13/10 - Revision history

Fredg999: Use c template instead of cent in tables

2026-06-28T07:41:25Z

Use c template instead of cent in tables

← Older revision		Revision as of 07:41, 28 June 2026
Line 24:		Line 24:
	\| 1		\| 1
	\| 454.2		\| 454.2
	\| 13/10<br>[[17/13]] (+10.2{{~~cent~~}})		\| 13/10<br>[[17/13]] (+10.2{{c}})
	\| <br>[[170/169]] (major naiadma)		\| <br>[[170/169]] (major naiadma)
	\|-		\|-
	\| 2		\| 2
	\| 908.4		\| 908.4
	\| [[27/16]] (-2.6{{~~cent~~}})<br>[[22/13]] (+2.4{{~~cent~~}})<br>[[17/10]] (+10.2{{~~cent~~}})		\| [[27/16]] (-2.6{{c}})<br>[[22/13]] (+2.4{{c}})<br>[[17/10]] (+10.2{{c}})
	\| [[676/675]] (island comma)<br>[[2200/2197]] (petrma)<br>[[170/169]] (major naiadma)		\| [[676/675]] (island comma)<br>[[2200/2197]] (petrma)<br>[[170/169]] (major naiadma)
	\|-		\|-
	\| 3		\| 3
	\| 1362.6		\| 1362.6
	\| [[11/5]] (+2.4{{~~cent~~}})		\| [[11/5]] (+2.4{{c}})
	\| [[2200/2197]] (petrma)		\| [[2200/2197]] (petrma)
	\|-		\|-
	\| 4		\| 4
	\| 1816.9		\| 1816.9
	\| [[20/7]] (+0.6{{~~cent~~}})		\| [[20/7]] (+0.6{{c}})
	\| [[200000/199927]]		\| [[200000/199927]]
	\|-		\|-
	\| 5		\| 5
	\| 2271.1		\| 2271.1
	\| [[26/7]] (+0.6{{~~cent~~}})		\| [[26/7]] (+0.6{{c}})
	\| [[200000/199927]]		\| [[200000/199927]]
	\|}		\|}

FloraC: Fix redundant hyphen

2026-01-22T16:29:33Z

Fix redundant hyphen

← Older revision		Revision as of 16:29, 22 January 2026
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	\| Sound = jid_13_10_pluck_adu_dr220.mp3		\| Sound = jid_13_10_pluck_adu_dr220.mp3
	}}		}}

	In [[13-limit]] [[just intonation]], '''13/10''', the '''tridecimal semisixth''' is an [[interseptimal]] interval measuring about 454.2 [[cent]]s. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes.		In [[13-limit]] [[just intonation]], '''13/10''', the '''tridecimal semisixth''' is an [[interseptimal]] interval measuring about 454.2 [[cent]]s. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes.

	In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), 13/10 is a fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[40/39]], which is a [[2187/2048\|Pythagorean apotome]] minus a stack consisting of an [[81/80\|syntonic comma (81/80)]] and a [[1053/1024\|tridecimal quartertone (1053/1024)]], none of which changes the [[scale\|scale degree]]. It functions as such in the harmonic thirteenth chord, [[4:5:6:7:9:11:13]].		In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), 13/10 is a fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[40/39]], which is a [[2187/2048\|Pythagorean apotome]] minus a stack consisting of an [[81/80\|syntonic comma (81/80)]] and a [[1053/1024\|tridecimal quartertone (1053/1024)]], none of which changes the [[scale\|scale degree]]. It functions as such in the harmonic thirteenth chord, [[4:5:6:7:9:11:13]].

	However, 13/10 also appears in the relatively-simple [[10:13:15]] triad, which consists of 13/10 and [[15/13]] that stack to make a [[3/2]] perfect fifth. This makes 13/10 function as an ultramajor third (if the chord is not taken as a suspension). It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[edo]] systems.		However, 13/10 also appears in the relatively simple [[10:13:15]] triad, which consists of 13/10 and [[15/13]] that stack to make a [[3/2]] perfect fifth. This makes 13/10 function as an ultramajor third (if the chord is not taken as a suspension). It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[edo]] systems.

	== Interval chain ==		== Interval chain ==

FloraC: Elaborate on its ambiguous quality

2026-01-22T16:21:35Z

Elaborate on its ambiguous quality

← Older revision		Revision as of 16:21, 22 January 2026
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	}}		}}

	In [[13-limit]] [[just intonation]], '''13/10''', the '''tridecimal semisixth''' is an [[interseptimal]] interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes. 13/10 ~~appears between the 10th~~ and ~~13th overtones~~ of the [[~~harmonic series~~]] ~~and appears~~ in ~~such chords as 8~~:10:13, ~~a quasi-augmented triad.~~ 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of ~~an interseptimal ultramajor third (~~13/10) and ~~an interseptimal inframinor third (~~[[15/13]]~~) which~~ stack to make a [[3/2]] perfect fifth. It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[~~EDO~~]] systems.		In [[13-limit]] [[just intonation]], '''13/10''', the '''tridecimal semisixth''' is an [[interseptimal]] interval measuring about 454.2 [[cent]]s. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes.

			In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), 13/10 is a fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[40/39]], which is a [[2187/2048\|Pythagorean apotome]] minus a stack consisting of an [[81/80\|syntonic comma (81/80)]] and a [[1053/1024\|tridecimal quartertone (1053/1024)]], none of which changes the [[scale\|scale degree]]. It functions as such in the harmonic thirteenth chord, [[4:5:6:7:9:11:13]].

			However, 13/10 also appears in the relatively-simple [[10:13:15]] triad, which consists of 13/10 and [[15/13]] that stack to make a [[3/2]] perfect fifth. This makes 13/10 function as an ultramajor third (if the chord is not taken as a suspension). It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[edo]] systems.

	== Interval chain ==		== Interval chain ==
	Because 13/10 is an interseptimal interval, stacking it four times will result in a good approximation of a septimal interval. In this case, (13/10)<sup>4</sup> approximates 20/7 (compound [[10/7]]) remarkably well, with less than 1{{cent}} error.		Because 13/10 is an interseptimal interval, stacking it four times will result in a good approximation of a septimal interval. In this case, (13/10)<sup>4</sup> approximates 20/7 (compound [[10/7]]) remarkably well, with less than 1{{cent}} error.

	Additionally, while it may seem as though (13/10)<sup>2</sup> ~~doesn't~~ approximate 17/10 very well at first glance, it allows for an elegant interpretation of the tetrad formed by stacking 13/10 three times on top of itself: [[~]]10:13:17:22.		Additionally, while it may seem as though (13/10)<sup>2</sup> does not approximate 17/10 very well at first glance, it allows for an elegant interpretation of the tetrad formed by stacking 13/10 three times on top of itself: [[~]]10:13:17:22.

	{\| class="wikitable"		{\| class="wikitable"
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	\| [[200000/199927]]		\| [[200000/199927]]
	\|}		\|}

	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|13/10}}		{{Interval edo approximation\|13/10}}

	== See also ==		== See also ==
	* [[20/13]] – its [[octave complement]]		* [[20/13]] – its [[octave complement]]

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:12:30Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:12, 3 November 2025
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	\|}		\|}
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 13/10}}		{{Interval edo approximation\|13/10}}
	== See also ==		== See also ==
	* [[20/13]] – its [[octave complement]]		* [[20/13]] – its [[octave complement]]

Pailiaq at 07:18, 3 November 2025

2025-11-03T07:18:22Z

← Older revision		Revision as of 07:18, 3 November 2025
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	\| [[200000/199927]]		\| [[200000/199927]]
	\|}		\|}
			== Approximation ==
			{{Interval_Edo_Approximation \| 13/10}}
	== See also ==		== See also ==
	* [[20/13]] – its [[octave complement]]		* [[20/13]] – its [[octave complement]]

Squib at 11:37, 1 August 2025

2025-08-01T11:37:22Z

← Older revision		Revision as of 11:37, 1 August 2025
Line 21:		Line 21:
	\| 1		\| 1
	\| 454.2		\| 454.2
	\| 13/10		\| 13/10<br>[[17/13]] (+10.2{{cent}})
	\|		\| <br>[[170/169]] (major naiadma)
	\|-		\|-
	\| 2		\| 2

Fredg999: Add interval chain section

2025-08-01T03:40:04Z

Add interval chain section

← Older revision		Revision as of 03:40, 1 August 2025
Line 6:		Line 6:

	In [[13-limit]] [[just intonation]], '''13/10''', the '''tridecimal semisixth''' is an [[interseptimal]] interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the [[harmonic series]] and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third ([[15/13]]) which stack to make a [[3/2]] perfect fifth. It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[EDO]] systems.		In [[13-limit]] [[just intonation]], '''13/10''', the '''tridecimal semisixth''' is an [[interseptimal]] interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the [[harmonic series]] and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third ([[15/13]]) which stack to make a [[3/2]] perfect fifth. It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[EDO]] systems.

			== Interval chain ==
			Because 13/10 is an interseptimal interval, stacking it four times will result in a good approximation of a septimal interval. In this case, (13/10)<sup>4</sup> approximates 20/7 (compound [[10/7]]) remarkably well, with less than 1{{cent}} error.

			Additionally, while it may seem as though (13/10)<sup>2</sup> doesn't approximate 17/10 very well at first glance, it allows for an elegant interpretation of the tetrad formed by stacking 13/10 three times on top of itself: [[~]]10:13:17:22.

			{\| class="wikitable"
			\|+ [[Interval chain]] generated by 13/10
			! #
			! [[Cent]]s
			! Approximated [[ratio]]s
			! Associated [[comma]]s
			\|-
			\| 1
			\| 454.2
			\| 13/10
			\|
			\|-
			\| 2
			\| 908.4
			\| [[27/16]] (-2.6{{cent}})<br>[[22/13]] (+2.4{{cent}})<br>[[17/10]] (+10.2{{cent}})
			\| [[676/675]] (island comma)<br>[[2200/2197]] (petrma)<br>[[170/169]] (major naiadma)
			\|-
			\| 3
			\| 1362.6
			\| [[11/5]] (+2.4{{cent}})
			\| [[2200/2197]] (petrma)
			\|-
			\| 4
			\| 1816.9
			\| [[20/7]] (+0.6{{cent}})
			\| [[200000/199927]]
			\|-
			\| 5
			\| 2271.1
			\| [[26/7]] (+0.6{{cent}})
			\| [[200000/199927]]
			\|}

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

FloraC: Recategorize

2024-09-30T08:40:05Z

Recategorize

← Older revision		Revision as of 08:40, 30 September 2024
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	[[Category:Third]]		[[Category:Third]]
	[[Category:Supermajor third]]		[[Category:Supermajor third]]
	[[Category:Over-5]]		[[Category:Over-5 intervals]]

Fredg999 category edits: Moving from Category:Interseptimal to Category:Interseptimal intervals using Cat-a-lot

2023-04-28T03:27:00Z

Moving from Category:Interseptimal to Category:Interseptimal intervals using Cat-a-lot

← Older revision		Revision as of 03:27, 28 April 2023
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	* [[The Archipelago]]		* [[The Archipelago]]

	[[Category:Interseptimal]]		[[Category:Interseptimal intervals]]
	[[Category:Naiadic]]		[[Category:Naiadic]]
	[[Category:Fourth]]		[[Category:Fourth]]

Plumtree: Normalising usage of Infobox Interval

2022-10-25T11:34:11Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 11:34, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 13/10~~		\| Name = Barbados third, tridecimal semisixth
	~~\| Monzo = -1 0 -1 0 0 1~~
	~~\| Cents = 454.21395~~
	\| Name = Barbados third, ~~<br>~~tridecimal semisixth
	\| Color name = 3og4, thogu 4th		\| Color name = 3og4, thogu 4th
	~~\| FJS name = d4<sup>13</sup><sub>5</sub>~~
	\| Sound = jid_13_10_pluck_adu_dr220.mp3		\| Sound = jid_13_10_pluck_adu_dr220.mp3
	}}		}}
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	* [[The Archipelago]]		* [[The Archipelago]]

	~~[[Category:13-limit]]~~
	[[Category:Interseptimal]]		[[Category:Interseptimal]]
	[[Category:Naiadic]]		[[Category:Naiadic]]