79ed12 - Revision history

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

2025-05-27T09:15:46Z

Cleanup; + subsets and supersets; + see also

← Older revision		Revision as of 09:15, 27 May 2025
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	{{ED intro}}		{{ED intro}}

	79ed12 is ~~very nearly identical~~ to [[22edo]], but with the [[12/1]] ~~rather than the 2/1~~ being just, resulting in octaves being [[stretched and compressed tuning\|compressed]] by about 1.99{{c}}. The local [[~~The_Riemann_zeta_function_and_tuning~~#~~Optimal_octave_stretch~~\|zeta peak]] around 22 is located at 22.025147, which has a step size of 54.483{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 79ed12 ~~extremely~~ close to optimal for 22edo.		== Theory ==
			79ed12 is closely related to [[22edo]], but with the 12th harmonic rather than the [[2/1\|octave]] being just, resulting in octaves being [[stretched and compressed tuning\|compressed]] by about 1.99{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch\|zeta peak]] around 22 is located at 22.025147, which has a step size of 54.483{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 79ed12 very close to optimal for 22edo.

	== Harmonics ==		=== Harmonics ===
	{{Harmonics in equal\|79\|12\|1\|~~prec~~=2\|columns=15}}		{{Harmonics in equal\|79\|12\|1\|intervals=integer\|columns=11}}
			{{Harmonics in equal\|79\|12\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 79ed12 (continued)}}

	[[~~Category:Edonoi~~]]		=== Subsets and supersets ===
			79ed12 is the 22nd [[prime equal division\|prime ed12]], so it does not contain any nontrivial subset ed12's.

			== See also ==
			* [[22edo]] – relative edo
			* [[35edt]] – relative edt
			* [[57ed6]] – relative ed6

ArrowHead294 at 15:01, 25 February 2025

2025-02-25T15:01:30Z

← Older revision		Revision as of 15:01, 25 February 2025
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	{{ED intro}}		{{ED intro}}

	~~79ED12~~ is very nearly identical to [[22edo~~\|22 EDO~~]], but with the [[12/1]] rather than the 2/1 being just, resulting in octaves being [[stretched and compressed tuning\|compressed]] by about 1.99{{c}}. The local [[The_Riemann_zeta_function_and_tuning#Optimal_octave_stretch\|zeta peak]] around 22 is located at 22.025147, which has a step size of 54.483{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 79ed12 ~~very~~ close to optimal for 22edo.		79ed12 is very nearly identical to [[22edo]], but with the [[12/1]] rather than the 2/1 being just, resulting in octaves being [[stretched and compressed tuning\|compressed]] by about 1.99{{c}}. The local [[The_Riemann_zeta_function_and_tuning#Optimal_octave_stretch\|zeta peak]] around 22 is located at 22.025147, which has a step size of 54.483{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 79ed12 extremely close to optimal for 22edo.

	== Harmonics ==		== Harmonics ==

ArrowHead294 at 16:40, 15 January 2025

2025-01-15T16:40:17Z

← Older revision		Revision as of 16:40, 15 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''[[Ed12\|Division of the twelfth harmonic]] into 79 equal parts''' (~~79ED12) is very nearly identical to [[22edo\|22 EDO]], but with the [[12/1]] rather than the 2/1 being just~~. The octave is about 1.99{{c}}~~ [[stretched and compressed tuning\|compressed]] ~~and the step size is~~ about 54.~~4551~~{{c}}. The local [[The_Riemann_zeta_function_and_tuning#Optimal_octave_stretch\|zeta peak]] around 22 is located at 22.025147, which has a step size of 54.483{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 79ed12 very close to optimal for 22edo.		{{ED intro}}

			79ED12 is very nearly identical to [[22edo\|22 EDO]], but with the [[12/1]] rather than the 2/1 being just, resulting in octaves being [[stretched and compressed tuning\|compressed]] by about 1.99{{c}}. The local [[The_Riemann_zeta_function_and_tuning#Optimal_octave_stretch\|zeta peak]] around 22 is located at 22.025147, which has a step size of 54.483{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 79ed12 very close to optimal for 22edo.

	== Harmonics ==		== Harmonics ==

ArrowHead294: Make page

2024-09-09T15:26:46Z

Make page

New page

{{Infobox ET}}
'''[[Ed12|Division of the twelfth harmonic]] into 79 equal parts''' (79ED12) is very nearly identical to [[22edo|22 EDO]], but with the [[12/1]] rather than the 2/1 being just. The octave is about 1.99{{c}} [[stretched and compressed tuning|compressed]] and the step size is about 54.4551{{c}}. The local [[The_Riemann_zeta_function_and_tuning#Optimal_octave_stretch|zeta peak]] around 22 is located at 22.025147, which has a step size of 54.483{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 79ed12 very close to optimal for 22edo.

== Harmonics ==
{{Harmonics in equal|79|12|1|prec=2|columns=15}}

[[Category:Edonoi]]