EDe - Revision history

Hotcrystal0 at 19:37, 23 February 2026

2026-02-23T19:37:01Z

← Older revision		Revision as of 19:37, 23 February 2026
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	{{Mathematical interest}}		{{Mathematical interest}}

	'''Equal division of the [[natave]]''' ('''EDe''' or '''EDN''') is the equal division of [[Acoustic e\|acoustic ''e'' (where ''e'' is treated as a musical interval in the same way as ''2'' is an octave or ''1.5'' is a perfect fifth).		'''Equal division of the [[natave]]''' ('''EDe''' or '''EDN''') is the equal division of [[Acoustic e\|acoustic ''e'']] (where ''e'' is treated as a musical interval in the same way as ''2'' is an octave or ''1.5'' is a perfect fifth).

	''e'' is of particular interest because of its relationship with logarithms, given the fact that pitch is perceived logarithmically, and the fact that equal divisions are logarithmic.		''e'' is of particular interest because of its relationship with logarithms, given the fact that pitch is perceived logarithmically, and the fact that equal divisions are logarithmic.

2026-02-23T19:36:50Z

Acoustic e

← Older revision		Revision as of 19:36, 23 February 2026
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	{{Mathematical interest}}		{{Mathematical interest}}

	'''Equal division of the [[natave]]''' ('''EDe''' or '''EDN''') is the equal division of ~~the constant~~ ''e'' (where ''e'' is treated as a musical interval in the same way as ''2'' is an octave or ''1.5'' is a perfect fifth).		'''Equal division of the [[natave]]''' ('''EDe''' or '''EDN''') is the equal division of [[Acoustic e\|acoustic ''e'' (where ''e'' is treated as a musical interval in the same way as ''2'' is an octave or ''1.5'' is a perfect fifth).

	''e'' is of particular interest because of its relationship with logarithms, given the fact that pitch is perceived logarithmically, and the fact that equal divisions are logarithmic.		''e'' is of particular interest because of its relationship with logarithms, given the fact that pitch is perceived logarithmically, and the fact that equal divisions are logarithmic.

2025-12-15T08:35:39Z

← Older revision		Revision as of 08:35, 15 December 2025
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	''e'' is of particular interest because of its relationship with logarithms, given the fact that pitch is perceived logarithmically, and the fact that equal divisions are logarithmic.		''e'' is of particular interest because of its relationship with logarithms, given the fact that pitch is perceived logarithmically, and the fact that equal divisions are logarithmic.

			Sometimes it is convenient to treat [[equal-step tuning]]s as (possibly non-integer) EDes in mathematics and computer programs, since it makes the logarithm used in equations the natural logarithm.

	== Correspondence of EDe to EDO ==		== Correspondence of EDe to EDO ==

2025-05-19T03:43:26Z

2025-05-19T02:23:05Z

17-EDe

← Older revision		Revision as of 02:23, 19 May 2025
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	=== 17-EDe ===		=== 17-EDe ===
	17-~~EDN~~ is very close to 12-EDO but with slightly sharp semitones (101.84 cents). This causes the octave to be far too sharp (1222.05 cents; essentially double a Pythagorean large tritone) and gives it a rather pleasant sharp fifth of 712.86 cents.		17-EDe is very close to 12-EDO but with slightly sharp semitones (101.84 cents). This causes the octave to be far too sharp (1222.05 cents; essentially double a Pythagorean large tritone) and gives it a rather pleasant sharp fifth of 712.86 cents.
	{{Harmonics in equal\|17\|1457\|536\|title=Approximation of harmonics in 17-EDe}}		{{Harmonics in equal\|17\|1457\|536\|title=Approximation of harmonics in 17-EDe}}

2025-05-19T02:22:52Z

Selected divisions

← Older revision		Revision as of 02:22, 19 May 2025
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	=== 10-EDe ===		=== 10-EDe ===
	{\| class="wikitable"		{\| class="wikitable"
	\|+ style="font-size: 105%;" \| Intervals of 10-~~EDN~~		\|+ style="font-size: 105%;" \| Intervals of 10-EDe
	\|-		\|-
	! Step		! Step

2025-05-19T02:22:18Z

Reword intro, replace EDN instances w EDe

2025-05-19T02:17:10Z

BudjarnLambeth moved page EDN to EDe: More intuitive name (discussed on Discord)

← Older revision	Revision as of 02:17, 19 May 2025
(No difference)

2025-04-10T13:16:25Z

2025-04-05T19:19:58Z

← Older revision		Revision as of 19:19, 5 April 2025
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			{{Mathematical interest}}

	Equal divisions of the [[natave]], which is the mathematical constant e used as a musical interval. e is of particular interest because of its relationship with logarithms, the fact that pitch is perceived logarithmically, and the fact that equal divisions are logarithmic.		Equal divisions of the [[natave]], which is the mathematical constant e used as a musical interval. e is of particular interest because of its relationship with logarithms, the fact that pitch is perceived logarithmically, and the fact that equal divisions are logarithmic.

← Older revision		Revision as of 03:43, 19 May 2025
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	24-EDe has third tones so far sharp of 17-EDO that it becomes a stretched 50-ED8 (50\24 is 3606.74 cents). However, 43\24 is essentially the 6th harmonic (1514.83+1586.965=3101.79 cents).		24-EDe has third tones so far sharp of 17-EDO that it becomes a stretched 50-ED8 (50\24 is 3606.74 cents). However, 43\24 is essentially the 6th harmonic (1514.83+1586.965=3101.79 cents).
	{{Harmonics in equal\|24\|1457\|536\|title=Approximation of harmonics in 24-EDe}}		{{Harmonics in equal\|24\|1457\|536\|title=Approximation of harmonics in 24-EDe}}

			== See also ==
			* [[Edϕ]]
			* [[Acoustic pi]]
			* [[User:Eliora/Phi to the phi]]

	[[Category:Transcendental]]		[[Category:Transcendental]]
	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]