84edt - Revision history

FloraC: /* See also */ +9ed9/8

2025-03-24T10:58:12Z

2025-03-24T10:44:03Z

+see also

2025-03-24T10:38:04Z

Theory: note consistency

← Older revision		Revision as of 10:38, 24 March 2025
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	== Theory ==		== Theory ==
	84edt is practically identical to [[53edo]], but with the 3/1 rather than the [[2/1]] being just. The octave is about 0.0430 cents stretched.		84edt is practically identical to [[53edo]], but with the 3/1 rather than the [[2/1]] being just. The octave is about 0.0430 cents stretched. Like 53edo, 84edt is [[consistent]] to the [[integer limit\|10-integer-limit]].

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

2025-03-24T10:37:12Z

Theory: +subsets and supersets

← Older revision		Revision as of 10:37, 24 March 2025
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	{{Harmonics in equal\|84\|3\|1\|intervals=integer}}		{{Harmonics in equal\|84\|3\|1\|intervals=integer}}
	{{Harmonics in equal\|84\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 84edt (continued)}}		{{Harmonics in equal\|84\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 84edt (continued)}}

			=== Subsets and supersets ===
			84 is a [[largely composite]] number. Since it factors into primes as {{nowrap\| 2<sup>2</sup> × 3 × 7 }}, 84edt has subset edts {{EDs\|equave=t\| 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 }}.

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

2025-03-24T10:34:53Z

Cleanup

@@ Line 1: / Line 1: @@
-{{Infobox ET}}{{todo|expand}}
+{{Infobox ET}}
-'''[[Edt|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.
+{{ED intro}}
 == Theory ==
-This tuning tempers out 99/98 and 121/120 in the 11-limit; and 120/119 in the 17-limit.
+edt is practically identical to [[53edo]], but with the 3/1 rather than the [[2/1]] being just. The octave is about 0.0430 cents stretched.
 == Intervals ==
 {{Interval table}}

2025-01-02T00:33:37Z

Todo

← Older revision		Revision as of 00:33, 2 January 2025
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	{{Infobox ET}}		{{Infobox ET}}{{todo\|expand}}
	'''[[Edt\|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo\|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.		'''[[Edt\|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo\|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.

2024-12-26T15:19:25Z

← Older revision		Revision as of 15:19, 26 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Edt\|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo\|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.		'''[[Edt\|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo\|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.

			== Theory ==
			This tuning tempers out 99/98 and 121/120 in the 11-limit; and 120/119 in the 17-limit.

	== Intervals ==		== Intervals ==

2024-10-06T07:43:12Z

Add intervals split harmonics

← Older revision		Revision as of 07:43, 6 October 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''[[Edt\|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo\|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.		'''[[Edt\|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo\|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.

			== Intervals ==
			{{Interval table}}

	== Harmonics ==		== Harmonics ==
	{{Harmonics in equal\|84\|3\|1\|~~prec~~=2\|~~columns~~=15}}		{{Harmonics in equal
			\| steps = 84
			\| num = 3
			\| denom = 1
			\| intervals = integer
			}}
			{{Harmonics in equal
			\| steps = 84
			\| num = 3
			\| denom = 1
			\| start = 12
			\| collapsed = 1
			\| intervals = integer
			}}

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

2024-05-17T12:19:10Z

← Older revision		Revision as of 12:19, 17 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Edt\|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo\|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.		'''[[Edt\|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo\|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.

			== Harmonics ==
			{{Harmonics in equal\|84\|3\|1\|prec=2\|columns=15}}

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

2022-10-05T20:06:03Z

Infobox ET added

← Older revision		Revision as of 20:06, 5 October 2022
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			{{Infobox ET}}
	'''[[Edt\|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo\|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.		'''[[Edt\|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo\|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.

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