59ed6 - Revision history

BudjarnLambeth at 09:00, 27 September 2025

2025-09-27T09:00:55Z

← Older revision		Revision as of 09:00, 27 September 2025
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

			== Scales ==
			* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic\|Gutierrez-Lambeth quasi-subharmonic pentatonic]]

	== See also ==		== See also ==
	* [[36edt]] – relative edt		* [[36edt]] – relative edt

FloraC: Copypasty (with data for this tuning) from 60ed6

2025-05-27T09:51:48Z

Copypasty (with data for this tuning) from 60ed6

← Older revision		Revision as of 09:51, 27 May 2025
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	~~{{Stub}}~~
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}
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	== Theory ==		== Theory ==
	59ed6 corresponds to 22.8243…edo. It can be viewed as a [[stretched and compressed tuning\|stretched]] version of [[23edo]] or a compressed version of [[36edt]].		59ed6 corresponds to 22.8243…edo. It can be viewed as a [[stretched and compressed tuning\|stretched]] version of [[23edo]] or a compressed version of [[36edt]].

			23edo's [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]] and [[11/1\|11]] are all more than 20 cents away from just, so they exhibit very little [[consonance]]. 59ed6 improves upon all of their tunings, bringing all of them within 10 cents of just. This dramatically increases the number of consonant intervals and chords available in the tuning.

			The trade-off is that 59ed6's octave is significantly worse than 23edo. It has just over 9 cents of error, compared to none. For some composers, 9 cents error on the octave may be unacceptable, but for others, it may be considered still close enough for consonance and [[octave equivalence]] to be well preserved, and they may see it a worthwhile sacrifice to unlock so many warm [[11-limit]] harmonies.

	=== Harmonics ===		=== Harmonics ===

FloraC: Cleanup; + subsets and supersets; + see also

2025-05-27T09:43:30Z

Cleanup; + subsets and supersets; + see also

← Older revision		Revision as of 09:43, 27 May 2025
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	== Theory ==		== Theory ==
	59ed6 corresponds to 22.8243…edo. It can be viewed as a stretched version of [[23edo]].		59ed6 corresponds to 22.8243…edo. It can be viewed as a [[stretched and compressed tuning\|stretched]] version of [[23edo]] or a compressed version of [[36edt]].

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|59\|6\|1\|intervals=integer\|columns=11}}		{{Harmonics in equal\|59\|6\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|59\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 59ed6 (continued)}}		{{Harmonics in equal\|59\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 59ed6 (continued)}}

			=== Subsets and supersets ===
			59ed6 is the 17th [[prime equal division\|prime ed6]], so it does not contain any nontrivial subset ed6's.

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

			== See also ==
			* [[36edt]] – relative edt

FloraC: Cleanup

2025-05-27T09:39:56Z

Cleanup

@@ Line 1: / Line 1: @@
 {{Stub}}
 {{Infobox ET}}
-{{ED intro}} It is a stretched version of [[23edo]], corresponding to ‘22.8243edo’.
+{{ED intro}}
 == Intervals ==
 {{Interval table}}

BudjarnLambeth: Intro intervals harmonics

2024-10-05T03:39:52Z

Intro intervals harmonics

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''59ED6''' is the [[Ed6|equal division of the sixth harmonic]] into 59 parts of 52.5755 [[cent|cents]] each, corresponding to 22.8243 [[edo]]. It is a stretched version of [[23edo]].
+{{ED intro}} It is a stretched version of [[23edo]], corresponding to ‘22.8243edo’.
-{{Stub}}

ArrowHead294 at 12:00, 26 July 2024

2024-07-26T12:00:33Z

← Older revision		Revision as of 12:00, 26 July 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''59ED6''' is the [[Ed6\|equal division of the sixth harmonic]] into 59 parts of 52.5755 [[cent\|cents]] each, corresponding to 22.8243 [[edo]]. It is a stretched version of [[23edo]].		'''59ED6''' is the [[Ed6\|equal division of the sixth harmonic]] into 59 parts of 52.5755 [[cent\|cents]] each, corresponding to 22.8243 [[edo]]. It is a stretched version of [[23edo]].
			{{Stub}}

ArrowHead294: Make page

2024-07-26T12:00:21Z

Make page

New page

{{Infobox ET}}
'''59ED6''' is the [[Ed6|equal division of the sixth harmonic]] into 59 parts of 52.5755 [[cent|cents]] each, corresponding to 22.8243 [[edo]]. It is a stretched version of [[23edo]].