58edf - Revision history

FloraC: Expand and +links

2025-04-18T13:20:22Z

Expand and +links

← Older revision		Revision as of 13:20, 18 April 2025
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	== Theory ==		== Theory ==
	58edf corresponds to 99.1517…edo. It is related to [[99edo]], but with the 3/2 rather than the [[2/1]] being just. The octave is about 1.~~8354~~ cents ~~compressed~~. 58edf is [[consistent]] to the [[integer limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit.		58edf corresponds to 99.1517…edo. It is related to [[99edo]], but with the [[3/2\|perfect fifth]] rather than the [[2/1\|octave]] being just. The octave is [[stretched and compressed tuning\|compressed]] by about 1.84 cents. 58edf is [[consistent]] to the [[integer limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit. 58edf has a flat tendency, with [[prime harmonic]]s 2, [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] all tuned flat of just.

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|58\|3\|2}}		{{Harmonics in equal\|58\|3\|2\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|58\|3\|2\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 58edf (continued)}}		{{Harmonics in equal\|58\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 58edf (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 58 factors into primes as {{nowrap\| 2 × 29 }}, 58edf contains [[2edf]] and [[29edf]] as ~~subsets~~.		Since 58 factors into primes as {{nowrap\| 2 × 29 }}, 58edf contains [[2edf]] and [[29edf]] as subset edts.

	== See also ==		== See also ==
	* [[99edo]] – relative edo		* [[99edo]] – relative edo
	* [[157edt]] – relative edt		* [[157edt]] – relative edt
			* [[256ed6]] – relative ed6

FloraC: -unuseful table. The interval table of 99edo already covers both sharp and flat mappings

2025-03-22T14:40:24Z

-unuseful table. The interval table of 99edo already covers both sharp and flat mappings

Show changes

FloraC: /* Theory */ +subsets and supersets

2025-03-22T14:39:33Z

Theory: +subsets and supersets

← Older revision		Revision as of 14:39, 22 March 2025
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	{{Harmonics in equal\|58\|3\|2}}		{{Harmonics in equal\|58\|3\|2}}
	{{Harmonics in equal\|58\|3\|2\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 58edf (continued)}}		{{Harmonics in equal\|58\|3\|2\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 58edf (continued)}}

			=== Subsets and supersets ===
			Since 58 factors into primes as {{nowrap\| 2 × 29 }}, 58edf contains [[2edf]] and [[29edf]] as subsets.

	== Intervals ==		== Intervals ==

FloraC: Cleanup

2025-03-22T14:38:20Z

Cleanup

← Older revision		Revision as of 14:38, 22 March 2025
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[EDF\|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). It is consistent to the 12-[[integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit.		{{ED intro}}

	== Harmonics ==		== Theory ==
	{{Harmonics in equal\|58\|3\|2\|~~intervals~~=~~prime~~}}		58edf corresponds to 99.1517…edo. It is related to [[99edo]], but with the 3/2 rather than the [[2/1]] being just. The octave is about 1.8354 cents compressed. 58edf is [[consistent]] to the [[integer limit\|12-integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit.

			=== Harmonics ===
			{{Harmonics in equal\|58\|3\|2}}
			{{Harmonics in equal\|58\|3\|2\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 58edf (continued)}}

	== Intervals ==		== Intervals ==
Line 627:		Line 631:

	== See also ==		== See also ==
	* [[99edo]]		* [[99edo]] – relative edo
	* [[157edt]]		* [[157edt]] – relative edt

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

BudjarnLambeth: Fix misleading links

2024-12-18T04:24:11Z

Fix misleading links

← Older revision		Revision as of 04:24, 18 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[EDF\|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). 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]].		'''[[EDF\|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). It is consistent to the 12-[[integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit.

	== Harmonics ==		== Harmonics ==

BudjarnLambeth: Add harmonics table

2024-12-18T03:37:02Z

Add harmonics table

← Older revision		Revision as of 03:37, 18 December 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''[[EDF\|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). 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]].		'''[[EDF\|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). 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]].

			== Harmonics ==
			{{Harmonics in equal\|58\|3\|2\|intervals=prime}}

	== Intervals ==		== Intervals ==

BudjarnLambeth: /* Intervals */ replace plain todo text with todo template

2024-12-18T03:33:40Z

Intervals: replace plain todo text with todo template

← Older revision		Revision as of 03:33, 18 December 2024
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	== Intervals ==		== Intervals ==
	''todo: mapping for 11 and 13 should differ from 99edo''		{{todo\|inline=1\|complete table\|text=The [[mapping]] for 11 and 13 should differ from [[99edo]].}}

	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-

Plumtree: Infobox ET added

2022-10-05T18:51:49Z

Infobox ET added

← Older revision		Revision as of 18:51, 5 October 2022
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			{{Infobox ET}}
	'''[[EDF\|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). 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]].		'''[[EDF\|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). 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

2020-09-03T05:46:24Z

Cleanup

← Older revision		Revision as of 05:46, 3 September 2020
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	'''[[EDF\|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo~~\|99 edo~~]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). 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]].		'''[[EDF\|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). 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]].

	~~Lookalikes: [[99edo]], [[157edt]]~~

	== Intervals ==		== Intervals ==
			''todo: mapping for 11 and 13 should differ from 99edo''
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! \|Degrees		! Degrees
	! \|Cents Value		! Cents Value
	!Five limit		! Five limit
	!Seven limit		! Seven limit
	!Eleven limit		! Eleven limit
	!Thirteen limit		! Thirteen limit
	\|-		\|-
	\| \|1		\| \|1
Line 621:		Line 620:
	\| colspan="4" \|9/4		\| colspan="4" \|9/4
	\|}		\|}

			== See also ==
			* [[99edo]]
			* [[157edt]]

	[[Category:Edf]]		[[Category:Edf]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
			[[Category:99edo]]

Moremajorthanmajor at 22:47, 19 August 2019

2019-08-19T22:47:10Z

← Older revision		Revision as of 22:47, 19 August 2019
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	! \|Degrees		! \|Degrees
	! \|Cents Value		! \|Cents Value
	\|Five limit		!Five limit
	\|Seven limit		!Seven limit
	\|Eleven limit		!Eleven limit
	\|Thirteen limit		!Thirteen limit
	\|-		\|-
	\| \|1		\| \|1