129ed12 - Revision history

ArrowHead294: /* Theory */

2025-06-20T15:33:41Z

Theory

← Older revision		Revision as of 15:33, 20 June 2025
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	== Theory ==		== Theory ==
	129ed12 is very nearly identical to [[36edo]] (sixth-tone tuning), but with the 12th harmonic rather than the [[2/1\|octave]] being just. This stretches the octave by about 0.546{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch\|zeta peak]] around 36 is located at 35.982388, which has a step size of 33.3496{{c}} and has octaves stretched by 0.587{{c}}; 129ed12's octave is extremely close to ~~ideal~~, being only 0.0418{{c}} ({{~~frac~~\|1\|23}} of a cent) off from the zeta peak.		129ed12 is very nearly identical to [[36edo]] (sixth-tone tuning), but with the 12th harmonic rather than the [[2/1\|octave]] being just. This stretches the octave by about 0.546{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch\|zeta peak]] around 36 is located at 35.982388, which has a step size of 33.3496{{c}} and has octaves stretched by 0.587{{c}}; 129ed12's octave is extremely close to optimal, being only 0.0418{{c}} ({{sfrac\|1\|23}} of a cent) off from the zeta peak.

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

ArrowHead294: /* Theory */

2025-06-20T15:33:28Z

Theory

← Older revision		Revision as of 15:33, 20 June 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	129ed12 is very nearly identical to [[36edo]] (sixth-tone tuning), but with the 12th harmonic rather than the [[2/1\|octave]] being just. This stretches the octave by about 0.546{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch\|zeta peak]] around 36 is located at 35.982388, which has a step size of 33.3496{{c}} and has octaves stretched by 0.587{{c}}~~, making~~ 129ed12 ~~very~~ close to ~~optimal for 36edo~~.		129ed12 is very nearly identical to [[36edo]] (sixth-tone tuning), but with the 12th harmonic rather than the [[2/1\|octave]] being just. This stretches the octave by about 0.546{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch\|zeta peak]] around 36 is located at 35.982388, which has a step size of 33.3496{{c}} and has octaves stretched by 0.587{{c}}; 129ed12's octave is extremely close to ideal, being only 0.0418{{c}} ({{frac\|1\|23}} of a cent) off from the zeta peak.

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

ArrowHead294 at 13:40, 18 June 2025

2025-06-18T13:40:26Z

← Older revision		Revision as of 13:40, 18 June 2025
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	* [[93ed6]] – relative ed6		* [[93ed6]] – relative ed6
	* [[101ed7]] – relative ed7		* [[101ed7]] – relative ed7

			[[Category:36edo]]
			[[Category:Zeta-optimized tunings]]

ArrowHead294: /* Theory */

2025-05-29T00:40:47Z

Theory

← Older revision		Revision as of 00:40, 29 May 2025
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	== Theory ==		== Theory ==
	129ed12 is very nearly identical to [[36edo]] (sixth-tone tuning), but with the 12th harmonic rather than the [[2/1\|octave]] being just. The octave is stretched by ~~about~~ 0.~~546~~{{c}}.		129ed12 is very nearly identical to [[36edo]] (sixth-tone tuning), but with the 12th harmonic rather than the [[2/1\|octave]] being just. This stretches the octave by about 0.546{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch\|zeta peak]] around 36 is located at 35.982388, which has a step size of 33.3496{{c}} and has octaves stretched by 0.587{{c}}, making 129ed12 very close to optimal for 36edo.

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

FloraC: Cleanup & expand

2025-05-27T10:43:07Z

Cleanup & expand

← Older revision		Revision as of 10:43, 27 May 2025
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	{{ED intro}}		{{ED intro}}

	~~129ED12~~ is very nearly identical to [[36edo]] (sixth-tone tuning), but with the [[12/1]] ~~rather than the 2/1~~ being just. The octave is stretched by 0.~~55[[cent]]s~~.		== Theory ==
			129ed12 is very nearly identical to [[36edo]] (sixth-tone tuning), but with the 12th harmonic rather than the [[2/1\|octave]] being just. The octave is stretched by about 0.546{{c}}.

	~~Lookalikes: [[21edf]], [[36edo]], [[57edt]], [[93ed6]], [[101ed7]]~~		=== Harmonics ===
			{{Harmonics in equal\|129\|12\|1\|intervals=integer\|columns=11}}
			{{Harmonics in equal\|129\|12\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 129ed12 (continued)}}

	== ~~Harmonics~~ ==		=== Subsets and supersets ===
	{{~~Harmonics in equal\|129\|12~~\|~~1\|prec=2\|columns=15~~}}		Since 129 factors into primes as {{nowrap\| 3 × 43 }}, 129ed12 contains subset ed12's [[3ed12]] and [[43ed12]].

	[[~~Category:Edonoi~~]]		== See also ==
			* [[21edf]] – relative edf
			* [[36edo]] – relative edo
			* [[57edt]] – relative edt
			* [[93ed6]] – relative ed6
			* [[101ed7]] – relative ed7

ArrowHead294 at 17:21, 21 January 2025

2025-01-21T17:21:36Z

← Older revision		Revision as of 17:21, 21 January 2025
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	129ED12 is very nearly identical to [[36edo]] (sixth-tone tuning), but with the [[12/1]] rather than the 2/1 being just. The octave is stretched by 0.55[[cent]]s.		129ED12 is very nearly identical to [[36edo]] (sixth-tone tuning), but with the [[12/1]] rather than the 2/1 being just. The octave is stretched by 0.55[[cent]]s.

			Lookalikes: [[21edf]], [[36edo]], [[57edt]], [[93ed6]], [[101ed7]]

	== Harmonics ==		== Harmonics ==

ArrowHead294 at 17:21, 21 January 2025

2025-01-21T17:21:15Z

← Older revision		Revision as of 17:21, 21 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed12\|Division of the twelfth harmonic]] into 129 equal parts''' (129ED12) is very nearly identical to [[36edo\|36 EDO]] (sixth-tone tuning), but with the [[12/1]] rather than the 2/1 being just. The octave is about 0.55 [[cent]]s stretched and the step size is about 33.35 cents.		{{ED intro}}

	==Harmonics==		129ED12 is very nearly identical to [[36edo]] (sixth-tone tuning), but with the [[12/1]] rather than the 2/1 being just. The octave is stretched by 0.55[[cent]]s.

			== Harmonics ==
	{{Harmonics in equal\|129\|12\|1\|prec=2\|columns=15}}		{{Harmonics in equal\|129\|12\|1\|prec=2\|columns=15}}

	[[Category:Edonoi]]		[[Category:Edonoi]]

ArrowHead294: Created page with

2024-05-09T17:11:04Z

Created page with

New page

{{Infobox ET}}
'''[[Ed12|Division of the twelfth harmonic]] into 129 equal parts''' (129ED12) is very nearly identical to [[36edo|36 EDO]] (sixth-tone tuning), but with the [[12/1]] rather than the 2/1 being just. The octave is about 0.55 [[cent]]s stretched and the step size is about 33.35 cents.

==Harmonics==
{{Harmonics in equal|129|12|1|prec=2|columns=15}}

[[Category:Edonoi]]