194edo - Revision history

Overthink: oops

2026-05-15T19:12:03Z

oops

← Older revision		Revision as of 19:12, 15 May 2026
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	{{ED intro}}		{{ED intro}}

	194edo is only [[consistent]] to the [[5-odd-limit]], though harmonics 3 are 5 are about halfway between steps. Harmonic [[7/1\|7]] is sharp, causing [[7/6]], [[7/5]], and their [[octave complement]]s to become inconsistent in the [[7-odd-limit]]. It is therefore best to treat 194edo as a 2.9.15.21.11.13.17.19-subgroup system, with all [[35-odd-limit]] intervals in this subgroup having less than 25% relative error~~. In this subgroup it supports the 13 & 181 temperament, which covers the full [[21-odd-limit]] subset of this subgroup with the 51-note [[mos scale]]~~.		194edo is only [[consistent]] to the [[5-odd-limit]], though harmonics 3 are 5 are about halfway between steps. Harmonic [[7/1\|7]] is sharp, causing [[7/6]], [[7/5]], and their [[octave complement]]s to become inconsistent in the [[7-odd-limit]]. It is therefore best to treat 194edo as a 2.9.15.21.11.13.17.19-subgroup system, with all [[35-odd-limit]] intervals in this subgroup having less than 25% relative error.

	If the patent val is used, the equal temperament [[tempering out\|tempers out]] 43046721/41943040 (lalagu comma) and 1224440064/1220703125 ([[parakleisma]]) in the 5-limit. It tempers out [[1728/1715]], 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and [[4000/3993]] in the 11-limit; [[351/350]], [[640/637]], [[1573/1568]], 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out [[245/243]], 65536/64827, and 78125/76832 in the 7-limit; [[385/384]], [[896/891]], 2420/2401, and 9375/9317 in the 11-limit; [[275/273]], 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 ([[diaschisma]]) and {{monzo\| 0 -41 28 }} ([[28edt]] no-twos comma) in the 5-limit; [[2401/2400]], 65536/64827, and 1071875/1062882 in the 7-limit; [[176/175]], 896/891, 3773/3750, and 6655/6561 in the 11-limit; [[325/324]], 572/567, [[847/845]], 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out [[225/224]], 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, [[540/539]], 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, [[1188/1183]], 1875/1859, [[4225/4224]], and 6561/6500 in the 13-limit.		If the patent val is used, the equal temperament [[tempering out\|tempers out]] 43046721/41943040 (lalagu comma) and 1224440064/1220703125 ([[parakleisma]]) in the 5-limit. It tempers out [[1728/1715]], 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and [[4000/3993]] in the 11-limit; [[351/350]], [[640/637]], [[1573/1568]], 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out [[245/243]], 65536/64827, and 78125/76832 in the 7-limit; [[385/384]], [[896/891]], 2420/2401, and 9375/9317 in the 11-limit; [[275/273]], 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 ([[diaschisma]]) and {{monzo\| 0 -41 28 }} ([[28edt]] no-twos comma) in the 5-limit; [[2401/2400]], 65536/64827, and 1071875/1062882 in the 7-limit; [[176/175]], 896/891, 3773/3750, and 6655/6561 in the 11-limit; [[325/324]], 572/567, [[847/845]], 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out [[225/224]], 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, [[540/539]], 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, [[1188/1183]], 1875/1859, [[4225/4224]], and 6561/6500 in the 13-limit.

Overthink: add more

2026-05-15T18:50:31Z

add more

← Older revision		Revision as of 18:50, 15 May 2026
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	{{ED intro}}		{{ED intro}}

	194edo is [[consistent]] to the [[5-odd-limit]], ~~but 194b~~ and ~~194bc~~ [[~~val~~]]s ~~are also possible~~ as having ~~a large~~ relative error ~~for~~ the 5-limit. ~~Using~~ the patent val, the equal temperament [[tempering out\|tempers out]] 43046721/41943040 (lalagu comma) and 1224440064/1220703125 ([[parakleisma]]) in the 5-limit. it tempers out [[1728/1715]], 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and [[4000/3993]] in the 11-limit; [[351/350]], [[640/637]], [[1573/1568]], 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out [[245/243]], 65536/64827, and 78125/76832 in the 7-limit; [[385/384]], [[896/891]], 2420/2401, and 9375/9317 in the 11-limit; [[275/273]], 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 ([[diaschisma]]) and {{monzo\| 0 -41 28 }} ([[28edt]] no-twos comma) in the 5-limit; [[2401/2400]], 65536/64827, and 1071875/1062882 in the 7-limit; [[176/175]], 896/891, 3773/3750, and 6655/6561 in the 11-limit; [[325/324]], 572/567, [[847/845]], 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out [[225/224]], 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, [[540/539]], 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, [[1188/1183]], 1875/1859, [[4225/4224]], and 6561/6500 in the 13-limit.		194edo is only [[consistent]] to the [[5-odd-limit]], though harmonics 3 are 5 are about halfway between steps. Harmonic [[7/1\|7]] is sharp, causing [[7/6]], [[7/5]], and their [[octave complement]]s to become inconsistent in the [[7-odd-limit]]. It is therefore best to treat 194edo as a 2.9.15.21.11.13.17.19-subgroup system, with all [[35-odd-limit]] intervals in this subgroup having less than 25% relative error. In this subgroup it supports the 13 & 181 temperament, which covers the full [[21-odd-limit]] subset of this subgroup with the 51-note [[mos scale]].

			If the patent val is used, the equal temperament [[tempering out\|tempers out]] 43046721/41943040 (lalagu comma) and 1224440064/1220703125 ([[parakleisma]]) in the 5-limit. It tempers out [[1728/1715]], 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and [[4000/3993]] in the 11-limit; [[351/350]], [[640/637]], [[1573/1568]], 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out [[245/243]], 65536/64827, and 78125/76832 in the 7-limit; [[385/384]], [[896/891]], 2420/2401, and 9375/9317 in the 11-limit; [[275/273]], 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 ([[diaschisma]]) and {{monzo\| 0 -41 28 }} ([[28edt]] no-twos comma) in the 5-limit; [[2401/2400]], 65536/64827, and 1071875/1062882 in the 7-limit; [[176/175]], 896/891, 3773/3750, and 6655/6561 in the 11-limit; [[325/324]], 572/567, [[847/845]], 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out [[225/224]], 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, [[540/539]], 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, [[1188/1183]], 1875/1859, [[4225/4224]], and 6561/6500 in the 13-limit.

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 194 factors into {{factorization\|194}}, 194edo contains [[2edo]] and [[97edo]] as subsets.		Since 194 factors into {{factorization\|194}}, 194edo contains [[2edo]] and [[97edo]] as subsets. [[388edo]], which doubles it, corrects harmonics 3, 5, and 7, and makes for a strong high-limit system, being consistent to the [[37-odd-limit]].

ArrowHead294 at 19:29, 20 February 2025

2025-02-20T19:29:19Z

← Older revision		Revision as of 19:29, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	194edo is [[consistent]] to the [[5-odd-limit]], but 194b and 194bc [[val]]s are also possible as having a large relative error for the 5-limit. Using the patent val, the equal temperament [[tempering out\|tempers out]] 43046721/41943040 (lalagu comma) and 1224440064/1220703125 ([[parakleisma]]) in the 5-limit. it tempers out [[1728/1715]], 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and [[4000/3993]] in the 11-limit; [[351/350]], [[640/637]], [[1573/1568]], 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out [[245/243]], 65536/64827, and 78125/76832 in the 7-limit; [[385/384]], [[896/891]], 2420/2401, and 9375/9317 in the 11-limit; [[275/273]], 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 ([[diaschisma]]) and {{monzo\| 0 -41 28 }} ([[28edt]] no-twos comma) in the 5-limit; [[2401/2400]], 65536/64827, and 1071875/1062882 in the 7-limit; [[176/175]], 896/891, 3773/3750, and 6655/6561 in the 11-limit; [[325/324]], 572/567, [[847/845]], 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out [[225/224]], 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, [[540/539]], 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, [[1188/1183]], 1875/1859, [[4225/4224]], and 6561/6500 in the 13-limit.		194edo is [[consistent]] to the [[5-odd-limit]], but 194b and 194bc [[val]]s are also possible as having a large relative error for the 5-limit. Using the patent val, the equal temperament [[tempering out\|tempers out]] 43046721/41943040 (lalagu comma) and 1224440064/1220703125 ([[parakleisma]]) in the 5-limit. it tempers out [[1728/1715]], 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and [[4000/3993]] in the 11-limit; [[351/350]], [[640/637]], [[1573/1568]], 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out [[245/243]], 65536/64827, and 78125/76832 in the 7-limit; [[385/384]], [[896/891]], 2420/2401, and 9375/9317 in the 11-limit; [[275/273]], 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 ([[diaschisma]]) and {{monzo\| 0 -41 28 }} ([[28edt]] no-twos comma) in the 5-limit; [[2401/2400]], 65536/64827, and 1071875/1062882 in the 7-limit; [[176/175]], 896/891, 3773/3750, and 6655/6561 in the 11-limit; [[325/324]], 572/567, [[847/845]], 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out [[225/224]], 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, [[540/539]], 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, [[1188/1183]], 1875/1859, [[4225/4224]], and 6561/6500 in the 13-limit.

FloraC: Cleanup; +error table; +subsets and supersets

2024-04-16T14:06:30Z

Cleanup; +error table; +subsets and supersets

← Older revision		Revision as of 14:06, 16 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''194edo''' is the [[~~EDO\|equal division of the octave]] into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as having a large relative error for the 5-limit. It tempers out 43046721/41943040 (lalagu comma) and 1224440064/1220703125 (parakleisma) in the 5-limit. Using the patent val, it tempers out 1728/1715, 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and 4000/3993 in the 11-limit; 351/350, 640/637, 1573/1568, 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out 245/243, 65536/64827, and 78125/76832 in the 7-limit; 385/384, 896/891, 2420/2401, and 9375/9317 in the 11-limit; 275/273, 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 (diaschisma) and \|0 -41 28> ([[28edt]] no-twos comma) in the 5-limit; 2401/2400, 65536/64827, and 1071875/1062882 in the 7-limit; 176/175, 896/891, 3773/3750, and 6655/6561 in the 11-limit; 325/324, 572/567, 847/845, 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out 225/224, 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, 540/539, 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, 1188/1183, 1875/1859, 4225/4224, and 6561/6500 in the 13-limit.		{{EDO intro}}

	[[~~Category:Equal divisions of~~ the ~~octave~~\|~~###~~]] <!-- 3-~~digit number~~ -->		194edo is [[consistent]] to the [[5-odd-limit]], but 194b and 194bc [[val]]s are also possible as having a large relative error for the 5-limit. Using the patent val, the equal temperament [[tempering out\|tempers out]] 43046721/41943040 (lalagu comma) and 1224440064/1220703125 ([[parakleisma]]) in the 5-limit. it tempers out [[1728/1715]], 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and [[4000/3993]] in the 11-limit; [[351/350]], [[640/637]], [[1573/1568]], 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out [[245/243]], 65536/64827, and 78125/76832 in the 7-limit; [[385/384]], [[896/891]], 2420/2401, and 9375/9317 in the 11-limit; [[275/273]], 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 ([[diaschisma]]) and {{monzo\| 0 -41 28 }} ([[28edt]] no-twos comma) in the 5-limit; [[2401/2400]], 65536/64827, and 1071875/1062882 in the 7-limit; [[176/175]], 896/891, 3773/3750, and 6655/6561 in the 11-limit; [[325/324]], 572/567, [[847/845]], 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out [[225/224]], 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, [[540/539]], 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, [[1188/1183]], 1875/1859, [[4225/4224]], and 6561/6500 in the 13-limit.

			=== Odd harmonics ===
			{{Harmonics in equal\|194}}

			=== Subsets and supersets ===
			Since 194 factors into {{factorization\|194}}, 194edo contains [[2edo]] and [[97edo]] as subsets.

Plumtree: Infobox ET added

2022-10-04T21:17:59Z

Infobox ET added

← Older revision		Revision as of 21:17, 4 October 2022
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			{{Infobox ET}}
	'''194edo''' is the [[EDO\|equal division of the octave]] into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as having a large relative error for the 5-limit. It tempers out 43046721/41943040 (lalagu comma) and 1224440064/1220703125 (parakleisma) in the 5-limit. Using the patent val, it tempers out 1728/1715, 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and 4000/3993 in the 11-limit; 351/350, 640/637, 1573/1568, 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out 245/243, 65536/64827, and 78125/76832 in the 7-limit; 385/384, 896/891, 2420/2401, and 9375/9317 in the 11-limit; 275/273, 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 (diaschisma) and \|0 -41 28> ([[28edt]] no-twos comma) in the 5-limit; 2401/2400, 65536/64827, and 1071875/1062882 in the 7-limit; 176/175, 896/891, 3773/3750, and 6655/6561 in the 11-limit; 325/324, 572/567, 847/845, 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out 225/224, 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, 540/539, 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, 1188/1183, 1875/1859, 4225/4224, and 6561/6500 in the 13-limit.		'''194edo''' is the [[EDO\|equal division of the octave]] into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as having a large relative error for the 5-limit. It tempers out 43046721/41943040 (lalagu comma) and 1224440064/1220703125 (parakleisma) in the 5-limit. Using the patent val, it tempers out 1728/1715, 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and 4000/3993 in the 11-limit; 351/350, 640/637, 1573/1568, 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out 245/243, 65536/64827, and 78125/76832 in the 7-limit; 385/384, 896/891, 2420/2401, and 9375/9317 in the 11-limit; 275/273, 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 (diaschisma) and \|0 -41 28> ([[28edt]] no-twos comma) in the 5-limit; 2401/2400, 65536/64827, and 1071875/1062882 in the 7-limit; 176/175, 896/891, 3773/3750, and 6655/6561 in the 11-limit; 325/324, 572/567, 847/845, 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out 225/224, 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, 540/539, 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, 1188/1183, 1875/1859, 4225/4224, and 6561/6500 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

2022-07-02T21:24:34Z

Sort key

← Older revision		Revision as of 21:24, 2 July 2022
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	'''194edo''' is the [[EDO\|equal division of the octave]] into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as having a large relative error for the 5-limit. It tempers out 43046721/41943040 (lalagu comma) and 1224440064/1220703125 (parakleisma) in the 5-limit. Using the patent val, it tempers out 1728/1715, 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and 4000/3993 in the 11-limit; 351/350, 640/637, 1573/1568, 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out 245/243, 65536/64827, and 78125/76832 in the 7-limit; 385/384, 896/891, 2420/2401, and 9375/9317 in the 11-limit; 275/273, 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 (diaschisma) and \|0 -41 28> ([[28edt]] no-twos comma) in the 5-limit; 2401/2400, 65536/64827, and 1071875/1062882 in the 7-limit; 176/175, 896/891, 3773/3750, and 6655/6561 in the 11-limit; 325/324, 572/567, 847/845, 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out 225/224, 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, 540/539, 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, 1188/1183, 1875/1859, 4225/4224, and 6561/6500 in the 13-limit.		'''194edo''' is the [[EDO\|equal division of the octave]] into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as having a large relative error for the 5-limit. It tempers out 43046721/41943040 (lalagu comma) and 1224440064/1220703125 (parakleisma) in the 5-limit. Using the patent val, it tempers out 1728/1715, 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and 4000/3993 in the 11-limit; 351/350, 640/637, 1573/1568, 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out 245/243, 65536/64827, and 78125/76832 in the 7-limit; 385/384, 896/891, 2420/2401, and 9375/9317 in the 11-limit; 275/273, 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 (diaschisma) and \|0 -41 28> ([[28edt]] no-twos comma) in the 5-limit; 2401/2400, 65536/64827, and 1071875/1062882 in the 7-limit; 176/175, 896/891, 3773/3750, and 6655/6561 in the 11-limit; 325/324, 572/567, 847/845, 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out 225/224, 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, 540/539, 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, 1188/1183, 1875/1859, 4225/4224, and 6561/6500 in the 13-limit.

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

TallKite: updated the color notation

2021-07-13T01:36:03Z

updated the color notation

← Older revision		Revision as of 01:36, 13 July 2021
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	'''194edo''' is the [[EDO\|equal division of the octave]] into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as having a large relative error for the 5-limit. It tempers out 43046721/41943040 (~~double large green~~ comma) and 1224440064/1220703125 (parakleisma) in the 5-limit. Using the patent val, it tempers out 1728/1715, 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and 4000/3993 in the 11-limit; 351/350, 640/637, 1573/1568, 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out 245/243, 65536/64827, and 78125/76832 in the 7-limit; 385/384, 896/891, 2420/2401, and 9375/9317 in the 11-limit; 275/273, 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 (diaschisma) and \|0 -41 28> ([[28edt]] no-twos comma) in the 5-limit; 2401/2400, 65536/64827, and 1071875/1062882 in the 7-limit; 176/175, 896/891, 3773/3750, and 6655/6561 in the 11-limit; 325/324, 572/567, 847/845, 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out 225/224, 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, 540/539, 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, 1188/1183, 1875/1859, 4225/4224, and 6561/6500 in the 13-limit.		'''194edo''' is the [[EDO\|equal division of the octave]] into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as having a large relative error for the 5-limit. It tempers out 43046721/41943040 (lalagu comma) and 1224440064/1220703125 (parakleisma) in the 5-limit. Using the patent val, it tempers out 1728/1715, 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and 4000/3993 in the 11-limit; 351/350, 640/637, 1573/1568, 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out 245/243, 65536/64827, and 78125/76832 in the 7-limit; 385/384, 896/891, 2420/2401, and 9375/9317 in the 11-limit; 275/273, 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 (diaschisma) and \|0 -41 28> ([[28edt]] no-twos comma) in the 5-limit; 2401/2400, 65536/64827, and 1071875/1062882 in the 7-limit; 176/175, 896/891, 3773/3750, and 6655/6561 in the 11-limit; 325/324, 572/567, 847/845, 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out 225/224, 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, 540/539, 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, 1188/1183, 1875/1859, 4225/4224, and 6561/6500 in the 13-limit.

	[[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
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	'''194edo''' is the [[EDO\|equal division of the octave]] into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as having a large relative error for the 5-limit. It tempers out 43046721/41943040 (double large green comma) and 1224440064/1220703125 (parakleisma) in the 5-limit. Using the patent val, it tempers out 1728/1715, 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and 4000/3993 in the 11-limit; 351/350, 640/637, 1573/1568, 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out 245/243, 65536/64827, and 78125/76832 in the 7-limit; 385/384, 896/891, 2420/2401, and 9375/9317 in the 11-limit; 275/273, 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 (diaschisma) and \|0 -41 28> ([[28edt]] no-twos comma) in the 5-limit; 2401/2400, 65536/64827, and 1071875/1062882 in the 7-limit; 176/175, 896/891, 3773/3750, and 6655/6561 in the 11-limit; 325/324, 572/567, 847/845, 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out 225/224, 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, 540/539, 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, 1188/1183, 1875/1859, 4225/4224, and 6561/6500 in the 13-limit.		'''194edo''' is the [[EDO\|equal division of the octave]] into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as having a large relative error for the 5-limit. It tempers out 43046721/41943040 (double large green comma) and 1224440064/1220703125 (parakleisma) in the 5-limit. Using the patent val, it tempers out 1728/1715, 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and 4000/3993 in the 11-limit; 351/350, 640/637, 1573/1568, 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out 245/243, 65536/64827, and 78125/76832 in the 7-limit; 385/384, 896/891, 2420/2401, and 9375/9317 in the 11-limit; 275/273, 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 (diaschisma) and \|0 -41 28> ([[28edt]] no-twos comma) in the 5-limit; 2401/2400, 65536/64827, and 1071875/1062882 in the 7-limit; 176/175, 896/891, 3773/3750, and 6655/6561 in the 11-limit; 325/324, 572/567, 847/845, 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out 225/224, 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, 540/539, 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, 1188/1183, 1875/1859, 4225/4224, and 6561/6500 in the 13-limit.

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

Xenllium: Created page with "'''194edo''' is the equal division of the octave into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as..."

2019-03-12T23:55:41Z

Created page with "'''194edo''' is the equal division of the octave into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as..."

New page

'''194edo''' is the [[EDO|equal division of the octave]] into 194 parts of 6.1856 cents each. 194edo is consistent to the 5-limit, but 194b and 194bc vals are also possible as having a large relative error for the 5-limit. It tempers out 43046721/41943040 (double large green comma) and 1224440064/1220703125 (parakleisma) in the 5-limit. Using the patent val, it tempers out 1728/1715, 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and 4000/3993 in the 11-limit; 351/350, 640/637, 1573/1568, 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out 245/243, 65536/64827, and 78125/76832 in the 7-limit; 385/384, 896/891, 2420/2401, and 9375/9317 in the 11-limit; 275/273, 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 (diaschisma) and |0 -41 28> ([[28edt]] no-twos comma) in the 5-limit; 2401/2400, 65536/64827, and 1071875/1062882 in the 7-limit; 176/175, 896/891, 3773/3750, and 6655/6561 in the 11-limit; 325/324, 572/567, 847/845, 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out 225/224, 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, 540/539, 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, 1188/1183, 1875/1859, 4225/4224, and 6561/6500 in the 13-limit.

[[Category:Edo]]