146edo - Revision history

ArrowHead294 at 17:59, 20 February 2025

2025-02-20T17:59:05Z

← Older revision		Revision as of 17:59, 20 February 2025
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	{{ED intro}}		{{ED intro}}

	146edo has an accurate [[harmonic]] [[5/1\|5]], only 0.012344 ~~cents compressed~~ from just. 146 is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. Combined with fairly accurate approximations of [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], it commends itself as a 2.9.5.7.11.13.17.19 [[subgroup]] system.		146edo has an accurate [[harmonic]] [[5/1\|5]], compressed by only 0.012344{{c}} from just. 146 is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. Combined with fairly accurate approximations of [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], it commends itself as a 2.9.5.7.11.13.17.19 [[subgroup]] system.

	However, it also provides the [[optimal patent val]] for the 11-limit [[newspeak]] temperament. Using the [[patent val]], it [[tempering out\|tempers out]] the 2109375/2097152 ([[semicomma]]), and {{monzo\| -6 17 -9 }} in the 5-limit; [[225/224]], [[1728/1715]], and 100442349/97656250 in the 7-limit; [[441/440]], 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; [[1001/1000]], [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit.		However, it also provides the [[optimal patent val]] for the 11-limit [[newspeak]] temperament. Using the [[patent val]], it [[tempering out\|tempers out]] the 2109375/2097152 ([[semicomma]]), and {{monzo\| -6 17 -9 }} in the 5-limit; [[225/224]], [[1728/1715]], and 100442349/97656250 in the 7-limit; [[441/440]], 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; [[1001/1000]], [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit.

Francium: changed EDO intro to ED intro

2025-02-19T17:57:51Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:57, 19 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	146edo has an accurate [[harmonic]] [[5/1\|5]], only 0.012344 cents compressed from just. 146 is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. Combined with fairly accurate approximations of [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], it commends itself as a 2.9.5.7.11.13.17.19 [[subgroup]] system.		146edo has an accurate [[harmonic]] [[5/1\|5]], only 0.012344 cents compressed from just. 146 is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. Combined with fairly accurate approximations of [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], it commends itself as a 2.9.5.7.11.13.17.19 [[subgroup]] system.

FloraC: Clarify (major third -> harmonic 5)

2024-05-18T15:05:36Z

Clarify (major third -> harmonic 5)

← Older revision		Revision as of 15:05, 18 May 2024
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	{{EDO intro}}		{{EDO intro}}

	146edo has an accurate ~~major third~~, only 0.012344 cents compressed from just ~~[[5/4]] interval~~. ~~146edo~~ is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. Combined with fairly accurate approximations of [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], it commends itself as a 2.9.5.7.11.13.17.19 [[subgroup]] system.		146edo has an accurate [[harmonic]] [[5/1\|5]], only 0.012344 cents compressed from just. 146 is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. Combined with fairly accurate approximations of [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], it commends itself as a 2.9.5.7.11.13.17.19 [[subgroup]] system.

	However, it also provides the [[optimal patent val]] for the 11-limit [[newspeak]] temperament. Using the [[patent val]], it [[tempering out\|tempers out]] the 2109375/2097152 ([[semicomma]]), and {{monzo\| -6 17 -9 }} in the 5-limit; [[225/224]], [[1728/1715]], and 100442349/97656250 in the 7-limit; [[441/440]], 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; [[1001/1000]], [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit.		However, it also provides the [[optimal patent val]] for the 11-limit [[newspeak]] temperament. Using the [[patent val]], it [[tempering out\|tempers out]] the 2109375/2097152 ([[semicomma]]), and {{monzo\| -6 17 -9 }} in the 5-limit; [[225/224]], [[1728/1715]], and 100442349/97656250 in the 7-limit; [[441/440]], 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; [[1001/1000]], [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit.

FloraC: Subgroup interpretation

2024-05-18T15:04:14Z

Subgroup interpretation

← Older revision		Revision as of 15:04, 18 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro}} 146edo has an accurate major third, only 0.012344 cents compressed from just [[5/4]] interval. 146edo is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]].		{{EDO intro}}

	However, it also provides the [[optimal patent val]] for the 11-limit [[newspeak]] temperament. It tempers out the 2109375/2097152 ([[semicomma]]), and {{monzo\| -6 17 -9 }} in the 5-limit; [[225/224]], [[1728/1715]], and 100442349/97656250 in the 7-limit; [[441/440]], 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; [[1001/1000]], [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit.		146edo has an accurate major third, only 0.012344 cents compressed from just [[5/4]] interval. 146edo is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. Combined with fairly accurate approximations of [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], it commends itself as a 2.9.5.7.11.13.17.19 [[subgroup]] system.

			However, it also provides the [[optimal patent val]] for the 11-limit [[newspeak]] temperament. Using the [[patent val]], it [[tempering out\|tempers out]] the 2109375/2097152 ([[semicomma]]), and {{monzo\| -6 17 -9 }} in the 5-limit; [[225/224]], [[1728/1715]], and 100442349/97656250 in the 7-limit; [[441/440]], 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; [[1001/1000]], [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit.

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories; misc. cleanup

2024-05-18T15:00:57Z

Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories; misc. cleanup

← Older revision		Revision as of 15:00, 18 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~146edo~~''' divides the octave into 146 equal parts of 8.219178 [[cent]]s each. It~~ has an accurate major third, only 0.012344 cents compressed from just [[5/4]] interval. 146edo is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. However, it also provides the optimal patent val for the 11-limit [[Semicomma family\|newspeak temperament]]. It tempers out the [[semicomma]], 2109375/2097152 and 129140163/125000000 in the 5-limit; 225/224, 1728/1715, and 100442349/97656250 in the 7-limit; 441/440, 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit.		{{EDO intro}} 146edo has an accurate major third, only 0.012344 cents compressed from just [[5/4]] interval. 146edo is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]].

	[[~~Category:Equal divisions of~~ the ~~octave\|###~~]] <!-- 3-~~digit number~~ -->		However, it also provides the [[optimal patent val]] for the 11-limit [[newspeak]] temperament. It tempers out the 2109375/2097152 ([[semicomma]]), and {{monzo\| -6 17 -9 }} in the 5-limit; [[225/224]], [[1728/1715]], and 100442349/97656250 in the 7-limit; [[441/440]], 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; [[1001/1000]], [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit.

			=== Odd harmonics ===
			{{Harmonics in equal\|146}}

			=== Subsets and supersets ===
			Since 146 factors into {{factorization\|146}}, 146edo contains [[2edo]] and [[73edo]] as its subsets.

Aura at 19:07, 4 October 2022

2022-10-04T19:07:33Z

← Older revision		Revision as of 19:07, 4 October 2022
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			{{Infobox ET}}
	The '''146edo''' divides the octave into 146 equal parts of 8.219178 [[cent]]s each. It has an accurate major third, only 0.012344 cents compressed from just [[5/4]] interval. 146edo is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. However, it also provides the optimal patent val for the 11-limit [[Semicomma family\|newspeak temperament]]. It tempers out the [[semicomma]], 2109375/2097152 and 129140163/125000000 in the 5-limit; 225/224, 1728/1715, and 100442349/97656250 in the 7-limit; 441/440, 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit.		The '''146edo''' divides the octave into 146 equal parts of 8.219178 [[cent]]s each. It has an accurate major third, only 0.012344 cents compressed from just [[5/4]] interval. 146edo is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. However, it also provides the optimal patent val for the 11-limit [[Semicomma family\|newspeak temperament]]. It tempers out the [[semicomma]], 2109375/2097152 and 129140163/125000000 in the 5-limit; 225/224, 1728/1715, and 100442349/97656250 in the 7-limit; 441/440, 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 1573/1568 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

2022-07-02T21:07:27Z

Sort key

← Older revision		Revision as of 21:07, 2 July 2022
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	The '''~~146 edo~~''' divides the octave into 146 equal parts of 8.219178 [[cent]]s each. It has an accurate major third, only 0.012344 cents compressed from just [[5/4]] interval. 146edo is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. However, it also provides the optimal patent val for the 11-limit [[Semicomma family\|newspeak temperament]]. It tempers out the [[semicomma]], 2109375/2097152 and 129140163/125000000 in the 5-limit; 225/224, 1728/1715, and 100442349/97656250 in the 7-limit; 441/440, 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit.		The '''146edo''' divides the octave into 146 equal parts of 8.219178 [[cent]]s each. It has an accurate major third, only 0.012344 cents compressed from just [[5/4]] interval. 146edo is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. However, it also provides the optimal patent val for the 11-limit [[Semicomma family\|newspeak temperament]]. It tempers out the [[semicomma]], 2109375/2097152 and 129140163/125000000 in the 5-limit; 225/224, 1728/1715, and 100442349/97656250 in the 7-limit; 441/440, 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 1573/1568 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

2020-12-04T23:13:09Z

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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	The '''146 edo''' divides the octave into 146 equal parts of 8.219178 [[cent]]s each. It has an accurate major third, only 0.012344 cents compressed from just [[5/4]] interval. 146edo is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. However, it also provides the optimal patent val for the 11-limit [[Semicomma family\|newspeak temperament]]. It tempers out the [[semicomma]], 2109375/2097152 and 129140163/125000000 in the 5-limit; 225/224, 1728/1715, and 100442349/97656250 in the 7-limit; 441/440, 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit.		The '''146 edo''' divides the octave into 146 equal parts of 8.219178 [[cent]]s each. It has an accurate major third, only 0.012344 cents compressed from just [[5/4]] interval. 146edo is the denominator of a convergent to log<sub>2</sub>5, after [[3edo\|3]], [[28edo\|28]] and [[59edo\|59]], and before [[643edo\|643]]. However, it also provides the optimal patent val for the 11-limit [[Semicomma family\|newspeak temperament]]. It tempers out the [[semicomma]], 2109375/2097152 and 129140163/125000000 in the 5-limit; 225/224, 1728/1715, and 100442349/97656250 in the 7-limit; 441/440, 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit.

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

Xenllium: Created page with "The '''146 edo''' divides the octave into 146 equal parts of 8.219178 cents each. It has an accurate major third, only 0.012344 cents compressed from just 5/4 interval..."

2018-12-03T08:34:54Z

Created page with "The '''146 edo''' divides the octave into 146 equal parts of 8.219178 cents each. It has an accurate major third, only 0.012344 cents compressed from just 5/4 interval..."

New page

The '''146 edo''' divides the octave into 146 equal parts of 8.219178 [[cent]]s each. It has an accurate major third, only 0.012344 cents compressed from just [[5/4]] interval. 146edo is the denominator of a convergent to log<sub>2</sub>5, after [[3edo|3]], [[28edo|28]] and [[59edo|59]], and before [[643edo|643]]. However, it also provides the optimal patent val for the 11-limit [[Semicomma family|newspeak temperament]]. It tempers out the [[semicomma]], 2109375/2097152 and 129140163/125000000 in the 5-limit; 225/224, 1728/1715, and 100442349/97656250 in the 7-limit; 441/440, 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit.

[[Category:Edo]]