170edo - Revision history

Francium: changed EDO intro to ED intro

2025-02-19T18:06:13Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:06, 19 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	170edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with four mappings possible for the 7-limit: {{val\| 170 269 395 477 }} ([[patent val]]), {{val\| 170 '''270''' 395 477 }} (170b), {{val\| 170 '''270''' 395 '''478''' }} (170bd), and {{val\| 170 269 '''394''' 477 }} (170c).		170edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with four mappings possible for the 7-limit: {{val\| 170 269 395 477 }} ([[patent val]]), {{val\| 170 '''270''' 395 477 }} (170b), {{val\| 170 '''270''' 395 '''478''' }} (170bd), and {{val\| 170 269 '''394''' 477 }} (170c).

FloraC: +prime error table; +subsets and supersets

2024-04-26T08:10:13Z

+prime error table; +subsets and supersets

← Older revision		Revision as of 08:10, 26 April 2024
Line 11:		Line 11:

	Using the 170bd val, it tempers out [[16875/16807]], 51200/50421, and [[420175/419904]] in the 7-limit; [[176/175]], 896/891, and 6875/6804 in the 11-limit; [[169/168]], [[640/637]], [[1001/1000]], 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; [[325/324]], 364/363, [[512/507]], [[625/624]], and 1625/1617 in the 13-limit.		Using the 170bd val, it tempers out [[16875/16807]], 51200/50421, and [[420175/419904]] in the 7-limit; [[176/175]], 896/891, and 6875/6804 in the 11-limit; [[169/168]], [[640/637]], [[1001/1000]], 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; [[325/324]], 364/363, [[512/507]], [[625/624]], and 1625/1617 in the 13-limit.

			=== Odd harmonics ===
			{{Harmonics in equal\|170}}

			=== Subsets and supersets ===
			Since 170 factors into {{factorization\|170}}, 170edo has subset edos {{EDOs\| 2, 5, 10, 17, 34, and 85 }}.

FloraC: Cleanup

2024-04-26T08:08:15Z

Cleanup

← Older revision		Revision as of 08:08, 26 April 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''170edo''' is the [[~~EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit. Using the 170c val, it tempers out the lalagu comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit [[Gamelismic clan\|unidec temperament]]; 975/968, 1188/1183, 1625/1617, and 3159/3136 in the 13-limit.		{{EDO intro}}

	[[~~Category~~:~~Equal divisions of~~ the ~~octave~~\|~~###~~]] <!-- 3-~~digit number~~ -->		170edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with four mappings possible for the 7-limit: {{val\| 170 269 395 477 }} ([[patent val]]), {{val\| 170 '''270''' 395 477 }} (170b), {{val\| 170 '''270''' 395 '''478''' }} (170bd), and {{val\| 170 269 '''394''' 477 }} (170c).

			Using the patent val, it [[tempering out\|tempers out]] the [[valentine comma]], 1990656/1953125 and 3486784401/3355443200 in the 5-limit; [[126/125]], [[1029/1024]], and 215233605/210827008 in the 7-limit, [[support]]ing the 7-limit [[valentine]] temperament; [[540/539]], 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; [[847/845]], [[1188/1183]], [[1287/1280]], and [[1575/1573]] in the 13-limit.

			Using the 170c val, it tempers out the [[python comma]], 43046721/41943040 and the [[sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, [[4375/4374]], and 78125/76832 in the 7-limit; [[385/384]], [[441/440]], and [[8019/8000]] in the 11-limit, supporting the 11-limit [[unidec]] temperament; 975/968, 1188/1183, 1625/1617, and 3159/3136 in the 13-limit.

			The 170b val is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[34edo]], tempering out the [[diaschisma]], 2048/2025 and the [[15625/15552\|kleisma]], 15625/15552. It tempers out 33614/32805, [[50421/50000]], and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and [[6250/6237]] in the 11-limit; [[196/195]], [[364/363]], 572/567, and 3146/3125 in the 13-limit.

			Using the 170bd val, it tempers out [[16875/16807]], 51200/50421, and [[420175/419904]] in the 7-limit; [[176/175]], 896/891, and 6875/6804 in the 11-limit; [[169/168]], [[640/637]], [[1001/1000]], 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; [[325/324]], 364/363, [[512/507]], [[625/624]], and 1625/1617 in the 13-limit.

Aura at 19:12, 4 October 2022

2022-10-04T19:12:55Z

← Older revision		Revision as of 19:12, 4 October 2022
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			{{Infobox ET}}
	'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit. Using the 170c val, it tempers out the lalagu comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit [[Gamelismic clan\|unidec temperament]]; 975/968, 1188/1183, 1625/1617, and 3159/3136 in the 13-limit.		'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit. Using the 170c val, it tempers out the lalagu comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit [[Gamelismic clan\|unidec temperament]]; 975/968, 1188/1183, 1625/1617, and 3159/3136 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

2022-07-02T21:17:43Z

Sort key

← Older revision		Revision as of 21:17, 2 July 2022
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	'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit. Using the 170c val, it tempers out the lalagu comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit [[Gamelismic clan\|unidec temperament]]; 975/968, 1188/1183, 1625/1617, and 3159/3136 in the 13-limit.		'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit. Using the 170c val, it tempers out the lalagu comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit [[Gamelismic clan\|unidec temperament]]; 975/968, 1188/1183, 1625/1617, and 3159/3136 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

2020-12-04T23:13:12Z

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:
	'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit. Using the 170c val, it tempers out the lalagu comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit [[Gamelismic clan\|unidec temperament]]; 975/968, 1188/1183, 1625/1617, and 3159/3136 in the 13-limit.		'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit. Using the 170c val, it tempers out the lalagu comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit [[Gamelismic clan\|unidec temperament]]; 975/968, 1188/1183, 1625/1617, and 3159/3136 in the 13-limit.

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

TallKite: updated the color names

2019-02-07T01:03:59Z

updated the color names

← Older revision		Revision as of 01:03, 7 February 2019
Line 1:		Line 1:
	'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit. Using the 170c val, it tempers out the ~~double large green~~ comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit [[Gamelismic clan\|unidec temperament]]; 975/968, 1188/1183, 1625/1617, and 3159/3136 in the 13-limit.		'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit. Using the 170c val, it tempers out the lalagu comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit [[Gamelismic clan\|unidec temperament]]; 975/968, 1188/1183, 1625/1617, and 3159/3136 in the 13-limit.

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

Xenllium at 13:59, 16 December 2018

2018-12-16T13:59:55Z

← Older revision		Revision as of 13:59, 16 December 2018
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	'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (~~optimal~~ patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit. Using the alternative ~~170bde~~ val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit. Using the 170c val, it tempers out the double large green comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit.		'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit. Using the 170c val, it tempers out the double large green comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit [[Gamelismic clan\|unidec temperament]]; 975/968, 1188/1183, 1625/1617, and 3159/3136 in the 13-limit.

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

Xenllium at 14:25, 13 December 2018

2018-12-13T14:25:03Z

← Older revision		Revision as of 14:25, 13 December 2018
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	'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (optimal patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the ~~optimal~~ patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit. Using the 170c val, it tempers out the double large green comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit.		'''170edo''' is the [[EDO\|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477\| (optimal patent val), <170 270 395 477\| (170b), <170 270 395 478\| (170bd), and <170 269 394 477\| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit. Using the 170b val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit. Using the alternative 170bde val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit. Using the 170c val, it tempers out the double large green comma, 43046721/41943040 and the [[Sycamore family\|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit.

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

Xenllium: Created page with "'''170edo''' is the equal division of the octave into 170 parts of 7.0588 cents each. It is inconsistent to the 5-limit and higher limit, with four mappings possib..."

2018-12-05T03:51:22Z

Created page with "'''170edo''' is the equal division of the octave into 170 parts of 7.0588 cents each. It is inconsistent to the 5-limit and higher limit, with four mappings possib..."

New page

'''170edo''' is the [[EDO|equal division of the octave]] into 170 parts of 7.0588 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477| (optimal patent val), <170 270 395 477| (170b), <170 270 395 478| (170bd), and <170 269 394 477| (170c). Using the optimal patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit. Using the 170b val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and the [[kleisma]], 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit. Using the 170c val, it tempers out the double large green comma, 43046721/41943040 and the [[Sycamore family|sycamore comma]], 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit.

[[Category:Edo]]