157edt - Revision history

FloraC: +links

2025-04-18T13:17:59Z

+links

← Older revision		Revision as of 13:17, 18 April 2025
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	== Theory ==		== Theory ==
	157edt is related to [[99edo]], but with the 3/1 rather than the [[2/1]] being just. The octave is about 0.~~6781~~ cents ~~compressed~~. 157edt is [[consistent]] to the [[integer limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit. 157edt is notable for its excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.		157edt is related to [[99edo]], but with the 3/1 rather than the [[2/1]] being just. The octave is [[stretched and compressed tuning\|compressed]] by about 0.678 cents. 157edt is [[consistent]] to the [[integer limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit. 157edt is notable for its excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.

	=== Harmonics ===		=== Harmonics ===
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	* [[58edf]] – relative edf		* [[58edf]] – relative edf
	* [[99edo]] – relative edo		* [[99edo]] – relative edo
			* [[256ed6]] – relative ed6

FloraC: +subsets and supersets

2025-03-22T14:35:09Z

+subsets and supersets

← Older revision		Revision as of 14:35, 22 March 2025
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	{{Harmonics in equal\|157\|3\|1}}		{{Harmonics in equal\|157\|3\|1}}
	{{Harmonics in equal\|157\|3\|1\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 157edt (continued)}}		{{Harmonics in equal\|157\|3\|1\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 157edt (continued)}}

			=== Subsets and supersets ===
			157edt is the 37th [[prime equal division\|prime edt]]. It does not contain any nontrivial edts as subsets.

	== See also ==		== See also ==
	* [[58edf]] – relative edf		* [[58edf]] – relative edf
	* [[99edo]] – relative edo		* [[99edo]] – relative edo

FloraC: Cleanup

2025-03-22T14:33:37Z

Cleanup

← Older revision		Revision as of 14:33, 22 March 2025
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Edt\|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit\|10-integer-limit]]. 157edt is notable for it's excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.		{{ED intro}}

	== Harmonics ==		== Theory ==
	{{Harmonics in equal		157edt is related to [[99edo]], but with the 3/1 rather than the [[2/1]] being just. The octave is about 0.6781 cents compressed. 157edt is [[consistent]] to the [[integer limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit. 157edt is notable for its excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.
	\| ~~steps =~~ 157
	\| ~~num =~~ 3		=== Harmonics ===
	\| ~~denom =~~ 1		{{Harmonics in equal\|157\|3\|1}}
	}}		{{Harmonics in equal\|157\|3\|1\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 157edt (continued)}}
	{{Harmonics in equal
	\| ~~steps =~~ 157
	\| ~~num =~~ 3
	\| ~~denom~~ = 1
	\| start = 12
	\| collapsed = 1
	}}

	== See also ==		== See also ==
	* [[~~99edo~~]]		* [[58edf]] – relative edf
	* [[~~58edf]]~~		* [[99edo]] – relative edo

	~~[[Category:Edt]]~~
	~~[[Category:Edonoi]]~~
	~~[[Category:~~99edo]]

BudjarnLambeth at 10:18, 5 October 2024

2024-10-05T10:18:55Z

← Older revision		Revision as of 10:18, 5 October 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Edt\|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit\|10-integer-limit]]. 157edt is notable for it's excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.		'''[[Edt\|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit\|10-integer-limit]]. 157edt is notable for it's excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.

	~~== Intervals ==~~
	~~{{Interval table}}~~

	== Harmonics ==		== Harmonics ==

BudjarnLambeth: Intervals harmonics

2024-10-05T09:06:38Z

Intervals harmonics

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 '''[[Edt|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit|10-integer-limit]]. 157edt is notable for it's excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.
 == See also ==

CompactStar at 02:25, 5 October 2023

2023-10-05T02:25:14Z

← Older revision		Revision as of 02:25, 5 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Edt\|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit\|10-integer-limit]]. 157edt is notable for it's excellent 5/3 and can be used effectively both with and without twos.		'''[[Edt\|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit\|10-integer-limit]]. 157edt is notable for it's excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.

	== See also ==		== See also ==

CompactStar at 02:24, 5 October 2023

2023-10-05T02:24:58Z

← Older revision		Revision as of 02:24, 5 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''[[Edt\|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit\|10-integer-limit]].		'''[[Edt\|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit\|10-integer-limit]]. 157edt is notable for it's excellent 5/3 and can be used effectively both with and without twos.

	== See also ==		== See also ==

Plumtree: Infobox ET added

2022-10-05T20:48:16Z

Infobox ET added

← Older revision		Revision as of 20:48, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''[[Edt\|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit\|10-integer-limit]].		'''[[Edt\|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit\|10-integer-limit]].

FloraC: Cleanup

2020-09-03T05:47:44Z

Cleanup

← Older revision		Revision as of 05:47, 3 September 2020
Line 1:		Line 1:
	'''[[Edt\|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo~~\|99 edo~~]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit\|10-integer-limit]].		'''[[Edt\|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit\|10-integer-limit]].

			== See also ==
			* [[99edo]]
			* [[58edf]]

	[[Category:Edt]]		[[Category:Edt]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
			[[Category:99edo]]

Xenllium: Created page with "'''Division of the third harmonic into 157 equal parts''' (157EDT) is related to 99 edo, but with the 3/1 rather than the 2/1 being just. The octave is about..."

2019-04-19T10:50:40Z

Created page with "'''Division of the third harmonic into 157 equal parts''' (157EDT) is related to 99 edo, but with the 3/1 rather than the 2/1 being just. The octave is about..."

New page

'''[[Edt|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo|99 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit|10-integer-limit]].

[[Category:Edt]]
[[Category:Edonoi]]