3178edo - Revision history

Francium: changed EDO intro to ED intro

2025-02-21T05:50:42Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:50, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	3178edo is quite accurate in the [[23-limit]], [[consistent]] to the [[27-odd-limit]], and has an exceptional approximation of [[harmonic]] [[13/1\|13]]. However, like most edos of this size, it is rather impractical to use. It [[tempering out\|tempers out]] several of the smaller 23-limit [[superparticular ratio\|superparticular commas]], including [[9801/9800]] in the 11-limit; [[10648/10647]] and [[123201/123200]] in the 13-limit; [[5832/5831]], [[14400/14399]], and [[28561/28560]] in the 17-limit; [[6175/6174]], 10830/10829, 12636/12635, 14080/14079, 14365/14364, 23409/23408, 28900/28899, and 43681/43680 in the 19-limit; 8625/8624, 11271/11270, 12168/12167 and 43264/43263 in the 23-limit.		3178edo is quite accurate in the [[23-limit]], [[consistent]] to the [[27-odd-limit]], and has an exceptional approximation of [[harmonic]] [[13/1\|13]]. However, like most edos of this size, it is rather impractical to use. It [[tempering out\|tempers out]] several of the smaller 23-limit [[superparticular ratio\|superparticular commas]], including [[9801/9800]] in the 11-limit; [[10648/10647]] and [[123201/123200]] in the 13-limit; [[5832/5831]], [[14400/14399]], and [[28561/28560]] in the 17-limit; [[6175/6174]], 10830/10829, 12636/12635, 14080/14079, 14365/14364, 23409/23408, 28900/28899, and 43681/43680 in the 19-limit; 8625/8624, 11271/11270, 12168/12167 and 43264/43263 in the 23-limit.

FloraC: +subsets and supersets

2025-01-12T10:46:40Z

+subsets and supersets

← Older revision		Revision as of 10:46, 12 January 2025
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|3178}}		{{Harmonics in equal\|3178}}

			=== Subsets and supersets ===
			Since 3178 factors into 2 × 7 × 227, 3178edo has subset edos {{EDOs\| 2, 7, 14, 227, 454, and 1589 }}.

FloraC: Expand with more commas

2025-01-12T10:44:08Z

Expand with more commas

← Older revision		Revision as of 10:44, 12 January 2025
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	{{EDO intro}}		{{EDO intro}}

	~~This edo~~ is quite accurate in the [[23-limit]] and has an exceptional approximation of [[harmonic]] [[13/1\|13]]. However, like most edos of this size, it is rather impractical to use. It tempers out several of the smaller 23-limit [[~~Superparticular~~ ratio\|superparticular commas]], including [[~~28561~~/~~28560~~]], [[~~28900~~/~~28899~~]], [[~~43264~~/~~43263~~]], and [[43681/43680]].		3178edo is quite accurate in the [[23-limit]], [[consistent]] to the [[27-odd-limit]], and has an exceptional approximation of [[harmonic]] [[13/1\|13]]. However, like most edos of this size, it is rather impractical to use. It [[tempering out\|tempers out]] several of the smaller 23-limit [[superparticular ratio\|superparticular commas]], including [[9801/9800]] in the 11-limit; [[10648/10647]] and [[123201/123200]] in the 13-limit; [[5832/5831]], [[14400/14399]], and [[28561/28560]] in the 17-limit; [[6175/6174]], 10830/10829, 12636/12635, 14080/14079, 14365/14364, 23409/23408, 28900/28899, and 43681/43680 in the 19-limit; 8625/8624, 11271/11270, 12168/12167 and 43264/43263 in the 23-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|3178}}		{{Harmonics in equal\|3178}}

FloraC: Cleanup

2024-08-03T08:18:38Z

Cleanup

← Older revision		Revision as of 08:18, 3 August 2024
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	{{EDO intro}}		{{EDO intro}}

	~~== Theory ==~~		This edo is quite accurate in the [[23-limit]] and has an exceptional approximation of [[harmonic]] [[13/1\|13]]. However, like most edos of this size, it is rather impractical to use. It tempers out several of the smaller 23-limit [[Superparticular ratio\|superparticular commas]], including [[28561/28560]], [[28900/28899]], [[43264/43263]], and [[43681/43680]].
	This ~~[[EDO\|~~edo]] is quite accurate in the [[23-limit]] and has an exceptional approximation of harmonic 13. However, like most edos of this size, it's rather impractical to use. It tempers out several of the smaller 23-limit [[Superparticular ratio\|superparticular commas]], including [[28561/28560]], [[28900/28899]], [[43264/43263]], and [[43681/43680]].
			=== Prime harmonics ===
	{{Harmonics in equal\|3178}}		{{Harmonics in equal\|3178}}

Tristanbay: /* Theory */Added 3178edo

2024-08-02T22:56:22Z

Theory: Added 3178edo

New page

{{Infobox ET}}
{{EDO intro}}

== Theory ==
This [[EDO|edo]] is quite accurate in the [[23-limit]] and has an exceptional approximation of harmonic 13. However, like most edos of this size, it's rather impractical to use. It tempers out several of the smaller 23-limit [[Superparticular ratio|superparticular commas]], including [[28561/28560]], [[28900/28899]], [[43264/43263]], and [[43681/43680]].
{{Harmonics in equal|3178}}