117edo - Revision history

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

2025-09-17T10:45:50Z

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

← Older revision		Revision as of 10:45, 17 September 2025
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	== Octave stretch ==		== Octave stretch ==
	117edo’s approximations of 3/1, 5/1, 7/1 and 17/1 are all noticeably improved by [[~~Gallery of arithmetic pitch sequences#APS of hekts~~\|~~APS7hekt~~]], a [[Octave shrinking\|compressed-octave]] version of 117edo. The trade-off is an unnoticeably worse 2/1 and 11/1, but noticeably worse 13/1.		117edo’s approximations of 3/1, 5/1, 7/1 and 17/1 are all noticeably improved by [[ed7\|329ed7]], a [[Octave shrinking\|compressed-octave]] version of 117edo. The trade-off is an unnoticeably worse 2/1 and 11/1, but noticeably worse 13/1.

	There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used ~~for this same purpose~~: 696zpi, 697zpi, 698zpi, 699zpi, 700zpi, 701zpi and 702zpi.		There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used to improve some harmonics at the expense of others: 696zpi, 697zpi, 698zpi, 699zpi, 700zpi, 701zpi and 702zpi.

	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.

FloraC: Fix linking

2025-08-27T13:08:28Z

Fix linking

← Older revision		Revision as of 13:08, 27 August 2025
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	117edo is in[[consistent]] to the [[5-odd-limit]] and higher odd limits, with four mappings possible for the [[11-limit]]: {{val\| 117 185 272 328 405 }} ([[patent val]]), {{val\| 117 186 '''272''' 329 '''405''' }} (117bd), {{val\| 117 185 '''271''' 328 '''404''' }} (117ce), and {{val\| 117 185 272 '''329''' 405 }} (117d).		117edo is in[[consistent]] to the [[5-odd-limit]] and higher odd limits, with four mappings possible for the [[11-limit]]: {{val\| 117 185 272 328 405 }} ([[patent val]]), {{val\| 117 186 '''272''' 329 '''405''' }} (117bd), {{val\| 117 185 '''271''' 328 '''404''' }} (117ce), and {{val\| 117 185 272 '''329''' 405 }} (117d).

	Using the patent val, it [[tempering out\|tempers out]] 81/80 ([[syntonic comma]]) and {{monzo\| 69 -1 -29 }} in the 5-limit; [[6144/6125]], 31104/30625, and 403368/390625 in the 7-limit, [[support]]ing the 7-limit [[mohajira]] temperament; [[540/539]], 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[~~Didymus rank three family #Terpsichore\|~~terpsichore]] temperament; [[144/143]], [[196/195]], [[364/363]], 729/715, and 3146/3125 in the 13-limit.		Using the patent val, it [[tempering out\|tempers out]] 81/80 ([[syntonic comma]]) and {{monzo\| 69 -1 -29 }} in the 5-limit; [[6144/6125]], 31104/30625, and 403368/390625 in the 7-limit, [[support]]ing the 7-limit [[mohajira]] temperament; [[540/539]], 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[terpsichore]] temperament; [[144/143]], [[196/195]], [[364/363]], 729/715, and 3146/3125 in the 13-limit.

	Using the 117d val, it tempers out [[126/125]], [[225/224]], and {{monzo\| 29 3 0 -12 }} in the 7-limit; [[99/98]], [[176/175]], [[441/440]], and 12582912/12400927 in the 11-limit; 144/143, [[640/637]], 648/637, [[1001/1000]], and [[Kuragesma\|43940/43923]] in the 13-limit, supporting the 13-limit [[grosstone]] temperament.		Using the 117d val, it tempers out [[126/125]], [[225/224]], and {{monzo\| 29 3 0 -12 }} in the 7-limit; [[99/98]], [[176/175]], [[441/440]], and 12582912/12400927 in the 11-limit; 144/143, [[640/637]], 648/637, [[1001/1000]], and [[Kuragesma\|43940/43923]] in the 13-limit, supporting the 13-limit [[grosstone]] temperament.

原井玉葱郎: link added

2025-04-15T23:15:06Z

link added

← Older revision		Revision as of 23:15, 15 April 2025
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	Using the patent val, it [[tempering out\|tempers out]] 81/80 ([[syntonic comma]]) and {{monzo\| 69 -1 -29 }} in the 5-limit; [[6144/6125]], 31104/30625, and 403368/390625 in the 7-limit, [[support]]ing the 7-limit [[mohajira]] temperament; [[540/539]], 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[Didymus rank three family #Terpsichore\|terpsichore]] temperament; [[144/143]], [[196/195]], [[364/363]], 729/715, and 3146/3125 in the 13-limit.		Using the patent val, it [[tempering out\|tempers out]] 81/80 ([[syntonic comma]]) and {{monzo\| 69 -1 -29 }} in the 5-limit; [[6144/6125]], 31104/30625, and 403368/390625 in the 7-limit, [[support]]ing the 7-limit [[mohajira]] temperament; [[540/539]], 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[Didymus rank three family #Terpsichore\|terpsichore]] temperament; [[144/143]], [[196/195]], [[364/363]], 729/715, and 3146/3125 in the 13-limit.

	Using the 117d val, it tempers out [[126/125]], [[225/224]], and {{monzo\| 29 3 0 -12 }} in the 7-limit; [[99/98]], [[176/175]], [[441/440]], and 12582912/12400927 in the 11-limit; 144/143, [[640/637]], 648/637, [[1001/1000]], and 43940/43923 in the 13-limit, supporting the 13-limit [[grosstone]] temperament.		Using the 117d val, it tempers out [[126/125]], [[225/224]], and {{monzo\| 29 3 0 -12 }} in the 7-limit; [[99/98]], [[176/175]], [[441/440]], and 12582912/12400927 in the 11-limit; 144/143, [[640/637]], 648/637, [[1001/1000]], and [[Kuragesma\|43940/43923]] in the 13-limit, supporting the 13-limit [[grosstone]] temperament.

	Using the 117ce val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo\| -31 24 -3 }} in the 5-limit; [[2401/2400]], 3645/3584, and [[4375/4374]] in the 7-limit; [[243/242]], 441/440, and 1815/1792 in the 11-limit; [[105/104]], [[275/273]], [[1287/1280]], and 2025/2002 in the 13-limit.		Using the 117ce val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo\| -31 24 -3 }} in the 5-limit; [[2401/2400]], 3645/3584, and [[4375/4374]] in the 7-limit; [[243/242]], 441/440, and 1815/1792 in the 11-limit; [[105/104]], [[275/273]], [[1287/1280]], and 2025/2002 in the 13-limit.

ArrowHead294 at 16:36, 20 February 2025

2025-02-20T16:36:38Z

← Older revision		Revision as of 16:36, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|117~~}}		{{ED intro}}

	117edo is in[[consistent]] to the [[5-odd-limit]] and higher odd limits, with four mappings possible for the [[11-limit]]: {{val\| 117 185 272 328 405 }} ([[patent val]]), {{val\| 117 186 '''272''' 329 '''405''' }} (117bd), {{val\| 117 185 '''271''' 328 '''404''' }} (117ce), and {{val\| 117 185 272 '''329''' 405 }} (117d).		117edo is in[[consistent]] to the [[5-odd-limit]] and higher odd limits, with four mappings possible for the [[11-limit]]: {{val\| 117 185 272 328 405 }} ([[patent val]]), {{val\| 117 186 '''272''' 329 '''405''' }} (117bd), {{val\| 117 185 '''271''' 328 '''404''' }} (117ce), and {{val\| 117 185 272 '''329''' 405 }} (117d).

BudjarnLambeth: Add section about octave stretch

2024-12-13T07:27:34Z

Add section about octave stretch

← Older revision		Revision as of 07:27, 13 December 2024
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	== Odd harmonics ==		== Odd harmonics ==
	{{Harmonics in equal\|117}}		{{Harmonics in equal\|117}}

			== Octave stretch ==
			117edo’s approximations of 3/1, 5/1, 7/1 and 17/1 are all noticeably improved by [[Gallery of arithmetic pitch sequences#APS of hekts\|APS7hekt]], a [[Octave shrinking\|compressed-octave]] version of 117edo. The trade-off is an unnoticeably worse 2/1 and 11/1, but noticeably worse 13/1.

			There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used for this same purpose: 696zpi, 697zpi, 698zpi, 699zpi, 700zpi, 701zpi and 702zpi.

			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 ==

BudjarnLambeth: +collapsed interval table

2024-10-02T12:45:03Z

+collapsed interval table

← Older revision		Revision as of 12:45, 2 October 2024
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	Using the 117bd val, it tempers out 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| 34 -17 -3 }} in the 5-limit; [[245/243]], [[3136/3125]], and 51200/50421 in the 7-limit; 176/175, 1232/1215, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], 640/637, [[832/825]], and 3200/3159 in the 13-limit.		Using the 117bd val, it tempers out 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| 34 -17 -3 }} in the 5-limit; [[245/243]], [[3136/3125]], and 51200/50421 in the 7-limit; 176/175, 1232/1215, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], 640/637, [[832/825]], and 3200/3159 in the 13-limit.

	=== Odd harmonics ===		== Odd harmonics ==
	{{Harmonics in equal\|117}}		{{Harmonics in equal\|117}}

	=== Subsets and supersets ===		== Subsets and supersets ==
	Since 117 factors into {{factorization\|117}}, 117edo has subset edos {{EDOs\| 3, 9, 13, and 39 }}. [[234edo]], which doubles it, provides a correction for the approximation to harmonic 3.		Since 117 factors into {{factorization\|117}}, 117edo has subset edos {{EDOs\| 3, 9, 13, and 39 }}. [[234edo]], which doubles it, provides a correction for the approximation to harmonic 3.

			== Intervals ==
			{{Interval table}}

Fredg999: Internal links

2024-07-06T16:58:59Z

Internal links

← Older revision		Revision as of 16:58, 6 July 2024
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	Using the 117ce val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo\| -31 24 -3 }} in the 5-limit; [[2401/2400]], 3645/3584, and [[4375/4374]] in the 7-limit; [[243/242]], 441/440, and 1815/1792 in the 11-limit; [[105/104]], [[275/273]], [[1287/1280]], and 2025/2002 in the 13-limit.		Using the 117ce val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo\| -31 24 -3 }} in the 5-limit; [[2401/2400]], 3645/3584, and [[4375/4374]] in the 7-limit; [[243/242]], 441/440, and 1815/1792 in the 11-limit; [[105/104]], [[275/273]], [[1287/1280]], and 2025/2002 in the 13-limit.

	Using the 117bd val, it tempers out 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| 34 -17 -3 }} in the 5-limit; [[245/243]], [[3136/3125]], and 51200/50421 in the 7-limit; 176/175, 1232/1215, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], 640/637, 832/825, and 3200/3159 in the 13-limit.		Using the 117bd val, it tempers out 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| 34 -17 -3 }} in the 5-limit; [[245/243]], [[3136/3125]], and 51200/50421 in the 7-limit; 176/175, 1232/1215, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], 640/637, [[832/825]], and 3200/3159 in the 13-limit.

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

FloraC: +subsets and supersets

2024-06-04T06:03:45Z

+subsets and supersets

← Older revision		Revision as of 06:03, 4 June 2024
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|117}}		{{Harmonics in equal\|117}}

			=== Subsets and supersets ===
			Since 117 factors into {{factorization\|117}}, 117edo has subset edos {{EDOs\| 3, 9, 13, and 39 }}. [[234edo]], which doubles it, provides a correction for the approximation to harmonic 3.

FloraC: Cleanup and group the vals by similarity

2024-06-04T05:59:41Z

Cleanup and group the vals by similarity

← Older revision		Revision as of 05:59, 4 June 2024
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	{{EDO intro\|117}}		{{EDO intro\|117}}

	~~== Theory ==~~		117edo is in[[consistent]] to the [[5-odd-limit]] and higher odd limits, with four mappings possible for the [[11-limit]]: {{val\| 117 185 272 328 405 }} ([[patent val]]), {{val\| 117 186 '''272''' 329 '''405''' }} (117bd), {{val\| 117 185 '''271''' 328 '''404''' }} (117ce), and {{val\| 117 185 272 '''329''' 405 }} (117d).
	117edo is in[[consistent]] to the 5-odd-limit and higher odd limits, with four mappings possible for the 11-limit: {{val\| 117 185 272 328 405 }} ([[patent val]]), {{val\| 117 186 272 329 405 }} (117bd), {{val\| 117 185 271 328 404 }} (117ce), and {{val\| 117 185 272 329 405 }} (117d).

	~~=== Commas ===~~		Using the patent val, it [[tempering out\|tempers out]] 81/80 ([[syntonic comma]]) and {{monzo\| 69 -1 -29 }} in the 5-limit; [[6144/6125]], 31104/30625, and 403368/390625 in the 7-limit, [[support]]ing the 7-limit [[mohajira]] temperament; [[540/539]], 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[Didymus rank three family #Terpsichore\|terpsichore]] temperament; [[144/143]], [[196/195]], [[364/363]], 729/715, and 3146/3125 in the 13-limit.
	Using the patent val, it tempers out ~~the syntonic comma~~ ([[~~81/80~~]]) and {{monzo\| 69 -1 -29 }} in the 5-limit; 6144/6125, 31104/30625, and 403368/390625 in the 7-limit, ~~supporting~~ the 7-limit [[mohajira]] temperament; 540/539, 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[Didymus rank three family\|terpsichore]] temperament; 144/143, 196/195, 364/363, 729/715, and 3146/3125 in the 13-limit.

	Using the ~~117bd~~ val, it tempers out ~~the kleisma (~~[[~~15625~~/~~15552~~]]~~) and 17179869184/16142520375 in the 5-limit; 245/243~~, ~~3136~~/~~3125~~, and ~~51200/50421~~ in the 7-limit; 176/175, ~~1232~~/~~1215, 1375/1372~~, and ~~2560~~/~~2541~~ in the 11-limit; ~~169~~/~~168~~, ~~364~~/~~363~~, ~~640~~/637, ~~832~~/~~825~~, and ~~3200~~/~~3159~~ in the 13-limit.		Using the 117d val, it tempers out [[126/125]], [[225/224]], and {{monzo\| 29 3 0 -12 }} in the 7-limit; [[99/98]], [[176/175]], [[441/440]], and 12582912/12400927 in the 11-limit; 144/143, [[640/637]], 648/637, [[1001/1000]], and 43940/43923 in the 13-limit, supporting the 13-limit [[grosstone]] temperament.

	Using the 117ce val, it tempers out ~~the magic comma~~ ([[~~3125/3072~~]]) and ~~282429536481/268435456000~~ in the 5-limit; 2401/2400, 3645/3584, and 4375/4374 in the 7-limit; 243/242, 441/440, and 1815/1792 in the 11-limit; 105/104, 275/273, 1287/1280, and 2025/2002 in the 13-limit.		Using the 117ce val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo\| -31 24 -3 }} in the 5-limit; [[2401/2400]], 3645/3584, and [[4375/4374]] in the 7-limit; [[243/242]], 441/440, and 1815/1792 in the 11-limit; [[105/104]], [[275/273]], [[1287/1280]], and 2025/2002 in the 13-limit.

	Using the ~~117d~~ val, it tempers out ~~126~~/~~125~~, ~~225~~/~~224~~, and ~~14495514624~~/~~13841287201~~ in the 7-limit; 99/98, ~~176~~/~~175~~, ~~441~~/~~440~~, and ~~12582912~~/~~12400927~~ in the 11-limit; ~~144~~/~~143~~, ~~640~~/~~637~~, ~~648~~/637, ~~1001~~/~~1000~~, and ~~43940~~/~~43923~~ in the 13-limit~~, supporting the 13-limit [[grosstone]] temperament~~.		Using the 117bd val, it tempers out 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| 34 -17 -3 }} in the 5-limit; [[245/243]], [[3136/3125]], and 51200/50421 in the 7-limit; 176/175, 1232/1215, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], 640/637, 832/825, and 3200/3159 in the 13-limit.

	=== ~~Harmonics~~ ===		=== Odd harmonics ===
	{{Harmonics in equal\|117}}		{{Harmonics in equal\|117}}

FloraC: Rework

2023-06-24T06:01:57Z

Rework

← Older revision		Revision as of 06:01, 24 June 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''117edo''' is the [[~~EDO\|~~equal division of the octave]] into~~ 117 ~~parts of 10.2564102564 [[cent]]s each.~~		{{EDO intro\|117}}

	It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 11-limit: <117 185 272 328 405\| (patent val), <117 186 272 329 405\| (117bd), <117 185 271 328 404\| (117ce), and <117 185 272 329 405\| (117d).

	== Theory ==		== Theory ==
			117edo is in[[consistent]] to the 5-odd-limit and higher odd limits, with four mappings possible for the 11-limit: {{val\| 117 185 272 328 405 }} ([[patent val]]), {{val\| 117 186 272 329 405 }} (117bd), {{val\| 117 185 271 328 404 }} (117ce), and {{val\| 117 185 272 329 405 }} (117d).

	=== Commas ===		=== Commas ===
	Using the patent val, it tempers out the [[syntonic comma]] (81/80) and \|69 -1 -29~~>~~ in the 5-limit; 6144/6125, 31104/30625, and 403368/390625 in the 7-limit, supporting the 7-limit [[~~Mohajira~~]] temperament; 540/539, 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the [[Didymus rank three family\|terpsichore ~~rank-3 temperament~~]]; 144/143, 196/195, 364/363, 729/715, and 3146/3125 in the 13-limit.		Using the patent val, it tempers out the syntonic comma ([[81/80]]) and {{monzo\| 69 -1 -29 }} in the 5-limit; 6144/6125, 31104/30625, and 403368/390625 in the 7-limit, supporting the 7-limit [[mohajira]] temperament; 540/539, 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[Didymus rank three family\|terpsichore]] temperament; 144/143, 196/195, 364/363, 729/715, and 3146/3125 in the 13-limit.

	Using the 117bd val, it tempers out the [[~~Kleismic family\|kleisma]],~~ 15625/15552 and 17179869184/16142520375 in the 5-limit; 245/243, 3136/3125, and 51200/50421 in the 7-limit; 176/175, 1232/1215, 1375/1372, and 2560/2541 in the 11-limit; 169/168, 364/363, 640/637, 832/825, and 3200/3159 in the 13-limit.		Using the 117bd val, it tempers out the kleisma ([[15625/15552]]) and 17179869184/16142520375 in the 5-limit; 245/243, 3136/3125, and 51200/50421 in the 7-limit; 176/175, 1232/1215, 1375/1372, and 2560/2541 in the 11-limit; 169/168, 364/363, 640/637, 832/825, and 3200/3159 in the 13-limit.

	Using the 117ce val, it tempers out the [[~~Magic family\|small diesis]],~~ 3125/3072 and 282429536481/268435456000 in the 5-limit; 2401/2400, 3645/3584, and 4375/4374 in the 7-limit; 243/242, 441/440, and 1815/1792 in the 11-limit; 105/104, 275/273, 1287/1280, and 2025/2002 in the 13-limit.		Using the 117ce val, it tempers out the magic comma ([[3125/3072]]) and 282429536481/268435456000 in the 5-limit; 2401/2400, 3645/3584, and 4375/4374 in the 7-limit; 243/242, 441/440, and 1815/1792 in the 11-limit; 105/104, 275/273, 1287/1280, and 2025/2002 in the 13-limit.

	Using the 117d val, it tempers out 126/125, 225/224, and 14495514624/13841287201 in the 7-limit; 99/98, 176/175, 441/440, and 12582912/12400927 in the 11-limit; 144/143, 640/637, 648/637, 1001/1000, and 43940/43923 in the 13-limit, supporting the 13-limit [[~~Grosstone~~]] temperament.		Using the 117d val, it tempers out 126/125, 225/224, and 14495514624/13841287201 in the 7-limit; 99/98, 176/175, 441/440, and 12582912/12400927 in the 11-limit; 144/143, 640/637, 648/637, 1001/1000, and 43940/43923 in the 13-limit, supporting the 13-limit [[grosstone]] temperament.

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|117}}		{{Harmonics in equal\|117}}
	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~

← Older revision		Revision as of 13:08, 27 August 2025
Line 4:		Line 4:
	117edo is in[[consistent]] to the [[5-odd-limit]] and higher odd limits, with four mappings possible for the [[11-limit]]: {{val\| 117 185 272 328 405 }} ([[patent val]]), {{val\| 117 186 '''272''' 329 '''405''' }} (117bd), {{val\| 117 185 '''271''' 328 '''404''' }} (117ce), and {{val\| 117 185 272 '''329''' 405 }} (117d).		117edo is in[[consistent]] to the [[5-odd-limit]] and higher odd limits, with four mappings possible for the [[11-limit]]: {{val\| 117 185 272 328 405 }} ([[patent val]]), {{val\| 117 186 '''272''' 329 '''405''' }} (117bd), {{val\| 117 185 '''271''' 328 '''404''' }} (117ce), and {{val\| 117 185 272 '''329''' 405 }} (117d).

	Using the patent val, it [[tempering out\|tempers out]] 81/80 ([[syntonic comma]]) and {{monzo\| 69 -1 -29 }} in the 5-limit; [[6144/6125]], 31104/30625, and 403368/390625 in the 7-limit, [[support]]ing the 7-limit [[mohajira]] temperament; [[540/539]], 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[~~Didymus rank three family #Terpsichore\|~~terpsichore]] temperament; [[144/143]], [[196/195]], [[364/363]], 729/715, and 3146/3125 in the 13-limit.		Using the patent val, it [[tempering out\|tempers out]] 81/80 ([[syntonic comma]]) and {{monzo\| 69 -1 -29 }} in the 5-limit; [[6144/6125]], 31104/30625, and 403368/390625 in the 7-limit, [[support]]ing the 7-limit [[mohajira]] temperament; [[540/539]], 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[terpsichore]] temperament; [[144/143]], [[196/195]], [[364/363]], 729/715, and 3146/3125 in the 13-limit.

	Using the 117d val, it tempers out [[126/125]], [[225/224]], and {{monzo\| 29 3 0 -12 }} in the 7-limit; [[99/98]], [[176/175]], [[441/440]], and 12582912/12400927 in the 11-limit; 144/143, [[640/637]], 648/637, [[1001/1000]], and [[Kuragesma\|43940/43923]] in the 13-limit, supporting the 13-limit [[grosstone]] temperament.		Using the 117d val, it tempers out [[126/125]], [[225/224]], and {{monzo\| 29 3 0 -12 }} in the 7-limit; [[99/98]], [[176/175]], [[441/440]], and 12582912/12400927 in the 11-limit; 144/143, [[640/637]], 648/637, [[1001/1000]], and [[Kuragesma\|43940/43923]] in the 13-limit, supporting the 13-limit [[grosstone]] temperament.

← Older revision		Revision as of 23:15, 15 April 2025
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	Using the patent val, it [[tempering out\|tempers out]] 81/80 ([[syntonic comma]]) and {{monzo\| 69 -1 -29 }} in the 5-limit; [[6144/6125]], 31104/30625, and 403368/390625 in the 7-limit, [[support]]ing the 7-limit [[mohajira]] temperament; [[540/539]], 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[Didymus rank three family #Terpsichore\|terpsichore]] temperament; [[144/143]], [[196/195]], [[364/363]], 729/715, and 3146/3125 in the 13-limit.		Using the patent val, it [[tempering out\|tempers out]] 81/80 ([[syntonic comma]]) and {{monzo\| 69 -1 -29 }} in the 5-limit; [[6144/6125]], 31104/30625, and 403368/390625 in the 7-limit, [[support]]ing the 7-limit [[mohajira]] temperament; [[540/539]], 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[Didymus rank three family #Terpsichore\|terpsichore]] temperament; [[144/143]], [[196/195]], [[364/363]], 729/715, and 3146/3125 in the 13-limit.

	Using the 117d val, it tempers out [[126/125]], [[225/224]], and {{monzo\| 29 3 0 -12 }} in the 7-limit; [[99/98]], [[176/175]], [[441/440]], and 12582912/12400927 in the 11-limit; 144/143, [[640/637]], 648/637, [[1001/1000]], and 43940/43923 in the 13-limit, supporting the 13-limit [[grosstone]] temperament.		Using the 117d val, it tempers out [[126/125]], [[225/224]], and {{monzo\| 29 3 0 -12 }} in the 7-limit; [[99/98]], [[176/175]], [[441/440]], and 12582912/12400927 in the 11-limit; 144/143, [[640/637]], 648/637, [[1001/1000]], and [[Kuragesma\|43940/43923]] in the 13-limit, supporting the 13-limit [[grosstone]] temperament.

	Using the 117ce val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo\| -31 24 -3 }} in the 5-limit; [[2401/2400]], 3645/3584, and [[4375/4374]] in the 7-limit; [[243/242]], 441/440, and 1815/1792 in the 11-limit; [[105/104]], [[275/273]], [[1287/1280]], and 2025/2002 in the 13-limit.		Using the 117ce val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo\| -31 24 -3 }} in the 5-limit; [[2401/2400]], 3645/3584, and [[4375/4374]] in the 7-limit; [[243/242]], 441/440, and 1815/1792 in the 11-limit; [[105/104]], [[275/273]], [[1287/1280]], and 2025/2002 in the 13-limit.