70ed6 - Revision history

BudjarnLambeth at 09:01, 27 September 2025

2025-09-27T09:01:08Z

← Older revision		Revision as of 09:01, 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 ==

ArrowHead294 at 19:09, 25 June 2025

2025-06-25T19:09:07Z

← Older revision		Revision as of 19:09, 25 June 2025
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	== See also ==		== See also ==
			* [[16edf]] – relative edf
	* [[27edo]] – relative edo		* [[27edo]] – relative edo
	* [[43edt]] – relative edt		* [[43edt]] – relative edt
			* [[90ed10]] – relative ed10
	* [[97ed12]] – relative ed12		* [[97ed12]] – relative ed12

	[[Category:27edo]]		[[Category:27edo]]
	[[Category:Zeta-optimized tunings]]		[[Category:Zeta-optimized tunings]]

ArrowHead294 at 14:01, 18 June 2025

2025-06-18T14:01:00Z

← Older revision		Revision as of 14:01, 18 June 2025
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	[[Category:27edo]]		[[Category:27edo]]
			[[Category:Zeta-optimized tunings]]

ArrowHead294 at 13:21, 10 June 2025

2025-06-10T13:21:15Z

← Older revision		Revision as of 13:21, 10 June 2025
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	* [[43edt]] – relative edt		* [[43edt]] – relative edt
	* [[97ed12]] – relative ed12		* [[97ed12]] – relative ed12

			[[Category:27edo]]

FloraC: /* Theory */ very nearly identical -> closely related. Misc. cleanup

2025-05-27T10:35:10Z

Theory: very nearly identical -> closely related. Misc. cleanup

← Older revision		Revision as of 10:35, 27 May 2025
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	== Theory ==		== Theory ==
	70ed6 is ~~very nearly identical~~ to [[27edo]], but with the [[6/1]] ~~rather than the 2/1~~ being just, which [[stretched and compressed tuning\|compresses the octave]] by 3.~~5316~~{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch\|zeta peak]] around 27 is located at 27.086614, which has a step size of 44.3023{{c}}, making 70ed6 very close to optimal for 27edo.		70ed6 is closely related to [[27edo]], but with the 6th harmonic rather than the [[2/1\|octave]] being just, which [[stretched and compressed tuning\|compresses the octave]] by about 3.53{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch\|zeta peak]] around 27 is located at 27.086614, which has a step size of 44.3023{{c}}, making 70ed6 very close to optimal for 27edo.

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|70\|6\|1}}		{{Harmonics in equal\|70\|6\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|70\|6\|1\|~~start~~=12\|~~columns~~=12\|collapsed=true\|title=Approximation of harmonics in 70ed6 (continued)}}		{{Harmonics in equal\|70\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 70ed6 (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 70 factors into primes as {{nowrap\| 2 × 5 × 7 }}, 70ed6 has subset ed6's {{EDs\|equave=6\| 2, 5, 7, 10, 14, and 35 }}.		Since 70 factors into primes as {{nowrap\| 2 × 5 × 7 }}, 70ed6 has subset ed6's {{EDs\|equave=6\| 2, 5, 7, 10, 14, and 35 }}.

	== Intervals ==		== Intervals ==

FloraC: /* See also */ oopsie

2025-03-04T08:18:39Z

FloraC: +see also

2025-03-04T08:14:21Z

+see also

← Older revision		Revision as of 08:14, 4 March 2025
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

			== See also ==
			* [[27edo]] – relative edo
			* [[41edt]] – relative edt
			* [[97ed12]] – relative ed12

FloraC: +subsets and supersets

2025-03-04T08:08:36Z

+subsets and supersets

← Older revision		Revision as of 08:08, 4 March 2025
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	{{Harmonics in equal\|70\|6\|1}}		{{Harmonics in equal\|70\|6\|1}}
	{{Harmonics in equal\|70\|6\|1\|start=12\|columns=12\|collapsed=true\|title=Approximation of harmonics in 70ed6 (continued)}}		{{Harmonics in equal\|70\|6\|1\|start=12\|columns=12\|collapsed=true\|title=Approximation of harmonics in 70ed6 (continued)}}

			=== Subsets and supersets ===
			Since 70 factors into primes as {{nowrap\| 2 × 5 × 7 }}, 70ed6 has subset ed6's {{EDs\|equave=6\| 2, 5, 7, 10, 14, and 35 }}.

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

FloraC: Cleanup

2025-03-04T08:06:36Z

Cleanup

← Older revision		Revision as of 08:06, 4 March 2025
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	{{ED intro}}		{{ED intro}}

	70ed6 is very nearly identical to [[27edo~~\|27 EDO~~]], but with the [[6/1]] rather than the 2/1 being just, which [[stretched and compressed tuning\|compresses the octave]] by 3.5316{{c}}. The local [[~~The_Riemann_zeta_function_and_tuning~~#~~Optimal_octave_stretch~~\|zeta peak]] around 27 is located at 27.086614, which has a step size of 44.3023{{c}}, making 70ed6 very close to optimal for 27edo.		== Theory ==
			70ed6 is very nearly identical to [[27edo]], but with the [[6/1]] rather than the 2/1 being just, which [[stretched and compressed tuning\|compresses the octave]] by 3.5316{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch\|zeta peak]] around 27 is located at 27.086614, which has a step size of 44.3023{{c}}, making 70ed6 very close to optimal for 27edo.

			=== Harmonics ===
			{{Harmonics in equal\|70\|6\|1}}
			{{Harmonics in equal\|70\|6\|1\|start=12\|columns=12\|collapsed=true\|title=Approximation of harmonics in 70ed6 (continued)}}

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

	~~== Harmonics ==~~
	~~{{Harmonics in equal\|70\|6\|1\|prec=2}}~~
	~~{{Harmonics in equal\|70\|6\|1\|prec=2\|intervals=prime\|start=6}}~~

	~~[[Category:Edonoi]]~~

ArrowHead294 at 15:00, 25 February 2025

2025-02-25T15:00:41Z

← Older revision		Revision as of 15:00, 25 February 2025
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	{{ED intro}}		{{ED intro}}

	~~70ED6~~ is very nearly identical to [[27edo\|27 EDO]], but with the [[6/1]] rather than the 2/1 being just, which [[stretched and compressed tuning\|compresses the octave]] by 3.5316{{c}}. The local [[The_Riemann_zeta_function_and_tuning#Optimal_octave_stretch\|zeta peak]] around 27 is located at 27.086614, which has a step size of 44.3023{{c}}, making 70ed6 very close to optimal for 27edo.		70ed6 is very nearly identical to [[27edo\|27 EDO]], but with the [[6/1]] rather than the 2/1 being just, which [[stretched and compressed tuning\|compresses the octave]] by 3.5316{{c}}. The local [[The_Riemann_zeta_function_and_tuning#Optimal_octave_stretch\|zeta peak]] around 27 is located at 27.086614, which has a step size of 44.3023{{c}}, making 70ed6 very close to optimal for 27edo.

	== Intervals ==		== Intervals ==

← Older revision		Revision as of 08:18, 4 March 2025
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	== See also ==		== See also ==
	* [[27edo]] – relative edo		* [[27edo]] – relative edo
	* [[~~41edt~~]] – relative edt		* [[43edt]] – relative edt
	* [[97ed12]] – relative ed12		* [[97ed12]] – relative ed12