BudjarnLambeth/Ed257/128 - Revision history

BudjarnLambeth: {{Editable user page}}

2025-05-18T02:59:18Z

← Older revision		Revision as of 02:59, 18 May 2025
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			{{Editable user page}}

	An '''equal division of reduced harmonic 257''' ('''ed257/128''') is an [[equal-step tuning]] in which the [[4/1\|4ve]]-reduced 257th harmonic ([[257/128]]) is [[Just intonation\|justly tuned]] and is divided in a given number of equal steps. 257/128 is very close to the [[octave]], 2/1, but it is slightly sharper. This makes it suitable as an alternative to edos whose consonances are too flat, such as [[7edo]].		An '''equal division of reduced harmonic 257''' ('''ed257/128''') is an [[equal-step tuning]] in which the [[4/1\|4ve]]-reduced 257th harmonic ([[257/128]]) is [[Just intonation\|justly tuned]] and is divided in a given number of equal steps. 257/128 is very close to the [[octave]], 2/1, but it is slightly sharper. This makes it suitable as an alternative to edos whose consonances are too flat, such as [[7edo]].

BudjarnLambeth: BudjarnLambeth moved page Ed257/128 to BudjarnLambeth/Ed257/128

2025-05-18T02:51:19Z

BudjarnLambeth moved page Ed257/128 to BudjarnLambeth/Ed257/128

← Older revision	Revision as of 02:51, 18 May 2025
(No difference)

BudjarnLambeth at 13:05, 13 December 2024

2024-12-13T13:05:17Z

← Older revision		Revision as of 13:05, 13 December 2024
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	Ed257/128s really only make sense for that purpose with 65 or fewer tones per [[pseudo-octave]]. With more tones than that, the relative error on 2/1 becomes unacceptably high and it makes more sense to switch to a different tuning like a [[zpi]] or ed513/256.		Ed257/128s really only make sense for that purpose with 65 or fewer tones per [[pseudo-octave]]. With more tones than that, the relative error on 2/1 becomes unacceptably high and it makes more sense to switch to a different tuning like a [[zpi]] or ed513/256.

			Ed257/128s are the complementary opposite of [[ed255/128]]s.

	== 7ed257/128 ==		== 7ed257/128 ==
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	== Related concepts ==		== Related concepts ==
	* [[Ed255/128]]
	* [[Substitute harmonic]]		* [[Substitute harmonic]]
	* [[Equal-step tuning]]		* [[Equal-step tuning]]

	[[Category:Edonoi]][[Category:7edo]][[Category:7-tone scales]]		[[Category:Edonoi]][[Category:7edo]][[Category:7-tone scales]]

BudjarnLambeth at 13:00, 13 December 2024

2024-12-13T13:00:47Z

← Older revision		Revision as of 13:00, 13 December 2024
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	An '''equal division of reduced harmonic 257''' ('''ed257/128''') is an [[equal-step tuning]] in which the [[4/1\|4ve]]-reduced 257th harmonic ([[257/128]]) is [[Just intonation\|justly tuned]] and is divided in a given number of equal steps. 257/128 is very close to the [[octave]], 2/1, but it is slightly sharper. This makes it suitable as an alternative to edos whose consonances are too flat, such as [[7edo]].		An '''equal division of reduced harmonic 257''' ('''ed257/128''') is an [[equal-step tuning]] in which the [[4/1\|4ve]]-reduced 257th harmonic ([[257/128]]) is [[Just intonation\|justly tuned]] and is divided in a given number of equal steps. 257/128 is very close to the [[octave]], 2/1, but it is slightly sharper. This makes it suitable as an alternative to edos whose consonances are too flat, such as [[7edo]].

			Ed257/128s really only make sense for that purpose with 65 or fewer tones per [[pseudo-octave]]. With more tones than that, the relative error on 2/1 becomes unacceptably high and it makes more sense to switch to a different tuning like a [[zpi]] or ed513/256.

	== 7ed257/128 ==		== 7ed257/128 ==

BudjarnLambeth at 11:52, 13 December 2024

2024-12-13T11:52:54Z

← Older revision		Revision as of 11:52, 13 December 2024
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	[[45edo]] for comparison:		[[45edo]] for comparison:
	{{Harmonics in equal\|54\|intervals=prime\|collapsed=1}}		{{Harmonics in equal\|54\|intervals=prime\|collapsed=1}}



			== 59ed257/128 ==
			=== Harmonics ===
			{{Harmonics in equal\|59\|257\|128\|intervals=prime}}


			[[59edo]] for comparison:
			{{Harmonics in equal\|59\|intervals=prime\|collapsed=1}}



			== 64ed257/128 ==
			=== Harmonics ===
			{{Harmonics in equal\|64\|257\|128\|intervals=prime}}


			[[64edo]] for comparison:
			{{Harmonics in equal\|64\|intervals=prime\|collapsed=1}}

BudjarnLambeth: Add 54

2024-12-13T08:02:29Z

Add 54

← Older revision		Revision as of 08:02, 13 December 2024
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	[[45edo]] for comparison:		[[45edo]] for comparison:
	{{Harmonics in equal\|45\|intervals=prime\|collapsed=1}}		{{Harmonics in equal\|45\|intervals=prime\|collapsed=1}}



			== 54ed257/128 ==
			=== Harmonics ===
			{{Harmonics in equal\|54\|257\|128\|intervals=prime}}


			[[45edo]] for comparison:
			{{Harmonics in equal\|54\|intervals=prime\|collapsed=1}}

BudjarnLambeth at 02:23, 13 December 2024

2024-12-13T02:23:25Z

← Older revision		Revision as of 02:23, 13 December 2024
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	* 1170.181		* 1170.181
	* 1206.749		* 1206.749



	== 38ed257/128 ==		== 38ed257/128 ==
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	[[38edo]] for comparison:		[[38edo]] for comparison:
	{{Harmonics in equal\|38\|intervals=prime\|collapsed=1}}		{{Harmonics in equal\|38\|intervals=prime\|collapsed=1}}



	== 42ed257/128 ==		== 42ed257/128 ==
	''See [[42ed257/128]].''		''See [[42ed257/128]].''



	== 45ed257/128 ==		== 45ed257/128 ==

BudjarnLambeth: /* 33ed257/128 */

2024-12-13T02:17:30Z

33ed257/128

← Older revision		Revision as of 02:17, 13 December 2024
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	== 33ed257/128 ==		== 33ed257/128 ==
			This is an excellent tuning for [[Meantone family#Dreamtone\|dreamtone]] temperament, much better than standard 33edo. It is almost exactly the TE tuning.

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|33\|257\|128\|intervals=prime}}		{{Harmonics in equal\|33\|257\|128\|intervals=prime}}
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	* 1170.181		* 1170.181
	* 1206.749		* 1206.749

	~~=== Regular temperament properties ===~~
	~~This is an excellent tuning for [[Meantone family#Dreamtone\|dreamtone]] temperament, much better than standard 33edo. It is almost exactly the TE tuning.~~


	== 38ed257/128 ==		== 38ed257/128 ==

BudjarnLambeth at 02:08, 13 December 2024

2024-12-13T02:08:12Z

← Older revision		Revision as of 02:08, 13 December 2024
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	== 7ed257/128 ==		== 7ed257/128 ==
	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|7\|257\|128\|intervals=~~integer~~}}		{{Harmonics in equal\|7\|257\|128\|intervals=prime}}


	7edo, [[16ed5]], [[22ed9]] for comparison:		7edo, [[16ed5]], [[22ed9]] for comparison:
	{{Harmonics in equal\|7\|intervals=~~integer~~\|collapsed=1}}		{{Harmonics in equal\|7\|intervals=prime\|collapsed=1}}
	{{Harmonics in equal\|16\|5\|1\|intervals=~~integer~~\|collapsed=1}}		{{Harmonics in equal\|16\|5\|1\|intervals=prime\|collapsed=1}}
	{{Harmonics in equal\|22\|9\|1\|intervals=~~integer~~\|collapsed=1}}		{{Harmonics in equal\|22\|9\|1\|intervals=prime\|collapsed=1}}

	=== Intervals ===		=== Intervals ===
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	== 9ed257/128 ==		== 9ed257/128 ==
	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|9\|257\|128\|intervals=~~integer~~}}		{{Harmonics in equal\|9\|257\|128\|intervals=prime}}


	[[9edo]] for comparison:		[[9edo]] for comparison:
	{{Harmonics in equal\|9\|intervals=~~integer~~\|collapsed=1}}		{{Harmonics in equal\|9\|intervals=prime\|collapsed=1}}

	=== Intervals ===		=== Intervals ===
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	== 14ed257/128 ==		== 14ed257/128 ==
	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|14\|257\|128\|intervals=~~integer~~}}		{{Harmonics in equal\|14\|257\|128\|intervals=prime}}


	[[14edo]] for comparison:		[[14edo]] for comparison:
	{{Harmonics in equal\|14\|intervals=~~integer~~\|collapsed=1}}		{{Harmonics in equal\|14\|intervals=prime\|collapsed=1}}

	=== Intervals ===		=== Intervals ===
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	== 16ed257/128 ==		== 16ed257/128 ==
	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|16\|257\|128\|intervals=~~integer~~}}		{{Harmonics in equal\|16\|257\|128\|intervals=prime}}


	[[16edo]] for comparison:		[[16edo]] for comparison:
	{{Harmonics in equal\|16\|intervals=~~integer~~\|collapsed=1}}		{{Harmonics in equal\|16\|intervals=prime\|collapsed=1}}

	=== Intervals ===		=== Intervals ===
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	== 19ed257/128 ==		== 19ed257/128 ==
	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|19\|257\|128\|intervals=~~integer~~}}		{{Harmonics in equal\|19\|257\|128\|intervals=prime}}


	[[19edo]] for comparison:		[[19edo]] for comparison:
	{{Harmonics in equal\|19\|intervals=~~integer~~\|collapsed=1}}		{{Harmonics in equal\|19\|intervals=prime\|collapsed=1}}

	=== Intervals ===		=== Intervals ===
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	== 33ed257/128 ==		== 33ed257/128 ==
	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|33\|257\|128\|intervals=~~integer~~}}		{{Harmonics in equal\|33\|257\|128\|intervals=prime}}


	[[33edo]] for comparison:		[[33edo]] for comparison:
	{{Harmonics in equal\|33\|intervals=~~integer~~\|collapsed=1}}		{{Harmonics in equal\|33\|intervals=prime\|collapsed=1}}

	=== Intervals ===		=== Intervals ===
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	== 38ed257/128 ==		== 38ed257/128 ==
	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|38\|257\|128\|intervals=~~integer~~}}		{{Harmonics in equal\|38\|257\|128\|intervals=prime}}


	[[38edo]] for comparison:		[[38edo]] for comparison:
	{{Harmonics in equal\|38\|intervals=~~integer~~\|collapsed=1}}		{{Harmonics in equal\|38\|intervals=prime\|collapsed=1}}


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	== 45ed257/128 ==		== 45ed257/128 ==
	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|45\|257\|128\|intervals=~~integer~~}}		{{Harmonics in equal\|45\|257\|128\|intervals=prime}}


	[[45edo]] for comparison:		[[45edo]] for comparison:
	{{Harmonics in equal\|45\|intervals=~~integer~~\|collapsed=1}}		{{Harmonics in equal\|45\|intervals=prime\|collapsed=1}}

BudjarnLambeth at 03:35, 6 December 2024

2024-12-06T03:35:32Z

← Older revision		Revision as of 03:35, 6 December 2024
Line 1:		Line 1:
	An '''equal division of reduced harmonic 257''' ('''ed257/128''') is an [[equal-step tuning]] in which the 4ve-reduced 257th harmonic ([[257/128]]) is [[Just intonation\|justly tuned]] and is divided in a given number of equal steps. 257/128 is very close to the [[octave]], 2/1, but it is slightly sharper. This makes it suitable as an alternative to edos whose consonances are too flat, such as [[7edo]].		An '''equal division of reduced harmonic 257''' ('''ed257/128''') is an [[equal-step tuning]] in which the [[4/1\|4ve]]-reduced 257th harmonic ([[257/128]]) is [[Just intonation\|justly tuned]] and is divided in a given number of equal steps. 257/128 is very close to the [[octave]], 2/1, but it is slightly sharper. This makes it suitable as an alternative to edos whose consonances are too flat, such as [[7edo]].

	== 7ed257/128 ==		== 7ed257/128 ==