Acoustic e - Revision history

Overthink: /* Approximations */ more accurate interval

2025-12-12T23:45:11Z

Approximations: more accurate interval

← Older revision		Revision as of 23:45, 12 December 2025
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	''e'' lies between the JI intervals [[8/3]] and [[11/4]] and is well-approximated by [[49/18]] and [[87/32]], making it a rather sharp eleventh. Due to the limit definition of ''e'', it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are {{EDOs\|2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253}}.		''e'' lies between the JI intervals [[8/3]] and [[11/4]] and is well-approximated by [[49/18]] and [[87/32]], making it a rather sharp eleventh. Due to the limit definition of ''e'', it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are {{EDOs\|2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253}}.
	==Approximations==		==Approximations==
	{{interval edo approximation\| interval = ~~271828~~/~~100000~~}}		{{interval edo approximation\| interval = 271801/99990}}

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

Pailiaq: /* Approxomations */

2025-11-27T01:06:44Z

Approxomations

← Older revision		Revision as of 01:06, 27 November 2025
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	''e'' lies between the JI intervals [[8/3]] and [[11/4]] and is well-approximated by [[49/18]] and [[87/32]], making it a rather sharp eleventh. Due to the limit definition of ''e'', it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are {{EDOs\|2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253}}.		''e'' lies between the JI intervals [[8/3]] and [[11/4]] and is well-approximated by [[49/18]] and [[87/32]], making it a rather sharp eleventh. Due to the limit definition of ''e'', it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are {{EDOs\|2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253}}.
	==~~Approxomations~~==		==Approximations==
	{{interval edo approximation\| interval = 271828/100000}}		{{interval edo approximation\| interval = 271828/100000}}

	== See also ==		== See also ==
	* [[Ede\|Ed''e'']], equal divisions of this interval		* [[Ede\|Ed''e'']], equal divisions of this interval

Pailiaq: added interval table for acoustic e

2025-11-26T22:27:00Z

added interval table for acoustic e

← Older revision		Revision as of 22:27, 26 November 2025
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	''e'' lies between the JI intervals [[8/3]] and [[11/4]] and is well-approximated by [[49/18]] and [[87/32]], making it a rather sharp eleventh. Due to the limit definition of ''e'', it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are {{EDOs\|2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253}}.		''e'' lies between the JI intervals [[8/3]] and [[11/4]] and is well-approximated by [[49/18]] and [[87/32]], making it a rather sharp eleventh. Due to the limit definition of ''e'', it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are {{EDOs\|2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253}}.
			==Approxomations==
			{{interval edo approximation\| interval = 271828/100000}}
	== See also ==		== See also ==
	* [[Ede\|Ed''e'']], equal divisions of this interval		* [[Ede\|Ed''e'']], equal divisions of this interval

FloraC: Style

2025-07-31T14:19:48Z

Style

← Older revision		Revision as of 14:19, 31 July 2025
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			{{DISPLAYTITLE:Acoustic ''e''}}
	{{Infobox Interval		{{Infobox Interval
	\| Ratio = e		\| Ratio = e
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	\| Name = natave		\| Name = natave
	}}		}}
	'''''e''''' is a mathematical constant associated with the natural logarithm. Because pitch is logarithmic with respect to frequency, it might be of interest in xenharmony as well, where the name '''natave''' (a portmanteau of "natural" and "octave") is suggested for the interval e, ~~aka~~ e/1.		'''''e''''' is a mathematical constant associated with the natural logarithm. Because pitch is logarithmic with respect to frequency, it might be of interest in xenharmony as well, where the name '''natave''' (a portmanteau of "natural" and "octave") is suggested for the interval ''e'', a.k.a. ''e''/1.

	''e'' lies between the JI intervals [[8/3]] and [[11/4]] and is well-approximated by [[49/18]] and [[87/32]], making it a rather sharp eleventh. Due to the limit definition of ''e'', it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are {{EDOs\|2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253}}.		''e'' lies between the JI intervals [[8/3]] and [[11/4]] and is well-approximated by [[49/18]] and [[87/32]], making it a rather sharp eleventh. Due to the limit definition of ''e'', it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are {{EDOs\|2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253}}.

	== See also ==		== See also ==
	* [[~~EDN~~]], equal divisions of this interval		* [[Ede\|Ed''e'']], equal divisions of this interval
	* [[Zetave]], the result of stacking 𝜏 nataves, of interest in regards to the [[zeta]] function		* [[Zetave]], the result of stacking 𝜏 nataves, of interest in regards to the [[zeta]] function

	[[Category:Transcendental]]		[[Category:Transcendental]]

FloraC: FloraC moved page Natave to Acoustic e: Follow similar pages

2025-07-31T14:16:54Z

FloraC moved page Natave to Acoustic e: Follow similar pages

← Older revision	Revision as of 14:16, 31 July 2025
(No difference)

BudjarnLambeth: Formatting

2025-05-19T02:25:40Z

Formatting

← Older revision		Revision as of 02:25, 19 May 2025
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	\| Name = natave		\| Name = natave
	}}		}}
	'''e''' is a mathematical constant associated with the natural logarithm. Because pitch is logarithmic with respect to frequency, it might be of interest in xenharmony as well, where the name ''natave'' (a portmanteau of "natural" and "octave") is suggested. It lies between the JI intervals [[8/3]] and [[11/4]] and is well-approximated by [[49/18]] and [[87/32]], making it a rather sharp eleventh. Due to the limit definition of e, it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are 2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253.		'''''e''''' is a mathematical constant associated with the natural logarithm. Because pitch is logarithmic with respect to frequency, it might be of interest in xenharmony as well, where the name '''natave''' (a portmanteau of "natural" and "octave") is suggested for the interval e, aka e/1.

			''e'' lies between the JI intervals [[8/3]] and [[11/4]] and is well-approximated by [[49/18]] and [[87/32]], making it a rather sharp eleventh. Due to the limit definition of ''e'', it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are {{EDOs\|2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253}}.

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

Lériendil at 14:49, 8 April 2025

2025-04-08T14:49:59Z

← Older revision		Revision as of 14:49, 8 April 2025
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	\| Name = natave		\| Name = natave
	}}		}}
	'''e''' is a mathematical constant associated with the natural logarithm. Because pitch is logarithmic with respect to frequency, it might be of interest in xenharmony as well, where the name ''natave'' (a portmanteau of "natural" and "octave") is suggested. It ~~is close to~~ the JI intervals 8/3~~, 43/16,~~ and 11/4, making it a rather sharp eleventh. Due to the limit definition of e, it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are 2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253.		'''e''' is a mathematical constant associated with the natural logarithm. Because pitch is logarithmic with respect to frequency, it might be of interest in xenharmony as well, where the name ''natave'' (a portmanteau of "natural" and "octave") is suggested. It lies between the JI intervals [[8/3]] and [[11/4]] and is well-approximated by [[49/18]] and [[87/32]], making it a rather sharp eleventh. Due to the limit definition of e, it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are 2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253.

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

VectorGraphics at 05:53, 26 March 2025

2025-03-26T05:53:57Z

← Older revision		Revision as of 05:53, 26 March 2025
Line 8:		Line 8:
	== See also ==		== See also ==
	* [[EDN]], equal divisions of this interval		* [[EDN]], equal divisions of this interval
			* [[Zetave]], the result of stacking 𝜏 nataves, of interest in regards to the [[zeta]] function
	[[Category:Transcendental]]		[[Category:Transcendental]]

Plumtree: Infobox Interval added

2022-10-27T18:56:43Z

Infobox Interval added

← Older revision		Revision as of 18:56, 27 October 2022
Line 1:		Line 1:
			{{Infobox Interval
			\| Ratio = e
			\| Cents = 1731.2340490667561
			\| Name = natave
			}}
	'''e''' is a mathematical constant associated with the natural logarithm. Because pitch is logarithmic with respect to frequency, it might be of interest in xenharmony as well, where the name ''natave'' (a portmanteau of "natural" and "octave") is suggested. It is close to the JI intervals 8/3, 43/16, and 11/4, making it a rather sharp eleventh. Due to the limit definition of e, it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are 2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253.		'''e''' is a mathematical constant associated with the natural logarithm. Because pitch is logarithmic with respect to frequency, it might be of interest in xenharmony as well, where the name ''natave'' (a portmanteau of "natural" and "octave") is suggested. It is close to the JI intervals 8/3, 43/16, and 11/4, making it a rather sharp eleventh. Due to the limit definition of e, it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are 2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253.

Yourmusic Productions: Convergent series

2022-06-19T18:53:56Z

Convergent series

← Older revision		Revision as of 18:53, 19 June 2022
Line 1:		Line 1:
	'''e''' is a mathematical constant associated with the natural logarithm. Because pitch is logarithmic with respect to frequency, it might be of interest in xenharmony as well, where the name ''natave'' (a portmanteau of "natural" and "octave") is suggested. It is close to the JI intervals 8/3, 43/16, and 11/4, making it a rather sharp eleventh. Due to the limit definition of e, it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc.		'''e''' is a mathematical constant associated with the natural logarithm. Because pitch is logarithmic with respect to frequency, it might be of interest in xenharmony as well, where the name ''natave'' (a portmanteau of "natural" and "octave") is suggested. It is close to the JI intervals 8/3, 43/16, and 11/4, making it a rather sharp eleventh. Due to the limit definition of e, it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are 2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253.

	== See also ==		== See also ==
	* [[EDN]], equal divisions of this interval		* [[EDN]], equal divisions of this interval
	[[Category:Transcendental]]		[[Category:Transcendental]]