2ed13/10 - Revision history

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:21:51Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:21, 1 August 2025
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	13/10		13/10
	</pre>		</pre>

	~~[[Category:Edonoi]]~~

Lériendil: /* */

2025-05-03T04:19:08Z

← Older revision		Revision as of 04:19, 3 May 2025
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	[[File:sqrt13_10_harmonic_contents.jpg\|alt=sqrt13_10_harmonic_contents.jpg\|sqrt13_10_harmonic_contents.jpg]]		[[File:sqrt13_10_harmonic_contents.jpg\|alt=sqrt13_10_harmonic_contents.jpg\|sqrt13_10_harmonic_contents.jpg]]

	~~=== ===~~

	== Music ==		== Music ==

Plumtree: Infobox ET added

2022-10-05T20:52:50Z

Infobox ET added

← Older revision		Revision as of 20:52, 5 October 2022
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			{{Infobox ET}}
	'''2 equal divisions of 13/10''', when viewed from a regular temperament perspective, is a nonoctave tuning system created by diving the interval of 13/10 into two steps of about 227.1 cents each. It is equivalent to about 5.284edo.		'''2 equal divisions of 13/10''', when viewed from a regular temperament perspective, is a nonoctave tuning system created by diving the interval of 13/10 into two steps of about 227.1 cents each. It is equivalent to about 5.284edo.

Eliora: /* Harmonic content */

2022-04-07T10:07:18Z

Harmonic content

← Older revision		Revision as of 10:07, 7 April 2022
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	===Harmonic content===		===Harmonic content===

			{{Harmonics in equal\|2\|13\|10}}

	Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords.		Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords.

FloraC: /* Music */ Formatting

2022-04-03T12:44:25Z

Music: Formatting

← Older revision		Revision as of 12:44, 3 April 2022
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	=== ===		=== ===

	==Music==		== Music ==

	[http://soundcloud.com/andrew_heathwaite/truffles Truffles?] by Andrew Heathwaite and Michael Gaiuranos		* [http://soundcloud.com/andrew_heathwaite/truffles Truffles?] by [[Andrew Heathwaite]] and [[Michael Gaiuranos]]

	~~===Scala file===~~

			== Scala file ==
			<pre>
	! sqrt13over10.scl		! sqrt13over10.scl

	The square root of 13:10 nonoctave temperament.		The square root of 13:10 nonoctave temperament.

	2		2

	!		!

	227.106973952238		227.106973952238

	13/10		13/10
			</pre>

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

Eliora: Wikification (and the past few edits also)

2022-04-03T11:50:13Z

Wikification (and the past few edits also)

← Older revision		Revision as of 11:50, 3 April 2022
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	13/10		13/10

			[[Category:Edonoi]]

Eliora at 11:49, 3 April 2022

2022-04-03T11:49:32Z

← Older revision		Revision as of 11:49, 3 April 2022
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	==13:10==		'''2 equal divisions of 13/10''', when viewed from a regular temperament perspective, is a nonoctave tuning system created by diving the interval of 13/10 into two steps of about 227.1 cents each. It is equivalent to about 5.284edo.

	[[13/10\|13:10]], as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a "third" and that of a "fourth" (see [[Interseptimal\|interseptimal]]). It appears in the [[OverToneSeries\|overtone series]] between the tenth and thirteen overtones.		==Theory==

	~~==sqrt~~ 13:10 as ~~an interval==~~		[[13/10\|13:10]], as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a "third" and that of a "fourth" (see [[interseptimal]]). It appears in the [[OverToneSeries\|overtone series]] between the tenth and thirteen overtones. The "square root of 13:10", then, means an interval which logarithmically bisects 13:10. It's an irrational number which measures, in cents, about 227.1.

	The "square root of 13:10", then, means an interval which logarithmically bisects 13:10. It's an irrational number which measures, in cents, about 227.1.

	~~==2ed13/10 as a scale==~~

	"The square root of 13:10" can also refer to the scale that is produced by repeatedly stacking the interval "the square root of 13:10". It is an [[edonoi\|EDONOI]], or "equal division of a nonoctave interval," and as such, it does not contain a perfect octave (2:1). It is also [[macrotonal\|macrotonal]], since the smallest step, at 227.1 cents, is larger than a semitone.		"The square root of 13:10" can also refer to the scale that is produced by repeatedly stacking the interval "the square root of 13:10". It is an [[edonoi\|EDONOI]], or "equal division of a nonoctave interval," and as such, it does not contain a perfect octave (2:1). It is also [[macrotonal\|macrotonal]], since the smallest step, at 227.1 cents, is larger than a semitone.

	In terms of [[EDO\|equal divisions of the octave]], it fits between [[5edo\|5edo]] and [[6edo\|6edo]] ~~(about 5.284edo)~~. Melodically, it can sound somewhat "pentatonic," but harmonically it is very different.		In terms of [[EDO\|equal divisions of the octave]], it fits between [[5edo\|5edo]] and [[6edo\|6edo]]. Melodically, it can sound somewhat "pentatonic," but harmonically it is very different.

	==~~harmonic~~ content==		===Harmonic content===

	Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords.		Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords.

Eliora: Fixing "page titles" and giving normal headers.

2022-04-03T11:47:02Z

Fixing "page titles" and giving normal headers.

← Older revision		Revision as of 11:47, 3 April 2022
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	[[13/10\|13:10]], as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a "third" and that of a "fourth" (see [[Interseptimal\|interseptimal]]). It appears in the [[OverToneSeries\|overtone series]] between the tenth and thirteen overtones.		[[13/10\|13:10]], as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a "third" and that of a "fourth" (see [[Interseptimal\|interseptimal]]). It appears in the [[OverToneSeries\|overtone series]] between the tenth and thirteen overtones.

	=sqrt 13:10 as an interval=		==sqrt 13:10 as an interval==

	The "square root of 13:10", then, means an interval which logarithmically bisects 13:10. It's an irrational number which measures, in cents, about 227.1.		The "square root of 13:10", then, means an interval which logarithmically bisects 13:10. It's an irrational number which measures, in cents, about 227.1.

Eliora at 11:46, 3 April 2022

2022-04-03T11:46:41Z

← Older revision		Revision as of 11:46, 3 April 2022
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	=13:10=		==13:10==

	[[13/10\|13:10]], as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a "third" and that of a "fourth" (see [[Interseptimal\|interseptimal]]). It appears in the [[OverToneSeries\|overtone series]] between the tenth and thirteen overtones.		[[13/10\|13:10]], as a frequency ratio, measures approximately 454.2 cents. It lies in the extremely xenharmonic and ambiguous territory between the perceptual category of a "third" and that of a "fourth" (see [[Interseptimal\|interseptimal]]). It appears in the [[OverToneSeries\|overtone series]] between the tenth and thirteen overtones.
Line 7:		Line 7:
	The "square root of 13:10", then, means an interval which logarithmically bisects 13:10. It's an irrational number which measures, in cents, about 227.1.		The "square root of 13:10", then, means an interval which logarithmically bisects 13:10. It's an irrational number which measures, in cents, about 227.1.

	=~~sqrt 13:~~10 as a scale=		==2ed13/10 as a scale==

	"The square root of 13:10" can also refer to the scale that is produced by repeatedly stacking the interval "the square root of 13:10". It is an [[edonoi\|EDONOI]], or "equal division of a nonoctave interval," and as such, it does not contain a perfect octave (2:1). It is also [[macrotonal\|macrotonal]], since the smallest step, at 227.1 cents, is larger than a semitone.		"The square root of 13:10" can also refer to the scale that is produced by repeatedly stacking the interval "the square root of 13:10". It is an [[edonoi\|EDONOI]], or "equal division of a nonoctave interval," and as such, it does not contain a perfect octave (2:1). It is also [[macrotonal\|macrotonal]], since the smallest step, at 227.1 cents, is larger than a semitone.

Eliora: Eliora moved page Square root of 13 over 10 to 2ed13/10: This is discussing the tuning system resulted by dividing 13/10 in two, not an interval of (13/10)^(1/2).

2022-04-03T11:46:16Z

Eliora moved page Square root of 13 over 10 to 2ed13/10: This is discussing the tuning system resulted by dividing 13/10 in two, not an interval of (13/10)^(1/2).

← Older revision	Revision as of 11:46, 3 April 2022
(No difference)