158edo - Revision history

Francium: changed EDO intro to ED intro

2025-02-19T18:01:19Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:01, 19 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	158edo is in[[consistent]] to the [[5-odd-limit]] and higher limits. It can be treated as a 2.9.5.21.33.39 [[subgroup]] temperament, which is every other step of [[316edo]], and [[tempering out\|tempers out]] the same commas: [[1716/1715]], [[2080/2079]], [[3025/3024]], [[3136/3125]], [[4096/4095]], [[4225/4224]], [[9801/9800]], etc.		158edo is in[[consistent]] to the [[5-odd-limit]] and higher limits. It can be treated as a 2.9.5.21.33.39 [[subgroup]] temperament, which is every other step of [[316edo]], and [[tempering out\|tempers out]] the same commas: [[1716/1715]], [[2080/2079]], [[3025/3024]], [[3136/3125]], [[4096/4095]], [[4225/4224]], [[9801/9800]], etc.

FloraC: Correction: this isn't the OPV for marvolo

2024-05-11T09:00:14Z

Correction: this isn't the OPV for marvolo

← Older revision		Revision as of 09:00, 11 May 2024
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	Otherwise, it has five mappings possible for the 13-limit: {{val\| 158 250 367 444 547 585 }} ([[patent val]]), {{val\| 158 '''251''' 367 444 547 585 }} (158b), {{val\| 158 250 '''366''' '''443''' '''546''' '''584''' }} (158cdef), {{val\| 158 250 367 '''443''' '''546''' 585 }} (158de), and {{val\| 158 250 367 '''443''' '''546''' '''584''' }} (158def).		Otherwise, it has five mappings possible for the 13-limit: {{val\| 158 250 367 444 547 585 }} ([[patent val]]), {{val\| 158 '''251''' 367 444 547 585 }} (158b), {{val\| 158 250 '''366''' '''443''' '''546''' '''584''' }} (158cdef), {{val\| 158 250 367 '''443''' '''546''' 585 }} (158de), and {{val\| 158 250 367 '''443''' '''546''' '''584''' }} (158def).

	Using the patent val, it tempers out the [[Würschmidt comma]], 393216/390625 and 3486784401/3355443200 in the 5-limit; [[225/224]], 8748/8575, and 40960000/40353607 in the 7-limit; [[441/440]], 1375/1372, [[4000/3993]], and 19683/19208 in the 11-limit, ~~providing the [[optimal patent val]] for~~ the 11-limit [[marvolo]] temperament; [[144/143]], [[640/637]], 2025/2002, [[2200/2197]] and 3159/3125 in the 13-limit.		Using the patent val, it tempers out the [[Würschmidt comma]], 393216/390625 and 3486784401/3355443200 in the 5-limit; [[225/224]], 8748/8575, and 40960000/40353607 in the 7-limit; [[441/440]], 1375/1372, [[4000/3993]], and 19683/19208 in the 11-limit, supporting the 11-limit [[marvolo]] temperament and giving a good tuning; [[144/143]], [[640/637]], 2025/2002, [[2200/2197]] and 3159/3125 in the 13-limit.

	Using the 158de val, it tempers out [[126/125]], 33075/32768, and 118098/117649 in the 7-limit; [[243/242]], [[385/384]], 1617/1600, and 117649/117128 in the 11-limit; [[196/195]], [[351/350]], [[1287/1280]], [[1575/1573]], and 4455/4394 in the 13-limit. Using the 158def val, it tempers out [[676/675]], [[847/845]], [[1573/1568]], 1701/1690, and 3159/3136 in the 13-limit.		Using the 158de val, it tempers out [[126/125]], 33075/32768, and 118098/117649 in the 7-limit; [[243/242]], [[385/384]], 1617/1600, and 117649/117128 in the 11-limit; [[196/195]], [[351/350]], [[1287/1280]], [[1575/1573]], and 4455/4394 in the 13-limit. Using the 158def val, it tempers out [[676/675]], [[847/845]], [[1573/1568]], 1701/1690, and 3159/3136 in the 13-limit.

FloraC: Elaborate on the subgroup interpretation

2024-05-11T08:53:28Z

Elaborate on the subgroup interpretation

← Older revision		Revision as of 08:53, 11 May 2024
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	{{EDO intro}}		{{EDO intro}}

	158edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, ~~with five mappings possible for~~ the ~~13-limit~~: ~~{{val\| 158 250 367 444 547 585 }} (~~[[~~patent val~~]]), ~~{{val\| 158 '''251''' 367 444 547 585 }} (158b)~~, ~~{{val\| 158 250 '''366''' '''443''' '''546''' '''584''' }} (158cdef)~~, ~~{{val\| 158 250 367 '''443''' '''546''' 585 }} (158de)~~, ~~and {{val\| 158 250 367 '''443''' '''546''' '''584''' }} (158def)~~.		158edo is in[[consistent]] to the [[5-odd-limit]] and higher limits. It can be treated as a 2.9.5.21.33.39 [[subgroup]] temperament, which is every other step of [[316edo]], and [[tempering out\|tempers out]] the same commas: [[1716/1715]], [[2080/2079]], [[3025/3024]], [[3136/3125]], [[4096/4095]], [[4225/4224]], [[9801/9800]], etc.

	Using the patent val, it ~~[[tempering out\|~~tempers out]] the [[Würschmidt comma]], 393216/390625 and 3486784401/3355443200 in the 5-limit; [[225/224]], 8748/8575, and 40960000/40353607 in the 7-limit; [[441/440]], 1375/1372, [[4000/3993]], and 19683/19208 in the 11-limit, providing the [[optimal patent val]] for the 11-limit [[marvolo]] temperament; [[144/143]], [[640/637]], 2025/2002, [[2200/2197]] and 3159/3125 in the 13-limit.		Otherwise, it has five mappings possible for the 13-limit: {{val\| 158 250 367 444 547 585 }} ([[patent val]]), {{val\| 158 '''251''' 367 444 547 585 }} (158b), {{val\| 158 250 '''366''' '''443''' '''546''' '''584''' }} (158cdef), {{val\| 158 250 367 '''443''' '''546''' 585 }} (158de), and {{val\| 158 250 367 '''443''' '''546''' '''584''' }} (158def).

			Using the patent val, it tempers out the [[Würschmidt comma]], 393216/390625 and 3486784401/3355443200 in the 5-limit; [[225/224]], 8748/8575, and 40960000/40353607 in the 7-limit; [[441/440]], 1375/1372, [[4000/3993]], and 19683/19208 in the 11-limit, providing the [[optimal patent val]] for the 11-limit [[marvolo]] temperament; [[144/143]], [[640/637]], 2025/2002, [[2200/2197]] and 3159/3125 in the 13-limit.

	Using the 158de val, it tempers out [[126/125]], 33075/32768, and 118098/117649 in the 7-limit; [[243/242]], [[385/384]], 1617/1600, and 117649/117128 in the 11-limit; [[196/195]], [[351/350]], [[1287/1280]], [[1575/1573]], and 4455/4394 in the 13-limit. Using the 158def val, it tempers out [[676/675]], [[847/845]], [[1573/1568]], 1701/1690, and 3159/3136 in the 13-limit.		Using the 158de val, it tempers out [[126/125]], 33075/32768, and 118098/117649 in the 7-limit; [[243/242]], [[385/384]], 1617/1600, and 117649/117128 in the 11-limit; [[196/195]], [[351/350]], [[1287/1280]], [[1575/1573]], and 4455/4394 in the 13-limit. Using the 158def val, it tempers out [[676/675]], [[847/845]], [[1573/1568]], 1701/1690, and 3159/3136 in the 13-limit.
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	Using the 158b val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo\| -1 -33 23 }} in the 5-limit; 245/243, 6144/6125 and 2500000/2470629 in the 7-limit; 1331/1323, 1375/1372, 2560/2541, and 4375/4356 in the 11-limit; 364/363, 572/567, [[625/624]], 640/637, and 1625/1617 in the 13-limit.		Using the 158b val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo\| -1 -33 23 }} in the 5-limit; 245/243, 6144/6125 and 2500000/2470629 in the 7-limit; 1331/1323, 1375/1372, 2560/2541, and 4375/4356 in the 11-limit; 364/363, 572/567, [[625/624]], 640/637, and 1625/1617 in the 13-limit.

	~~158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out [[9801/9800]], 35750/35721, and {{monzo\| -1 0 0 4 -19 15 }}.~~

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 158 factors into {{factorization\|158}}, 158edo contains [[2edo]] and [[79edo]] as its subsets. [[316edo]], which doubles it, provides good correction to the approximation to harmonics 3, 7, and 11.		Since 158 factors into {{factorization\|158}}, 158edo contains [[2edo]] and [[79edo]] as its subsets. 316edo, which doubles it, provides good correction to the approximation to harmonics 3, 7, and 11.

FloraC: +prime error table; +subsets and supersets

2024-05-11T08:47:56Z

+prime error table; +subsets and supersets

← Older revision		Revision as of 08:47, 11 May 2024
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	158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out [[9801/9800]], 35750/35721, and {{monzo\| -1 0 0 4 -19 15 }}.		158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out [[9801/9800]], 35750/35721, and {{monzo\| -1 0 0 4 -19 15 }}.

			=== Odd harmonics ===
			{{Harmonics in equal\|158}}

			=== Subsets and supersets ===
			Since 158 factors into {{factorization\|158}}, 158edo contains [[2edo]] and [[79edo]] as its subsets. [[316edo]], which doubles it, provides good correction to the approximation to harmonics 3, 7, and 11.

FloraC: Paragraphing, grouping vals by similarity

2024-05-11T08:44:29Z

Paragraphing, grouping vals by similarity

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro}}
-edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and {{monzo| -1 0 0 4 -19 15 }}.
+edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with five mappings possible for the 13-limit: {{val| 158 250 367 444 547 585 }} ([[patent val]]), {{val| 158 '''251''' 367 444 547 585 }} (158b), {{val| 158 250 '''366''' '''443''' '''546''' '''584''' }} (158cdef), {{val| 158 250 367 '''443''' '''546''' 585 }} (158de), and {{val| 158 250 367 '''443''' '''546''' '''584''' }} (158def).

FloraC: Adopt template: EDO intro; cleanup; -redundant categories

2024-05-11T08:41:50Z

Adopt template: EDO intro; cleanup; -redundant categories

← Older revision		Revision as of 08:41, 11 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''~~158edo~~'''~~ is ~~the~~ [[~~EDO\|equal division of the octave~~]] ~~into 158 parts of 7.594937~~ [[~~cent]]s each. It is inconsistent to the~~ 5-limit and higher ~~limit~~, with five mappings possible for the 13-limit: ~~<~~158 250 367 444 547 585\| (patent val), ~~<~~158 251 367 444 547 585\| (158b), ~~<~~158 250 366 443 546 584\| (158cdef), ~~<~~158 250 367 443 546 585\| (158de), and ~~<~~158 250 367 443 546 584\| (158def). Using the patent val, it tempers out the [[Würschmidt comma]], 393216/390625 and 3486784401/3355443200 in the 5-limit; 225/224, 8748/8575, and 40960000/40353607 in the 7-limit; 441/440, 1375/1372, 4000/3993, and 19683/19208 in the 11-limit, providing the optimal patent val for the 11-limit [[~~Marvel temperaments\|~~marvolo ~~temperament~~]]; 144/143, 640/637, 2025/2002, 2200/2197 and 3159/3125 in the 13-limit. Using the 158b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|-1 -33 23~~>~~ in the 5-limit; 245/243, 6144/6125 and 2500000/2470629 in the 7-limit; 1331/1323, 1375/1372, 2560/2541, and 4375/4356 in the 11-limit; 364/363, 572/567, 625/624, 640/637, and 1625/1617 in the 13-limit. Using the 158cdef val, it tempers out the [[~~Magic family\|small diesis~~]], 3125/3072 and the ~~lalagu~~ comma, 43046721/41943040 in the 5-limit; 2401/2400, 19683/19600, and 78125/76832 in the 7-limit; 243/242, 441/440, 4000/3993, and 33275/32768 in the 11-limit; 325/324, 975/968, 1287/1280, 1573/1568, and 1875/1859 in the 13-limit, supporting the 13-limit [[~~Gravity family\|~~harry ~~temperament~~]]. Using the 158de val, it tempers out 126/125, 33075/32768, and 118098/117649 in the 7-limit; 243/242, 385/384, 1617/1600, and 117649/117128 in the 11-limit; 196/195, 351/350, 1287/1280, 1575/1573, and 4455/4394 in the 13-limit. Using the 158def val, it tempers out 676/675, 847/845, 1573/1568, 1701/1690, and 3159/3136 in the 13-limit.		{{EDO intro}}
			158edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with five mappings possible for the 13-limit: {{val\| 158 250 367 444 547 585 }} ([[patent val]]), {{val\| 158 '''251''' 367 444 547 585 }} (158b), {{val\| 158 250 '''366''' '''443''' '''546''' '''584''' }} (158cdef), {{val\| 158 250 367 '''443''' '''546''' 585 }} (158de), and {{val\| 158 250 367 '''443''' '''546''' '''584''' }} (158def). Using the patent val, it [[tempering out\|tempers out]] the [[Würschmidt comma]], 393216/390625 and 3486784401/3355443200 in the 5-limit; 225/224, 8748/8575, and 40960000/40353607 in the 7-limit; 441/440, 1375/1372, 4000/3993, and 19683/19208 in the 11-limit, providing the optimal patent val for the 11-limit [[marvolo]] temperament; 144/143, 640/637, 2025/2002, 2200/2197 and 3159/3125 in the 13-limit. Using the 158b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and {{monzo\| -1 -33 23 }} in the 5-limit; 245/243, 6144/6125 and 2500000/2470629 in the 7-limit; 1331/1323, 1375/1372, 2560/2541, and 4375/4356 in the 11-limit; 364/363, 572/567, 625/624, 640/637, and 1625/1617 in the 13-limit. Using the 158cdef val, it tempers out the [[magic comma]], 3125/3072 and the [[python comma]], 43046721/41943040 in the 5-limit; 2401/2400, 19683/19600, and 78125/76832 in the 7-limit; 243/242, 441/440, 4000/3993, and 33275/32768 in the 11-limit; 325/324, 975/968, 1287/1280, 1573/1568, and 1875/1859 in the 13-limit, supporting the 13-limit [[harry]] temperament. Using the 158de val, it tempers out 126/125, 33075/32768, and 118098/117649 in the 7-limit; 243/242, 385/384, 1617/1600, and 117649/117128 in the 11-limit; 196/195, 351/350, 1287/1280, 1575/1573, and 4455/4394 in the 13-limit. Using the 158def val, it tempers out 676/675, 847/845, 1573/1568, 1701/1690, and 3159/3136 in the 13-limit.

	158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and \|-1 0 0 4 -19 15~~>~~.		158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and {{monzo\| -1 0 0 4 -19 15 }}.

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

Aura at 19:09, 4 October 2022

2022-10-04T19:09:21Z

← Older revision		Revision as of 19:09, 4 October 2022
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			{{Infobox ET}}
	'''158edo''' is the [[EDO\|equal division of the octave]] into 158 parts of 7.594937 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with five mappings possible for the 13-limit: <158 250 367 444 547 585\| (patent val), <158 251 367 444 547 585\| (158b), <158 250 366 443 546 584\| (158cdef), <158 250 367 443 546 585\| (158de), and <158 250 367 443 546 584\| (158def). Using the patent val, it tempers out the [[Würschmidt comma]], 393216/390625 and 3486784401/3355443200 in the 5-limit; 225/224, 8748/8575, and 40960000/40353607 in the 7-limit; 441/440, 1375/1372, 4000/3993, and 19683/19208 in the 11-limit, providing the optimal patent val for the 11-limit [[Marvel temperaments\|marvolo temperament]]; 144/143, 640/637, 2025/2002, 2200/2197 and 3159/3125 in the 13-limit. Using the 158b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|-1 -33 23> in the 5-limit; 245/243, 6144/6125 and 2500000/2470629 in the 7-limit; 1331/1323, 1375/1372, 2560/2541, and 4375/4356 in the 11-limit; 364/363, 572/567, 625/624, 640/637, and 1625/1617 in the 13-limit. Using the 158cdef val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and the lalagu comma, 43046721/41943040 in the 5-limit; 2401/2400, 19683/19600, and 78125/76832 in the 7-limit; 243/242, 441/440, 4000/3993, and 33275/32768 in the 11-limit; 325/324, 975/968, 1287/1280, 1573/1568, and 1875/1859 in the 13-limit, supporting the 13-limit [[Gravity family\|harry temperament]]. Using the 158de val, it tempers out 126/125, 33075/32768, and 118098/117649 in the 7-limit; 243/242, 385/384, 1617/1600, and 117649/117128 in the 11-limit; 196/195, 351/350, 1287/1280, 1575/1573, and 4455/4394 in the 13-limit. Using the 158def val, it tempers out 676/675, 847/845, 1573/1568, 1701/1690, and 3159/3136 in the 13-limit.		'''158edo''' is the [[EDO\|equal division of the octave]] into 158 parts of 7.594937 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with five mappings possible for the 13-limit: <158 250 367 444 547 585\| (patent val), <158 251 367 444 547 585\| (158b), <158 250 366 443 546 584\| (158cdef), <158 250 367 443 546 585\| (158de), and <158 250 367 443 546 584\| (158def). Using the patent val, it tempers out the [[Würschmidt comma]], 393216/390625 and 3486784401/3355443200 in the 5-limit; 225/224, 8748/8575, and 40960000/40353607 in the 7-limit; 441/440, 1375/1372, 4000/3993, and 19683/19208 in the 11-limit, providing the optimal patent val for the 11-limit [[Marvel temperaments\|marvolo temperament]]; 144/143, 640/637, 2025/2002, 2200/2197 and 3159/3125 in the 13-limit. Using the 158b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|-1 -33 23> in the 5-limit; 245/243, 6144/6125 and 2500000/2470629 in the 7-limit; 1331/1323, 1375/1372, 2560/2541, and 4375/4356 in the 11-limit; 364/363, 572/567, 625/624, 640/637, and 1625/1617 in the 13-limit. Using the 158cdef val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and the lalagu comma, 43046721/41943040 in the 5-limit; 2401/2400, 19683/19600, and 78125/76832 in the 7-limit; 243/242, 441/440, 4000/3993, and 33275/32768 in the 11-limit; 325/324, 975/968, 1287/1280, 1573/1568, and 1875/1859 in the 13-limit, supporting the 13-limit [[Gravity family\|harry temperament]]. Using the 158de val, it tempers out 126/125, 33075/32768, and 118098/117649 in the 7-limit; 243/242, 385/384, 1617/1600, and 117649/117128 in the 11-limit; 196/195, 351/350, 1287/1280, 1575/1573, and 4455/4394 in the 13-limit. Using the 158def val, it tempers out 676/675, 847/845, 1573/1568, 1701/1690, and 3159/3136 in the 13-limit.

Fredg999 category edits: Sort key

2022-07-02T21:10:03Z

Sort key

← Older revision		Revision as of 21:10, 2 July 2022
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	158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and \|-1 0 0 4 -19 15>.		158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and \|-1 0 0 4 -19 15>.

	[[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

2020-12-04T23:13:10Z

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:
	158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and \|-1 0 0 4 -19 15>.		158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and \|-1 0 0 4 -19 15>.

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

TallKite: updated the color names

2019-02-07T01:07:56Z

updated the color names

← Older revision		Revision as of 01:07, 7 February 2019
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	'''158edo''' is the [[EDO\|equal division of the octave]] into 158 parts of 7.594937 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with five mappings possible for the 13-limit: <158 250 367 444 547 585\| (patent val), <158 251 367 444 547 585\| (158b), <158 250 366 443 546 584\| (158cdef), <158 250 367 443 546 585\| (158de), and <158 250 367 443 546 584\| (158def). Using the patent val, it tempers out the [[Würschmidt comma]], 393216/390625 and 3486784401/3355443200 in the 5-limit; 225/224, 8748/8575, and 40960000/40353607 in the 7-limit; 441/440, 1375/1372, 4000/3993, and 19683/19208 in the 11-limit, providing the optimal patent val for the 11-limit [[Marvel temperaments\|marvolo temperament]]; 144/143, 640/637, 2025/2002, 2200/2197 and 3159/3125 in the 13-limit. Using the 158b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|-1 -33 23> in the 5-limit; 245/243, 6144/6125 and 2500000/2470629 in the 7-limit; 1331/1323, 1375/1372, 2560/2541, and 4375/4356 in the 11-limit; 364/363, 572/567, 625/624, 640/637, and 1625/1617 in the 13-limit. Using the 158cdef val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and the ~~double large green~~ comma, 43046721/41943040 in the 5-limit; 2401/2400, 19683/19600, and 78125/76832 in the 7-limit; 243/242, 441/440, 4000/3993, and 33275/32768 in the 11-limit; 325/324, 975/968, 1287/1280, 1573/1568, and 1875/1859 in the 13-limit, supporting the 13-limit [[Gravity family\|harry temperament]]. Using the 158de val, it tempers out 126/125, 33075/32768, and 118098/117649 in the 7-limit; 243/242, 385/384, 1617/1600, and 117649/117128 in the 11-limit; 196/195, 351/350, 1287/1280, 1575/1573, and 4455/4394 in the 13-limit. Using the 158def val, it tempers out 676/675, 847/845, 1573/1568, 1701/1690, and 3159/3136 in the 13-limit.		'''158edo''' is the [[EDO\|equal division of the octave]] into 158 parts of 7.594937 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with five mappings possible for the 13-limit: <158 250 367 444 547 585\| (patent val), <158 251 367 444 547 585\| (158b), <158 250 366 443 546 584\| (158cdef), <158 250 367 443 546 585\| (158de), and <158 250 367 443 546 584\| (158def). Using the patent val, it tempers out the [[Würschmidt comma]], 393216/390625 and 3486784401/3355443200 in the 5-limit; 225/224, 8748/8575, and 40960000/40353607 in the 7-limit; 441/440, 1375/1372, 4000/3993, and 19683/19208 in the 11-limit, providing the optimal patent val for the 11-limit [[Marvel temperaments\|marvolo temperament]]; 144/143, 640/637, 2025/2002, 2200/2197 and 3159/3125 in the 13-limit. Using the 158b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|-1 -33 23> in the 5-limit; 245/243, 6144/6125 and 2500000/2470629 in the 7-limit; 1331/1323, 1375/1372, 2560/2541, and 4375/4356 in the 11-limit; 364/363, 572/567, 625/624, 640/637, and 1625/1617 in the 13-limit. Using the 158cdef val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and the lalagu comma, 43046721/41943040 in the 5-limit; 2401/2400, 19683/19600, and 78125/76832 in the 7-limit; 243/242, 441/440, 4000/3993, and 33275/32768 in the 11-limit; 325/324, 975/968, 1287/1280, 1573/1568, and 1875/1859 in the 13-limit, supporting the 13-limit [[Gravity family\|harry temperament]]. Using the 158de val, it tempers out 126/125, 33075/32768, and 118098/117649 in the 7-limit; 243/242, 385/384, 1617/1600, and 117649/117128 in the 11-limit; 196/195, 351/350, 1287/1280, 1575/1573, and 4455/4394 in the 13-limit. Using the 158def val, it tempers out 676/675, 847/845, 1573/1568, 1701/1690, and 3159/3136 in the 13-limit.

	158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and \|-1 0 0 4 -19 15>.		158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and \|-1 0 0 4 -19 15>.

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