60ed6 - Revision history

FloraC: +subsets and supersets; +see also

2025-05-27T09:48:35Z

+subsets and supersets; +see also

← Older revision		Revision as of 09:48, 27 May 2025
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	{{Harmonics in equal\|60\|6\|1\|intervals=integer\|columns=11}}		{{Harmonics in equal\|60\|6\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|60\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 60ed6 (continued)}}		{{Harmonics in equal\|60\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 60ed6 (continued)}}

			=== Subsets and supersets ===
			60ed6 is the 9th [[highly composite equal division\|highly composite ed6]], with subset ed6's {{EDs\|equave=6\| 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 }}.

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

	~~{{todo\|expand}}~~		== See also ==
			* [[37edt]] – relative edt


	[[Category:23edo]]		[[Category:23edo]]

FloraC: Cleanup

2025-05-27T09:46:32Z

Cleanup

← Older revision		Revision as of 09:46, 27 May 2025
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	{{ED intro}}		{{ED intro}}

	~~It is similar to~~ [[23edo]]~~, but~~ with the ~~octave (~~2/1) being [[~~octave shrinking~~\|compressed]] by 10.9 cents, and with the ~~interval [[6/1]]~~ being [[just]], instead of ~~2/1~~ being just.		== Theory ==
			60ed6 can be viewed as [[23edo]] with the [[2/1\|octave]] being [[stretched and compressed tuning\|compressed]] by 10.9 cents, and with the 6th harmonic being [[just]], instead of the octave being just.

	~~== Harmonics ==~~		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]]. 60ed6 improves upon all of their tunings, bringing all of them within 16 cents of just, and bringing 3, 5 and 7 within 11 cents of just. This dramatically increases the number of consonant intervals and chords available in the tuning.
	~~23edo’s~~ 3/1, 5/1, 7/1 and 11/1 are all more than 20 cents away from just, ~~causing them to~~ exhibit very little [[consonance]]. 60ed6 improves upon all of their tunings, bringing all of them within 16 cents of just, and bringing 3, 5 and 7 within 11 cents of just. This dramatically increases the number of consonant intervals and chords available in the tuning.

	The trade-off is that ~~60ed6’s~~ octave ~~- 2/1 -~~ is significantly worse than 23edo. It has almost 11 cents of error, compared to 0. For some composers, 11 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.		The trade-off is that 60ed6's octave is significantly worse than 23edo. It has almost 11 cents of error, compared to none. For some composers, 11 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 in equal\|60\|6\|1\|intervals=prime}}~~

			=== Harmonics ===
	~~23edo for comparison:~~		{{Harmonics in equal\|60\|6\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|23\|2\|1\|intervals=~~prime~~}}		{{Harmonics in equal\|60\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 60ed6 (continued)}}

	== Intervals ==		== Intervals ==

BudjarnLambeth at 07:04, 7 January 2025

2025-01-07T07:04:01Z

← Older revision		Revision as of 07:04, 7 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

	It is similar to [[23edo]], but with the octave (2/1) being [[octave shrinking\|compressed]] by 10.9 cents, and with the interval [[6/1]] being [[just]], instead of 2/1 being just.		It is similar to [[23edo]], but with the octave (2/1) being [[octave shrinking\|compressed]] by 10.9 cents, and with the interval [[6/1]] being [[just]], instead of 2/1 being just.

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	{{todo\|expand}}		{{todo\|expand}}
			[[Category:23edo]]

BudjarnLambeth: Add detailed comparison with 23edo

2025-01-07T07:02:54Z

Add detailed comparison with 23edo

← Older revision		Revision as of 07:02, 7 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}
			It is similar to [[23edo]], but with the octave (2/1) being [[octave shrinking\|compressed]] by 10.9 cents, and with the interval [[6/1]] being [[just]], instead of 2/1 being just.

	== Harmonics ==		== Harmonics ==
			23edo’s 3/1, 5/1, 7/1 and 11/1 are all more than 20 cents away from just, causing them to exhibit very little [[consonance]]. 60ed6 improves upon all of their tunings, bringing all of them within 16 cents of just, and bringing 3, 5 and 7 within 11 cents of just. This dramatically increases the number of consonant intervals and chords available in the tuning.

			The trade-off is that 60ed6’s octave - 2/1 - is significantly worse than 23edo. It has almost 11 cents of error, compared to 0. For some composers, 11 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 in equal\|60\|6\|1\|intervals=prime}}		{{Harmonics in equal\|60\|6\|1\|intervals=prime}}


	{{~~stub~~}}		23edo for comparison:
			{{Harmonics in equal\|23\|2\|1\|intervals=prime}}

			== Intervals ==
			{{Interval table}}

			{{todo\|expand}}

BudjarnLambeth: Harmonics stub

2024-12-16T16:38:34Z

Harmonics stub

← Older revision		Revision as of 16:38, 16 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

			== Harmonics ==
			{{Harmonics in equal\|60\|6\|1\|intervals=prime}}


			{{stub}}

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

2024-12-16T16:31:09Z

Created page with "{{Infobox ET}} {{ED intro}}"

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