 1089/1088, 1225/1224, 2025/2023, and 14365/14336 in the 2.5.7.9.11.13.17 subgroup.		196edo can also treated as a 2.5.7.9.11.13.17 subgroup temperament (with the patent 9), providing a distinct flat tendency for harmonics 5, 7, 9, 11, 13, and 17. With the patent 9, it tempers out 321489/320000, 420175/419904, and 703125/702464 in the 2.5.7.9 subgroup; 441/440, 8019/8000, 41503/41472, and 9453125/9437184 in the 2.5.7.9.11 subgroup; 729/728, 1001/1000, 1575/1573, 6656/6655, and 10985/10976 in the 2.5.7.9.11.13 subgroup; 833/832, 936/935, 1089/1088, 1225/1224, 2025/2023, and 14365/14336 in the 2.5.7.9.11.13.17 subgroup.

	Since it's part of the Fibonacci sequence beginning with 5 and 12, it closely approximates peppermint temperament.		Since it's part of the Fibonacci sequence beginning with 5 and 12, it closely approximates [[peppermint]] temperament.

			== Harmonics ==
			{{Harmonics in equal\|196}}

			== Intervals ==
			{{Interval table}}

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

Plumtree: Infobox ET added

2022-10-04T21:18:29Z

Infobox ET added

← Older revision		Revision as of 21:18, 4 October 2022
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			{{Infobox ET}}
	'''196edo''' is the [[EDO\|equal division of the octave]] into 196 parts of 6.1224 cents each. It tempers out 9765625/9565938 (fifive comma) and 4294967296/4271484375 (escapade comma) in the 5-limit. Using the patent val, it tempers out 245/243, 65625/65536, and 235298/234375 in the 7-limit; 385/384, 896/891, 3388/3375, and 117649/117128 in the 11-limit; 352/351, 364/363, 625/624, 1001/1000, and 9295/9261 in the 13-limit; 289/288, 442/441, 715/714, and 1156/1155 in the 17-limit.		'''196edo''' is the [[EDO\|equal division of the octave]] into 196 parts of 6.1224 cents each. It tempers out 9765625/9565938 (fifive comma) and 4294967296/4271484375 (escapade comma) in the 5-limit. Using the patent val, it tempers out 245/243, 65625/65536, and 235298/234375 in the 7-limit; 385/384, 896/891, 3388/3375, and 117649/117128 in the 11-limit; 352/351, 364/363, 625/624, 1001/1000, and 9295/9261 in the 13-limit; 289/288, 442/441, 715/714, and 1156/1155 in the 17-limit.

Fredg999 category edits: Sort key

2022-07-02T21:24:46Z

Sort key

← Older revision		Revision as of 21:24, 2 July 2022
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	Since it's part of the Fibonacci sequence beginning with 5 and 12, it closely approximates peppermint temperament.		Since it's part of the Fibonacci sequence beginning with 5 and 12, it closely approximates peppermint temperament.

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

AthiTrydhen at 00:42, 22 April 2022

2022-04-22T00:42:41Z

← Older revision		Revision as of 00:42, 22 April 2022
Line 2:		Line 2:

	196edo can also treated as a 2.5.7.9.11.13.17 subgroup temperament (with the patent 9), providing a distinct flat tendency for harmonics 5, 7, 9, 11, 13, and 17. With the patent 9, it tempers out 321489/320000, 420175/419904, and 703125/702464 in the 2.5.7.9 subgroup; 441/440, 8019/8000, 41503/41472, and 9453125/9437184 in the 2.5.7.9.11 subgroup; 729/728, 1001/1000, 1575/1573, 6656/6655, and 10985/10976 in the 2.5.7.9.11.13 subgroup; 833/832, 936/935, 1089/1088, 1225/1224, 2025/2023, and 14365/14336 in the 2.5.7.9.11.13.17 subgroup.		196edo can also treated as a 2.5.7.9.11.13.17 subgroup temperament (with the patent 9), providing a distinct flat tendency for harmonics 5, 7, 9, 11, 13, and 17. With the patent 9, it tempers out 321489/320000, 420175/419904, and 703125/702464 in the 2.5.7.9 subgroup; 441/440, 8019/8000, 41503/41472, and 9453125/9437184 in the 2.5.7.9.11 subgroup; 729/728, 1001/1000, 1575/1573, 6656/6655, and 10985/10976 in the 2.5.7.9.11.13 subgroup; 833/832, 936/935, 1089/1088, 1225/1224, 2025/2023, and 14365/14336 in the 2.5.7.9.11.13.17 subgroup.

			Since it's part of the Fibonacci sequence beginning with 5 and 12, it closely approximates peppermint temperament.

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

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

2020-12-04T23:13:15Z

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 3:		Line 3:
	196edo can also treated as a 2.5.7.9.11.13.17 subgroup temperament (with the patent 9), providing a distinct flat tendency for harmonics 5, 7, 9, 11, 13, and 17. With the patent 9, it tempers out 321489/320000, 420175/419904, and 703125/702464 in the 2.5.7.9 subgroup; 441/440, 8019/8000, 41503/41472, and 9453125/9437184 in the 2.5.7.9.11 subgroup; 729/728, 1001/1000, 1575/1573, 6656/6655, and 10985/10976 in the 2.5.7.9.11.13 subgroup; 833/832, 936/935, 1089/1088, 1225/1224, 2025/2023, and 14365/14336 in the 2.5.7.9.11.13.17 subgroup.		196edo can also treated as a 2.5.7.9.11.13.17 subgroup temperament (with the patent 9), providing a distinct flat tendency for harmonics 5, 7, 9, 11, 13, and 17. With the patent 9, it tempers out 321489/320000, 420175/419904, and 703125/702464 in the 2.5.7.9 subgroup; 441/440, 8019/8000, 41503/41472, and 9453125/9437184 in the 2.5.7.9.11 subgroup; 729/728, 1001/1000, 1575/1573, 6656/6655, and 10985/10976 in the 2.5.7.9.11.13 subgroup; 833/832, 936/935, 1089/1088, 1225/1224, 2025/2023, and 14365/14336 in the 2.5.7.9.11.13.17 subgroup.

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

Xenllium at 08:02, 16 March 2019

2019-03-16T08:02:34Z

← Older revision		Revision as of 08:02, 16 March 2019
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	'''196edo''' is the [[EDO\|equal division of the octave]] into 196 parts of 6.1224 cents each. It tempers out 9765625/9565938 (fifive comma) and 4294967296/4271484375 (escapade comma) in the 5-limit. Using the patent val, it tempers out 245/243, 65625/65536, and 235298/234375 in the 7-limit; 385/384, 896/891, 3388/3375, and 117649/117128 in the 11-limit; 352/351, 364/363, 625/624, 1001/1000, and 9295/9261 in the 13-limit; 289/288, 442/441, 715/714, and 1156/1155 in the 17-limit.		'''196edo''' is the [[EDO\|equal division of the octave]] into 196 parts of 6.1224 cents each. It tempers out 9765625/9565938 (fifive comma) and 4294967296/4271484375 (escapade comma) in the 5-limit. Using the patent val, it tempers out 245/243, 65625/65536, and 235298/234375 in the 7-limit; 385/384, 896/891, 3388/3375, and 117649/117128 in the 11-limit; 352/351, 364/363, 625/624, 1001/1000, and 9295/9261 in the 13-limit; 289/288, 442/441, 715/714, and 1156/1155 in the 17-limit.

			196edo can also treated as a 2.5.7.9.11.13.17 subgroup temperament (with the patent 9), providing a distinct flat tendency for harmonics 5, 7, 9, 11, 13, and 17. With the patent 9, it tempers out 321489/320000, 420175/419904, and 703125/702464 in the 2.5.7.9 subgroup; 441/440, 8019/8000, 41503/41472, and 9453125/9437184 in the 2.5.7.9.11 subgroup; 729/728, 1001/1000, 1575/1573, 6656/6655, and 10985/10976 in the 2.5.7.9.11.13 subgroup; 833/832, 936/935, 1089/1088, 1225/1224, 2025/2023, and 14365/14336 in the 2.5.7.9.11.13.17 subgroup.

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