139ed5 - Revision history

FloraC: /* Theory */ expand a bit

2025-05-28T12:50:31Z

Theory: expand a bit

← Older revision		Revision as of 12:50, 28 May 2025
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	== Theory ==		== Theory ==
	139ed5 is similar to [[60edo]], but with the 5th harmonic being [[just]], instead of the [[2/1\|octave]] being just. The octave is [[stretched and compressed tuning\|stretched]] by about 2.73 cents.		139ed5 is similar to [[60edo]], but with the 5th harmonic being [[just]], instead of the [[2/1\|octave]] being just. The octave is [[stretched and compressed tuning\|stretched]] by about 2.73 cents. Like 60edo, 139ed5 is [[consistent]] to the [[integer limit\|10-integer-limit]].

	On the harmonics 2, [[3/1\|3]], 5, 7, 11, 60edo has 0%, 10%, 32%, 44% and 43% relative error. On those same harmonics, 139ed5 has 14%, 12%, 0%, 6% and 10% relative error. This is a large improvement relative to the step size of the tuning, and is the main reason why a composer might choose to use 139ed5.		On the harmonics 2, [[3/1\|3]], 5, [[7/1\|7]], [[11/1\|11]], 60edo has 0%, -10%, -32%, -44% and +43% relative error. On those same harmonics, 139ed5 has +14%, +12%, 0%, -6% and -10% relative error. This is a large improvement relative to the step size of the tuning if the focus is on the higher [[prime harmonic\|primes]], and is the main reason why a composer might choose to use 139ed5.

	=== Harmonics ===		=== Harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	139ed5 is the 34th [[prime equal division\|prime ed5]]. It does not contain any nontrivial subset ed5's.		139ed5 is the 34th [[prime equal division\|prime ed5]]. It does not contain any nontrivial subset ed5's.

	== Intervals ==		== Intervals ==

FloraC: +subsets and supersets; +see also

2025-05-28T12:46:10Z

+subsets and supersets; +see also

← Older revision		Revision as of 12:46, 28 May 2025
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	{{Harmonics in equal\|139\|5\|1\|intervals=integer\|columns=11}}		{{Harmonics in equal\|139\|5\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|139\|5\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 139ed5 (continued)}}		{{Harmonics in equal\|139\|5\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 139ed5 (continued)}}

			=== Subsets and supersets ===
			139ed5 is the 34th [[prime equal division\|prime ed5]]. It does not contain any nontrivial subset ed5's.

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

			== See also ==
			* [[35edf]] – relative edf
			* [[60edo]] – relative edo
			* [[95edt]] – relative edt
			* [[155edt]] – relative ed6


	[[Category:60edo]]		[[Category:60edo]]

FloraC: Cleanup

2025-05-28T12:41:29Z

Cleanup

← Older revision		Revision as of 12:41, 28 May 2025
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	{{ED intro}}		{{ED intro}}

	It is similar to [[60edo]], but with the ~~octave (2/1)~~ being [[~~octave stretch\|stretched~~]] ~~by about 2.7 cents~~, ~~and with~~ the ~~interval~~ [[5/1]] being [[~~just~~]]~~, instead of~~ 2~~/1 being just~~.		== Theory ==
			139ed5 is similar to [[60edo]], but with the 5th harmonic being [[just]], instead of the [[2/1\|octave]] being just. The octave is [[stretched and compressed tuning\|stretched]] by about 2.73 cents.

	~~== Harmonics ==~~		On the harmonics 2, [[3/1\|3]], 5, 7, 11, 60edo has 0%, 10%, 32%, 44% and 43% relative error. On those same harmonics, 139ed5 has 14%, 12%, 0%, 6% and 10% relative error. This is a large improvement relative to the step size of the tuning, and is the main reason why a composer might choose to use 139ed5.
	On harmonics 2.3.5.7.11, 60edo has 0%, 10%, 32%, 44% and 43% relative error.

	~~On those same harmonics, 139ed5 has 14%, 12%, 0%, 6% and 10% relative error.~~		=== Harmonics ===
			{{Harmonics in equal\|139\|5\|1\|intervals=integer\|columns=11}}
	~~This is a large improvement relative to the step size of the tuning, and is the main reason why a composer might choose to use 139ed5.~~		{{Harmonics in equal\|139\|5\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 139ed5 (continued)}}
	{{Harmonics in equal\|139\|5\|1\|intervals=~~prime~~}}


	~~60edo for comparison:~~
	{{Harmonics in equal\|60\|2\|1\|intervals=~~prime~~}}

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

	~~{{todo\|expand}}~~
	[[Category:60edo]]		[[Category:60edo]]

BudjarnLambeth: Expanded stub

2025-01-07T07:56:04Z

Expanded stub

← Older revision		Revision as of 07:56, 7 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

			It is similar to [[60edo]], but with the octave (2/1) being [[octave stretch\|stretched]] by about 2.7 cents, and with the interval [[5/1]] being [[just]], instead of 2/1 being just.

			== Harmonics ==
			On harmonics 2.3.5.7.11, 60edo has 0%, 10%, 32%, 44% and 43% relative error.

			On those same harmonics, 139ed5 has 14%, 12%, 0%, 6% and 10% relative error.

			This is a large improvement relative to the step size of the tuning, and is the main reason why a composer might choose to use 139ed5.
			{{Harmonics in equal\|139\|5\|1\|intervals=prime}}


			60edo for comparison:
			{{Harmonics in equal\|60\|2\|1\|intervals=prime}}

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

	~~==== Odd harmonics ====~~		{{todo\|expand}}
	{{~~Harmonics in equal~~\|~~139\|5\|1~~}}		[[Category:60edo]]


	~~{{Stub}}~~

BudjarnLambeth: Subheading

2024-12-25T18:48:50Z

Subheading

← Older revision		Revision as of 18:48, 25 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

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

MisterShafXen at 14:25, 25 December 2024

2024-12-25T14:25:16Z

← Older revision		Revision as of 14:25, 25 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}
			{{Interval table}}

	==== Odd harmonics ====		==== Odd harmonics ====

BudjarnLambeth: Intro harmonics stub

2024-12-14T21:56:26Z

Intro harmonics stub

← Older revision		Revision as of 21:56, 14 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
			{{ED intro}}

			==== Odd harmonics ====
			{{Harmonics in equal\|139\|5\|1}}


			{{Stub}}

MisterShafXen: Created page with "{{Infobox ET}}"

2024-12-14T14:05:57Z

Created page with "{{Infobox ET}}"

New page