20567edo - Revision history

FloraC: 79-limit vs 81-odd-limit

2026-02-02T19:01:55Z

79-limit vs 81-odd-limit

← Older revision		Revision as of 19:01, 2 February 2026
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	20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.		20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.

	~~Despite inconsistencies~~, it can be used all the way to the no-61 [[~~81-odd~~-limit]], ~~of which~~ the only inconsistent intervals ~~are~~ 81/47, 81/55, 81/59, 81/67, 63/47, 63/55, 63/59, 67/63, 67/49, 59/41, 59/42, 59/49, 59/51, 59/54, and [[octave complement]]~~<nowiki/>~~s.		Although [[prime interval\|prime]] [[61/1\|61]] is poorly approximated, the next four primes are fairly accurate, so it can be used all the way to the no-61 [[79-limit]], with the only inconsistent intervals in the no-61 81-odd-limit being 81/47, 81/55, 81/59, 81/67, 63/47, 63/55, 63/59, 67/63, 67/49, 59/41, 59/42, 59/49, 59/51, 59/54, and their [[octave complement]]s.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20567\|columns=11}}		{{Harmonics in equal\|20567\|columns=11}}
	{{Harmonics in equal\|20567\|columns=11\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}		{{Harmonics in equal\|20567\|columns=11\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}

Eufalesio: I doubled checked that these are all the inconsistencies but ffs don't delete the entire thing if it has one mistake; build upon it instead

2026-01-31T00:13:07Z

I doubled checked that these are all the inconsistencies but ffs don't delete the entire thing if it has one mistake; build upon it instead

← Older revision		Revision as of 00:13, 31 January 2026
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	20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.		20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.

			Despite inconsistencies, it can be used all the way to the no-61 [[81-odd-limit]], of which the only inconsistent intervals are 81/47, 81/55, 81/59, 81/67, 63/47, 63/55, 63/59, 67/63, 67/49, 59/41, 59/42, 59/49, 59/51, 59/54, and [[octave complement]]<nowiki/>s.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20567\|columns=11}}		{{Harmonics in equal\|20567\|columns=11}}
	{{Harmonics in equal\|20567\|columns=11\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}		{{Harmonics in equal\|20567\|columns=11\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}

FloraC: 81/43 isn't inconsistent. There are other inconsistent pairs. Don't draw conclusions until you're sure of your result.

2026-01-30T12:48:08Z

81/43 isn't inconsistent. There are other inconsistent pairs. Don't draw conclusions until you're sure of your result.

← Older revision		Revision as of 12:48, 30 January 2026
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	20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.		20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.

	Despite inconsistencies, it can be used all the way to the no-61 [[81-odd-limit]], of which the only inconsistent intervals are 81/43, 81/59, 81/67, 63/47, 63/59, 67/63, 59/51, and [[octave complement]]<nowiki/>s.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20567\|columns=11}}		{{Harmonics in equal\|20567\|columns=11}}
	{{Harmonics in equal\|20567\|columns=11\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}		{{Harmonics in equal\|20567\|columns=11\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}

Eufalesio: Declared use in up to the 81-odd-limit, I don't know if those are all the inconsistent interval pairs

2026-01-30T11:54:37Z

Declared use in up to the 81-odd-limit, I don't know if those are all the inconsistent interval pairs

← Older revision		Revision as of 11:54, 30 January 2026
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	20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.		20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.

			Despite inconsistencies, it can be used all the way to the no-61 [[81-odd-limit]], of which the only inconsistent intervals are 81/43, 81/59, 81/67, 63/47, 63/59, 67/63, 59/51, and [[octave complement]]<nowiki/>s.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20567\|columns=11}}		{{Harmonics in equal\|20567\|columns=11}}
	{{Harmonics in equal\|20567\|columns=11\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}		{{Harmonics in equal\|20567\|columns=11\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}

Overthink: Undo revision 220571 by Overthink (talk) wait they're actually needed in case the default changes

2026-01-05T03:11:26Z

Undo revision 220571 by Overthink (talk) wait they're actually needed in case the default changes

← Older revision		Revision as of 03:11, 5 January 2026
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20567}}		{{Harmonics in equal\|20567\|columns=11}}
	{{Harmonics in equal\|20567\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}		{{Harmonics in equal\|20567\|columns=11\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}

FloraC: Fixed and thanks cuz we don't need it here

2026-01-02T13:43:20Z

Fixed and thanks cuz we don't need it here

← Older revision		Revision as of 13:43, 2 January 2026
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	{{Infobox ET\|Consistency=57\|Distinct consistency=57}}		{{Infobox ET\|Consistency=57\|Distinct consistency=57}}
	{{ED intro}}		{{ED intro}}

	~~== Theory ==~~

	20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.		20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.
Line 9:		Line 7:
	{{Harmonics in equal\|20567}}		{{Harmonics in equal\|20567}}
	{{Harmonics in equal\|20567\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}		{{Harmonics in equal\|20567\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}

	~~== Approximation to JI ==~~
	~~{{Q-odd-limit intervals\|20567\|57}}~~
	~~{{todo\|fix template\|inline=1\|text=The error seems to be due to the consistency only calculating to 43, while 20567edo has a higher consistency limit, causing an error.}}~~

Overthink: sectioning, note template broken

2026-01-02T05:32:41Z

sectioning, note template broken

← Older revision		Revision as of 05:32, 2 January 2026
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	{{Infobox ET\|Consistency=57\|Distinct consistency=57}}		{{Infobox ET\|Consistency=57\|Distinct consistency=57}}
	{{ED intro}}		{{ED intro}}

			== Theory ==

	20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.		20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.
Line 7:		Line 9:
	{{Harmonics in equal\|20567}}		{{Harmonics in equal\|20567}}
	{{Harmonics in equal\|20567\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}		{{Harmonics in equal\|20567\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}

			== Approximation to JI ==
			{{Q-odd-limit intervals\|20567\|57}}
			{{todo\|fix template\|inline=1\|text=The error seems to be due to the consistency only calculating to 43, while 20567edo has a higher consistency limit, causing an error.}}

Overthink: - redundant parameters

2026-01-02T05:11:24Z

- redundant parameters

← Older revision		Revision as of 05:11, 2 January 2026
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20567~~\|columns=11~~}}		{{Harmonics in equal\|20567}}
	{{Harmonics in equal\|20567~~\|columns=11~~\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}		{{Harmonics in equal\|20567\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}

Overthink: No need to columns=12 (83 and 89 are almost perfectly off, and 37 doesn't need to be in the first table

2026-01-02T05:10:29Z

No need to columns=12 (83 and 89 are almost perfectly off, and 37 doesn't need to be in the first table

← Older revision		Revision as of 05:10, 2 January 2026
Line 5:		Line 5:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20567\|columns=12}}		{{Harmonics in equal\|20567\|columns=11}}
	{{Harmonics in equal\|20567\|columns=12\|start=13\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}		{{Harmonics in equal\|20567\|columns=11\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}

Iwuqety: fix typo

2025-08-14T08:22:38Z

fix typo

← Older revision		Revision as of 08:22, 14 August 2025
Line 2:		Line 2:
	{{ED intro}}		{{ED intro}}

	20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]] ~~as all odd harmonics 57 and below,~~ , with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.		20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|20567\|columns=12}}		{{Harmonics in equal\|20567\|columns=12}}
	{{Harmonics in equal\|20567\|columns=12\|start=13\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}		{{Harmonics in equal\|20567\|columns=12\|start=13\|collapsed=1\|title=Approximation of prime harmonics in 20567edo (continued)}}