182edo - Revision history

BudjarnLambeth: /* Octave stretch */ replace my esoteric APS with an almost identical ed7

2025-09-17T10:51:10Z

Octave stretch: replace my esoteric APS with an almost identical ed7

← Older revision		Revision as of 10:51, 17 September 2025
Line 14:		Line 14:

	=== Octave stretch ===		=== Octave stretch ===
	182edo’s approximations of 3/1, 5/1, 7/1 and 13/1 are all improved by ~~the~~ [[~~Gallery of arithmetic pitch sequences#APS of tinas~~\|~~Argentina scale~~]] ~~(APS47tina)~~, a [[Octave stretch\|stretched-octave]] version of 182edo. The trade-off is a slightly worse 2/1 and 11/1.		182edo’s approximations of 3/1, 5/1, 7/1 and 13/1 are all improved by [[ed7\|510ed7]], a [[Octave stretch\|stretched-octave]] version of 182edo. The trade-off is a slightly worse 2/1 and 11/1.

	There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used ~~for this same purpose~~: 1199zpi, 1200zpi, 1201zpi, 1202zpi, 1203zpi, 1204zpi and 1205zpi.		There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used to improve some harmonics at the expense of others: 1199zpi, 1200zpi, 1201zpi, 1202zpi, 1203zpi, 1204zpi and 1205zpi.

	The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)\|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.		The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)\|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.

ArrowHead294 at 16:38, 20 February 2025

2025-02-20T16:38:28Z

← Older revision		Revision as of 16:38, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|182~~}}		{{ED intro}}

	182edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings suitable for the 11-limit: {{val\| 182 288 423 511 630 }} ([[patent val]]), {{val\| 182 289 423 511 630 }} (182b), and {{val\| 182 288 422 511 629 }} (182ce). It does have a potential as a 2.9.15.7.17.19 [[subgroup]] temperament.		182edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings suitable for the 11-limit: {{val\| 182 288 423 511 630 }} ([[patent val]]), {{val\| 182 289 423 511 630 }} (182b), and {{val\| 182 288 422 511 629 }} (182ce). It does have a potential as a 2.9.15.7.17.19 [[subgroup]] temperament.

BudjarnLambeth at 07:28, 13 December 2024

2024-12-13T07:28:10Z

← Older revision		Revision as of 07:28, 13 December 2024
Line 14:		Line 14:

	=== Octave stretch ===		=== Octave stretch ===
	~~182’s~~ approximations of 3/1, 5/1, 7/1 and 13/1 are all improved by the [[Gallery of arithmetic pitch sequences#APS of tinas\|Argentina scale]] (APS47tina), a [[Octave stretch\|stretched-octave]] version of 182edo. The trade-off is a slightly worse 2/1 and 11/1.		182edo’s approximations of 3/1, 5/1, 7/1 and 13/1 are all improved by the [[Gallery of arithmetic pitch sequences#APS of tinas\|Argentina scale]] (APS47tina), a [[Octave stretch\|stretched-octave]] version of 182edo. The trade-off is a slightly worse 2/1 and 11/1.

	There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used for this same purpose: 1199zpi, 1200zpi, 1201zpi, 1202zpi, 1203zpi, 1204zpi and 1205zpi.		There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used for this same purpose: 1199zpi, 1200zpi, 1201zpi, 1202zpi, 1203zpi, 1204zpi and 1205zpi.

BudjarnLambeth: Add section on octave stretch

2024-12-13T07:18:18Z

Add section on octave stretch

← Older revision		Revision as of 07:18, 13 December 2024
Line 12:		Line 12:
	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|182}}		{{Harmonics in equal\|182}}

			=== Octave stretch ===
			182’s approximations of 3/1, 5/1, 7/1 and 13/1 are all improved by the [[Gallery of arithmetic pitch sequences#APS of tinas\|Argentina scale]] (APS47tina), a [[Octave stretch\|stretched-octave]] version of 182edo. The trade-off is a slightly worse 2/1 and 11/1.

			There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used for this same purpose: 1199zpi, 1200zpi, 1201zpi, 1202zpi, 1203zpi, 1204zpi and 1205zpi.

			The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)\|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 182 factors into {{factorization\|182}}, 182edo has subset edos {{EDOs\| 2, 7, 13, 14, 26, and 91 }}.		Since 182 factors into {{factorization\|182}}, 182edo has subset edos {{EDOs\| 2, 7, 13, 14, 26, and 91 }}.

FloraC: +subsets and supersets

2024-04-25T09:10:41Z

+subsets and supersets

← Older revision		Revision as of 09:10, 25 April 2024
Line 2:		Line 2:
	{{EDO intro\|182}}		{{EDO intro\|182}}

	~~== Theory ==~~
	182edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings suitable for the 11-limit: {{val\| 182 288 423 511 630 }} ([[patent val]]), {{val\| 182 289 423 511 630 }} (182b), and {{val\| 182 288 422 511 629 }} (182ce). It does have a potential as a 2.9.15.7.17.19 [[subgroup]] temperament.		182edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings suitable for the 11-limit: {{val\| 182 288 423 511 630 }} ([[patent val]]), {{val\| 182 289 423 511 630 }} (182b), and {{val\| 182 288 422 511 629 }} (182ce). It does have a potential as a 2.9.15.7.17.19 [[subgroup]] temperament.

Line 13:		Line 12:
	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|182}}		{{Harmonics in equal\|182}}

			=== Subsets and supersets ===
			Since 182 factors into {{factorization\|182}}, 182edo has subset edos {{EDOs\| 2, 7, 13, 14, 26, and 91 }}.

FloraC: Rework

2024-04-25T09:09:08Z

Rework

← Older revision		Revision as of 09:09, 25 April 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|182}}		{{EDO intro\|182}}

	== Theory ==		== Theory ==
	182edo is ~~inconsistent~~ to the 5-limit and higher ~~limit~~, with three mappings suitable for the 11-limit: {{val\|182 288 423 511 630}} (patent val), {{val\|182 289 423 511 630}} (182b), and {{val\|182 288 422 511 629}} (182ce). It does have a potential as a 2.7.9.15.17.19 subgroup temperament.		182edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings suitable for the 11-limit: {{val\| 182 288 423 511 630 }} ([[patent val]]), {{val\| 182 289 423 511 630 }} (182b), and {{val\| 182 288 422 511 629 }} (182ce). It does have a potential as a 2.9.15.7.17.19 [[subgroup]] temperament.

	~~182edo (182bef~~ val~~) is a tuning for~~ the [[~~shrutar~~]] ~~temperament~~ in the 19-limit and [[~~petrtri~~]] in the 2.11/5.13~~/5 subgroup~~.		Using the patent val, it tempers out the mynic comma, 10077696/9765625 and {{monzo\| -27 20 -2 }} in the 5-limit; [[126/125]], [[1728/1715]], and {{monzo\| -28 18 1 -1 }} in the 7-limit; 2187/2156, 2835/2816, [[5632/5625]], and 14700/14641 in the 11-limit; [[364/363]], [[676/675]], [[1287/1280]], and 1701/1690 in the 13-limit. Using the 182f val, [[144/143]], [[847/845]], [[1001/1000]], and [[1716/1715]] are tempered out in the 13-limit.

	~~=== Odd harmonics ===~~		Using the 182ce val, it tempers out the kleisma, [[15625/15552]] and the [[python comma]], 43046721/41943040 in the 5-limit; [[2430/2401]], 33075/32768, and 78125/76832 in the 7-limit; [[243/242]], [[385/384]], 2420/2401, and [[6250/6237]] in the 11-limit; [[351/350]], [[1188/1183]], 1287/1280, [[1575/1573]], and 1625/1617 in the 13-limit.
	~~{{harmonics in equal\|182}}~~
	~~== Regular temperament properties ==~~
	~~=== Commas ===~~
	Using the ~~patent~~ val, it tempers out the ~~quinbigu comma~~, ~~10077696~~/~~9765625~~ and ~~3486784401~~/~~3355443200~~ in the 5-limit; ~~126~~/~~125~~, ~~1728~~/~~1715~~, and ~~1937102445~~/~~1879048192~~ in the 7-limit; ~~2187~~/~~2156~~, ~~2835~~/~~2816~~, ~~5632~~/~~5625~~, and ~~14700~~/~~14641~~ in the 11-limit; ~~364~~/~~363~~, ~~676~~/~~675~~, 1287/1280, and ~~1701~~/~~1690~~ in the 13-limit.

	Using the 182b val, it tempers out the [[~~Diaschismic family\|diaschisma]],~~ 2048/2025 and {{monzo\|-4 -37 27}}; in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit.		Using the 182b val, it tempers out the diaschisma, [[2048/2025]] and {{monzo\| -4 -37 27 }}; in the 5-limit; [[245/243]], [[6144/6125]], and 9882516/9765625 in the 7-limit; [[3025/3024]], 3773/3750, and [[4000/3993]] in the 11-limit. Using the 182bf val, [[196/195]], [[325/324]], 364/363, and 1001/1000 are tempered out in the 13-limit. The 182bef val supports the [[shrutar]] temperament in the 19-limit and [[petrtri]] in the 2.11/5.13/5 subgroup.

	Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family\|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit.		=== Odd harmonics ===
			{{Harmonics in equal\|182}}
	~~Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out~~ in ~~the 13-limit.~~

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

Eliora: Complete, cleanup

2023-09-15T22:44:45Z

Complete, cleanup

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''182edo''' is the [[EDO|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 11-limit: &lt;182 288 423 511 630| (patent val), &lt;182 289 423 511 630| (182b), and &lt;182 288 422 511 629| (182ce). Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182b val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and |-4 -37 27&gt; in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.
+{{EDO intro|182}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:15:22Z

Infobox ET added

← Older revision		Revision as of 21:15, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''182edo''' is the [[EDO\|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 11-limit: <182 288 423 511 630\| (patent val), <182 289 423 511 630\| (182b), and <182 288 422 511 629\| (182ce). Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|-4 -37 27> in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family\|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.		'''182edo''' is the [[EDO\|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 11-limit: <182 288 423 511 630\| (patent val), <182 289 423 511 630\| (182b), and <182 288 422 511 629\| (182ce). Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|-4 -37 27> in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family\|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out 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

2022-07-02T21:22:36Z

Sort key

← Older revision		Revision as of 21:22, 2 July 2022
Line 1:		Line 1:
	'''182edo''' is the [[EDO\|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 11-limit: <182 288 423 511 630\| (patent val), <182 289 423 511 630\| (182b), and <182 288 422 511 629\| (182ce). Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|-4 -37 27> in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family\|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.		'''182edo''' is the [[EDO\|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 11-limit: <182 288 423 511 630\| (patent val), <182 289 423 511 630\| (182b), and <182 288 422 511 629\| (182ce). Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|-4 -37 27> in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family\|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out 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

2020-12-04T23:13:14Z

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:
	'''182edo''' is the [[EDO\|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 11-limit: <182 288 423 511 630\| (patent val), <182 289 423 511 630\| (182b), and <182 288 422 511 629\| (182ce). Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|-4 -37 27> in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family\|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.		'''182edo''' is the [[EDO\|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 11-limit: <182 288 423 511 630\| (patent val), <182 289 423 511 630\| (182b), and <182 288 422 511 629\| (182ce). Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|-4 -37 27> in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family\|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.

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