20203edo - Revision history

FloraC: Expand and simplify the comma basis

2025-10-02T19:02:23Z

Expand and simplify the comma basis

← Older revision		Revision as of 19:02, 2 October 2025
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	{{ED intro}}		{{ED intro}}

	20203edo is a very strong high-limit system, and specializes in the 17- and 19-limit, with a lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative ~~error~~]] than any smaller edo until [[102557edo\|102557]] and 128215, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower relative error than any smaller ~~distinctly consistent 41-limit patent val~~ except [[17461edo\|17461]]. ~~It tempers out~~ 47151/47150, 52326/52325, 69875/69874, 81796/81795, ~~111112~~/~~111111~~, ~~127281~~/~~127280~~, ~~156520~~/~~156519~~, ~~315495~~/~~315491, 395200~~/~~395199, 728365~~/~~728364, 1324323~~/~~1324300~~, ~~1518804~~/~~1518803~~, and ~~3845961~~/~~3845920~~ in the 43-limit.		20203edo is a very strong high-limit system, and specializes in the [[17-limit\|17-]] and [[19-limit]], with lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative errors]] than any smaller edo until [[102557edo\|102557]] and 128215, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower [[43-limit]] relative error than any smaller edo except for [[7361edo\|7361]], [[14348edo\|14348]] and [[17461edo\|17461]].

			A 43-limit [[comma basis]] for this temperament is {29792/29791, 32799/32798, 43264/43263, 45696/45695, 47151/47150, 52326/52325, 53361/53360, 69875/69874, 81796/81795, 83521/83520, 87465/87464, 96876/96875, 111112/111111}. In the [[13-limit]] it tempers out [[123201/123200]] and [[1990656/1990625]]; in the [[17-limit]] [[194481/194480]] and [[336141/336140]]; in the [[19-limit]] 89376/89375, 104976/104975, and 165376/165375; in the [[23-limit]] 43264/43263 and 52326/52325 among others.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20203\|columns=11}}		{{Harmonics in equal\|20203\|columns=11}}
	{{Harmonics in equal\|20203\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 20203edo (continued)}}		{{Harmonics in equal\|20203\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 20203edo (continued)}}

FloraC: Wrap the harmonics table

2025-10-02T15:43:01Z

Wrap the harmonics table

← Older revision		Revision as of 15:43, 2 October 2025
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20203\|columns=15}}		{{Harmonics in equal\|20203\|columns=11}}
			{{Harmonics in equal\|20203\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 20203edo (continued)}}

ArrowHead294 at 14:13, 20 February 2025

2025-02-20T14:13:27Z

← Older revision		Revision as of 14:13, 20 February 2025
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	{{Infobox ET\|Consistency=45\|Distinct consistency=45}}		{{Infobox ET\|Consistency=45\|Distinct consistency=45}}
	{{~~EDO~~ intro~~\|20203~~}}		{{ED intro}}

	20203edo is a very strong high-limit system, and specializes in the 17- and 19-limit, with a lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any smaller edo until [[102557edo\|102557]] and 128215, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except [[17461edo\|17461]]. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.		20203edo is a very strong high-limit system, and specializes in the 17- and 19-limit, with a lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any smaller edo until [[102557edo\|102557]] and 128215, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except [[17461edo\|17461]]. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.

FloraC: +link

2024-07-15T17:12:39Z

+link

← Older revision		Revision as of 17:12, 15 July 2024
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	{{EDO intro\|20203}}		{{EDO intro\|20203}}

	20203edo is a very strong high-limit system, and specializes in the 17- and 19-limit, with a lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any smaller edo until 102557 and 128215, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except [[17461edo\|17461]]. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.		20203edo is a very strong high-limit system, and specializes in the 17- and 19-limit, with a lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any smaller edo until [[102557edo\|102557]] and 128215, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except [[17461edo\|17461]]. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20203\|columns=15}}		{{Harmonics in equal\|20203\|columns=15}}

Aura at 23:28, 13 December 2023

2023-12-13T23:28:04Z

← Older revision		Revision as of 23:28, 13 December 2023
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20203}}		{{Harmonics in equal\|20203\|columns=15}}

BudjarnLambeth at 07:14, 9 July 2023

2023-07-09T07:14:57Z

← Older revision		Revision as of 07:14, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET\|Consistency=45\|Distinct consistency=45}}		{{Infobox ET\|Consistency=45\|Distinct consistency=45}}
	{{EDO intro\|20203}}		{{EDO intro\|20203}}

BudjarnLambeth at 04:10, 9 July 2023

2023-07-09T04:10:53Z

← Older revision		Revision as of 04:10, 9 July 2023
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	{{Infobox ET\|Consistency=45\|Distinct consistency=45}}		{{novelty}}{{stub}}{{Infobox ET\|Consistency=45\|Distinct consistency=45}}
	{{EDO intro\|20203}}		{{EDO intro\|20203}}

FloraC: Double checked the edos and found a typo

2023-02-19T13:01:10Z

Double checked the edos and found a typo

← Older revision		Revision as of 13:01, 19 February 2023
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	{{EDO intro\|20203}}		{{EDO intro\|20203}}

	20203edo is a very strong high-limit system, and specializes in the 17- and 19-limit, with a lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any smaller edo until 102557 and ~~128125~~, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except [[17461edo\|17461]]. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.		20203edo is a very strong high-limit system, and specializes in the 17- and 19-limit, with a lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any smaller edo until 102557 and 128215, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except [[17461edo\|17461]]. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20203}}		{{Harmonics in equal\|20203}}

FloraC: Notability in the 17-limit

2023-02-19T11:02:57Z

Notability in the 17-limit

← Older revision		Revision as of 11:02, 19 February 2023
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	{{EDO intro\|20203}}		{{EDO intro\|20203}}

	20203edo is a very strong high-limit ~~edo~~, with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any edo until 128125. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except [[17461edo\|17461]]. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.		20203edo is a very strong high-limit system, and specializes in the 17- and 19-limit, with a lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any smaller edo until 102557 and 128125, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except [[17461edo\|17461]]. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20203}}		{{Harmonics in equal\|20203}}

FloraC: Cleanup; -section title for now as there are no other sections

2023-02-14T10:45:20Z

Cleanup; -section title for now as there are no other sections

← Older revision		Revision as of 10:45, 14 February 2023
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	{{Infobox ET\|Consistency=45\|Distinct consistency=45}}		{{Infobox ET\|Consistency=45\|Distinct consistency=45}}
	{{EDO intro\|20203}}		{{EDO intro\|20203}}
	~~==Theory==~~
	20203edo is a very strong high limit edo, with a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] than any edo until 128125. It is also distinctly consistent through the [[45-odd-limit\|45-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except 17461. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.
	~~===Prime harmonics===~~
	~~{{harmonics in equal\|20203}}~~

	[[~~Category:Equal divisions of the octave~~\|~~#####~~]] <!-- 5-~~digit number~~ -->		20203edo is a very strong high-limit edo, with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any edo until 128125. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except [[17461edo\|17461]]. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.

			=== Prime harmonics ===
			{{Harmonics in equal\|20203}}

← Older revision		Revision as of 10:45, 14 February 2023
Line 1:		Line 1:
	{{Infobox ET\|Consistency=45\|Distinct consistency=45}}		{{Infobox ET\|Consistency=45\|Distinct consistency=45}}
	{{EDO intro\|20203}}		{{EDO intro\|20203}}
	~~==Theory==~~
	20203edo is a very strong high limit edo, with a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] than any edo until 128125. It is also distinctly consistent through the [[45-odd-limit\|45-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except 17461. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.
	~~===Prime harmonics===~~
	~~{{harmonics in equal\|20203}}~~

	[[~~Category:Equal divisions of the octave~~\|~~#####~~]] <!-- 5-~~digit number~~ -->		20203edo is a very strong high-limit edo, with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any edo until 128125. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except [[17461edo\|17461]]. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.

			=== Prime harmonics ===
			{{Harmonics in equal\|20203}}