93ed6 - Revision history

ArrowHead294: /* See also */

2025-06-25T19:13:19Z

ArrowHead294 at 13:41, 18 June 2025

2025-06-18T13:41:20Z

← Older revision		Revision as of 13:41, 18 June 2025
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	[[Category:36edo]]		[[Category:36edo]]
	~~[[Category:Edonoi]]~~

ArrowHead294 at 13:41, 18 June 2025

2025-06-18T13:41:09Z

← Older revision		Revision as of 13:41, 18 June 2025
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	* [[101ed7]] – relative ed7		* [[101ed7]] – relative ed7
	* [[129ed12]] – relative ed12		* [[129ed12]] – relative ed12

			[[Category:36edo]]
			[[Category:Edonoi]]

ArrowHead294: /* Theory */

2025-05-31T02:24:01Z

Theory

← Older revision		Revision as of 02:24, 31 May 2025
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	93ed6 is nearly identical to [[36edo]], but with the 6th harmonic rather than the [[2/1\|octave]] being just. The octave is stretched by about 0.757 [[cent]]s (almost identical to [[101ed7]], where the octave is stretched by about 0.770 cents). Like 36edo, 93ed6 is [[consistent]] to the [[integer limit\|8-integer-limit]].		93ed6 is nearly identical to [[36edo]], but with the 6th harmonic rather than the [[2/1\|octave]] being just. The octave is stretched by about 0.757 [[cent]]s (almost identical to [[101ed7]], where the octave is stretched by about 0.770 cents). Like 36edo, 93ed6 is [[consistent]] to the [[integer limit\|8-integer-limit]].

	Compared to 36edo, 93ed6 is pretty well optimized for the 2.3.7.13.17 [[subgroup]], with slightly better [[3/1\|3]], [[7/1\|7]], [[13/1\|13]] and [[17/1\|17]], and a slightly worse 2 versus 36edo. Using the [[patent val]], the [[5/1\|5]] is also less accurate. Overall this means 36edo is still better in the [[5-limit]], but 93ed6 is better in the [[13-limit\|13-]] and [[17-limit]], especially when treating it as a dual-5 dual-11 tuning.		Compared to 36edo, 93ed6 is pretty well optimized for the 2.3.7.13.17 [[subgroup]], with slightly better [[3/1\|3]], [[7/1\|7]], [[13/1\|13]] and [[17/1\|17]], and a slightly worse 2 versus 36edo. Using the [[patent val]], the [[5/1\|5]] is also less accurate. Overall this means 36edo is still better in the [[5-limit]], but 93ed6 is better in the [[13-limit\|13-]] and [[17-limit]], especially when treating it as a dual-5 dual-11 tuning.

			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 93ed6 very close to optimal for 36edo.

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

FloraC: /* Theory */ copypasty from 101ed7

2025-05-28T13:36:50Z

Theory: copypasty from 101ed7

← Older revision		Revision as of 13:36, 28 May 2025
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	== Theory ==		== Theory ==
	93ed6 is nearly identical to [[36edo]], but with the 6th harmonic rather than the [[2/1\|octave]] being just. The octave is stretched by about 0.757 [[cent]]s.		93ed6 is nearly identical to [[36edo]], but with the 6th harmonic rather than the [[2/1\|octave]] being just. The octave is stretched by about 0.757 [[cent]]s (almost identical to [[101ed7]], where the octave is stretched by about 0.770 cents). Like 36edo, 93ed6 is [[consistent]] to the [[integer limit\|8-integer-limit]].

			Compared to 36edo, 93ed6 is pretty well optimized for the 2.3.7.13.17 [[subgroup]], with slightly better [[3/1\|3]], [[7/1\|7]], [[13/1\|13]] and [[17/1\|17]], and a slightly worse 2 versus 36edo. Using the [[patent val]], the [[5/1\|5]] is also less accurate. Overall this means 36edo is still better in the [[5-limit]], but 93ed6 is better in the [[13-limit\|13-]] and [[17-limit]], especially when treating it as a dual-5 dual-11 tuning.

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

FloraC: /* Theory */ +subsets and supersets

2025-05-27T10:40:28Z

Theory: +subsets and supersets

← Older revision		Revision as of 10:40, 27 May 2025
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	{{Harmonics in equal\|93\|6\|1\|intervals=integer\|columns=11}}		{{Harmonics in equal\|93\|6\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|93\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 93ed6 (continued)}}		{{Harmonics in equal\|93\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 93ed6 (continued)}}

			=== Subsets and supersets ===
			Since 93 factors into primes as {{nowrap\| 3 × 31 }}, 93ed6 contains subset ed6's [[3ed6]] and [[31ed6]].

	== See also ==		== See also ==

FloraC: Cleanup

2025-05-27T10:39:52Z

Cleanup

← Older revision		Revision as of 10:39, 27 May 2025
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	{{ED intro}}		{{ED intro}}

	~~93ED6~~ is ~~very~~ nearly identical to [[36edo]], but with the [[6/1]] ~~rather than the 2/1~~ being just. The octave is stretched by about 0.76 [[cent]]s.		== Theory ==
			93ed6 is nearly identical to [[36edo]], but with the 6th harmonic rather than the [[2/1\|octave]] being just. The octave is stretched by about 0.757 [[cent]]s.

	~~Lookalikes: [[21edf]], [[36edo]], [[57edt]], [[101ed7]], [[129ed12]]~~		=== Harmonics ===
			{{Harmonics in equal\|93\|6\|1\|intervals=integer\|columns=11}}
			{{Harmonics in equal\|93\|6\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 93ed6 (continued)}}

	== ~~Harmonics~~ ==		== See also ==
	~~{{Harmonics in equal\|93\|6\|1\|prec=2}}~~		* [[21edf]] – relative edf
			* [[36edo]] – relative edo
			* [[57edt]] – relative edt
	~~{{stub}}~~		* [[101ed7]] – relative ed7
	[[~~Category:Edonoi~~]]		* [[129ed12]] – relative ed12

ArrowHead294 at 17:20, 21 January 2025

2025-01-21T17:20:41Z

← Older revision		Revision as of 17:20, 21 January 2025
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	93ED6 is very nearly identical to [[36edo]], but with the [[6/1]] rather than the 2/1 being just. The octave is stretched by about 0.76 [[cent]]s.		93ED6 is very nearly identical to [[36edo]], but with the [[6/1]] rather than the 2/1 being just. The octave is stretched by about 0.76 [[cent]]s.

	Lookalikes: [[21edf]], [[36edo]], [[57edt]], [[101ed7]]		Lookalikes: [[21edf]], [[36edo]], [[57edt]], [[101ed7]], [[129ed12]]

	== Harmonics ==		== Harmonics ==

ArrowHead294 at 17:19, 21 January 2025

2025-01-21T17:19:13Z

← Older revision		Revision as of 17:19, 21 January 2025
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	93ED6 is very nearly identical to [[36edo]], but with the [[6/1]] rather than the 2/1 being just. The octave is stretched by about 0.76 [[cent]]s.		93ED6 is very nearly identical to [[36edo]], but with the [[6/1]] rather than the 2/1 being just. The octave is stretched by about 0.76 [[cent]]s.

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

	== Harmonics ==		== Harmonics ==

ArrowHead294 at 17:18, 21 January 2025

2025-01-21T17:18:49Z

← Older revision		Revision as of 17:18, 21 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed6\|Division of the sixth harmonic]] into 93 equal parts''' (93ED6) is very nearly identical to [[36edo\|36 EDO]], but with the [[6/1]] rather than the 2/1 being just. The octave is about 0.76 [[cent]]s stretched and the step size is about 33.35 cents.		{{ED intro}}

	==Harmonics==		93ED6 is very nearly identical to [[36edo]], but with the [[6/1]] rather than the 2/1 being just. The octave is stretched by about 0.76 [[cent]]s.

			== Harmonics ==
	{{Harmonics in equal\|93\|6\|1\|prec=2}}		{{Harmonics in equal\|93\|6\|1\|prec=2}}

← Older revision		Revision as of 19:13, 25 June 2025
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	* [[57edt]] – relative edt		* [[57edt]] – relative edt
	* [[101ed7]] – relative ed7		* [[101ed7]] – relative ed7
	* [[129ed12]] – relative ed12		* [[129ed12]] – relative ed12, close to the zeta-optimized tuning for 36edo

	[[Category:36edo]]		[[Category:36edo]]