6/5 - Revision history

ArrowHead294: /* Approximation */

2025-11-06T17:29:42Z

Approximation

← Older revision		Revision as of 17:29, 6 November 2025
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	== Approximation ==		== Approximation ==
	6/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.		6/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.
	{{Interval edo approximation~~\|{{PAGENAME}}~~}}		{{Interval edo approximation}}

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

Pailiaq at 19:40, 3 November 2025

2025-11-03T19:40:47Z

← Older revision		Revision as of 19:40, 3 November 2025
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	== Approximation ==		== Approximation ==
	6/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.		6/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.
	{{Interval edo approximation\|~~PAGENUM~~}}		{{Interval edo approximation\|{{PAGENAME}}}}

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

Pailiaq at 19:40, 3 November 2025

2025-11-03T19:40:17Z

← Older revision		Revision as of 19:40, 3 November 2025
Line 11:		Line 11:
	== Approximation ==		== Approximation ==
	6/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.		6/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.
	{{Interval edo approximation\|~~25/24~~}}		{{Interval edo approximation\|PAGENUM}}

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

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

2025-11-03T13:10:58Z

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

← Older revision		Revision as of 13:10, 3 November 2025
Line 11:		Line 11:
	== Approximation ==		== Approximation ==
	6/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.		6/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.
	{{~~Interval_Edo_Approximation~~ \| 25/24}}		{{Interval edo approximation\|25/24}}

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

Pailiaq: Removed previous table, changed it for the updated and modifiable table

2025-11-03T07:04:13Z

Removed previous table, changed it for the updated and modifiable table

@@ Line 9: / Line 9: @@
 In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.
-== Approximation by edos ==
+== Approximation ==
 /5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.
+ {{Interval_Edo_Approximation | 25/24}}
 == See also ==

FloraC: Recategorize

2024-09-30T08:38:48Z

Recategorize

← Older revision		Revision as of 08:38, 30 September 2024
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	[[Category:Third]]		[[Category:Third]]
	[[Category:Minor third]]		[[Category:Minor third]]
	[[Category:Over-5]]		[[Category:Over-5 intervals]]

FloraC: Reference moved

2023-08-15T10:32:17Z

Reference moved

← Older revision		Revision as of 10:32, 15 August 2023
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	}}		}}
	{{Wikipedia\|Minor third}}		{{Wikipedia\|Minor third}}
	In [[5-limit]] [[just intonation]], '''6/5''' is the '''just minor third''', '''classic(al) minor third''', or '''ptolemaic minor third'''<ref>For reference, see [[5/4]]. </ref>, measuring about 315.6[[cent\|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO\|edos]]. It arises in the [[harmonic series]] between the 5th and 6th harmonics and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15.		In [[5-limit]] [[just intonation]], '''6/5''' is the '''just minor third''', '''classic(al) minor third''', or '''ptolemaic minor third'''<ref>For reference, see [[5-limit]]. </ref>, measuring about 315.6[[cent\|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO\|edos]]. It arises in the [[harmonic series]] between the 5th and 6th harmonics and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15.

	In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.		In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.

Aura at 15:09, 25 January 2023

2023-01-25T15:09:55Z

← Older revision		Revision as of 15:09, 25 January 2023
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	}}		}}
	{{Wikipedia\|Minor third}}		{{Wikipedia\|Minor third}}
	In [[5-limit]] [[just intonation]], '''6/5''' is the '''just''', '''classic(al)''', or '''ptolemaic minor third'''<ref>For reference, see [[5/4]]. </ref>, measuring about 315.6[[cent\|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO\|edos]]. It arises in the [[harmonic series]] between the 5th and 6th harmonics and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15.		In [[5-limit]] [[just intonation]], '''6/5''' is the '''just minor third''', '''classic(al) minor third''', or '''ptolemaic minor third'''<ref>For reference, see [[5/4]]. </ref>, measuring about 315.6[[cent\|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO\|edos]]. It arises in the [[harmonic series]] between the 5th and 6th harmonics and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15.

	In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.		In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.

FloraC: Names

2023-01-12T12:22:25Z

Names

← Older revision		Revision as of 12:22, 12 January 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = classic~~/just~~ minor third		\| Name = just minor third, classic(al) minor third, ptolemaic minor third
	\| Color name = g3, gu 3rd		\| Color name = g3, gu 3rd
	\| Sound = jid_6_5_pluck_adu_dr220.mp3		\| Sound = jid_6_5_pluck_adu_dr220.mp3
	}}		}}
	{{Wikipedia\|Minor third}}		{{Wikipedia\|Minor third}}
	In [[5-limit]] [[just intonation]], '''6/5''' is the '''classic''' or '''~~just~~ minor third''', measuring about 315.6[[cent\|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO\|edos]]. It arises in the [[harmonic series]] between the 5th and 6th harmonics and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15.		In [[5-limit]] [[just intonation]], '''6/5''' is the '''just''', '''classic(al)''', or '''ptolemaic minor third'''<ref>For reference, see [[5/4]]. </ref>, measuring about 315.6[[cent\|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO\|edos]]. It arises in the [[harmonic series]] between the 5th and 6th harmonics and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15.

	In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.		In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.

	== Approximation by ~~EDOs~~ ==		== Approximation by edos ==
	It is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.		6/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.

	The following [[~~EDO~~]]s (up to 200) contain good approximations<ref>error magnitude below 7, both, absolute (in ¢) and relative (in r¢)</ref> of the interval 6/5. Errors are given by magnitude, the arrows in the table show if the ~~EDO~~ representation is sharp (↑) or flat (↓).		The following [[edo]]s (up to 200) contain good approximations<ref>error magnitude below 7, both, absolute (in ¢) and relative (in r¢)</ref> of the interval 6/5. Errors are given by magnitude, the arrows in the table show if the edo representation is sharp (↑) or flat (↓).

	{\| class="wikitable sortable right-1 center-2 right-3 right-4 center-5"		{\| class="wikitable sortable right-1 center-2 right-3 right-4 center-5"
	\|-		\|-
	! [[~~EDO~~]]		! [[Edo]]
	! class="unsortable" \| deg\edo		! class="unsortable" \| deg\edo
	! Absolute <br> error ([[Cent\|¢]])		! Absolute <br> error ([[Cent\|¢]])
	! Relative <br> error ([[Relative cent\|r¢]])		! Relative <br> error ([[Relative cent\|r¢]])
	! ↕		! ↕
	! class="unsortable" \| Equally acceptable multiples <ref>Super ~~EDOs~~ up to 200 within the same error tolerance</ref>		! class="unsortable" \| Equally acceptable multiples <ref>Super-edos up to 200 within the same error tolerance</ref>
	\|-		\|-
	\| [[15edo\|15]] \|\| 4\15 \|\| 4.3587 \|\| 5.4484 \|\| ↑ \|\|		\| [[15edo\|15]] \|\| 4\15 \|\| 4.3587 \|\| 5.4484 \|\| ↑ \|\|
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	\| [[194edo\|194]] \|\| 51\194 \|\| 0.1774 \|\| 2.8675 \|\| ↓ \|\|		\| [[194edo\|194]] \|\| 51\194 \|\| 0.1774 \|\| 2.8675 \|\| ↓ \|\|
	\|}		\|}
	~~<references/>~~

	== See also ==		== See also ==
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[:File:Ji-6-5-csound-foscil-220hz.mp3]] – another sound example		* [[:File:Ji-6-5-csound-foscil-220hz.mp3]] – another sound example

			== Notes ==
			<references/>

	[[Category:Third]]		[[Category:Third]]
	[[Category:Minor third]]		[[Category:Minor third]]
	[[Category:Over-5]]		[[Category:Over-5]]

Plumtree: Normalising usage of Infobox Interval

2022-10-25T16:25:36Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 16:25, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 6/5~~
	~~\| Monzo = 1 1 -1~~
	~~\| Cents = 315.64129~~
	\| Name = classic/just minor third		\| Name = classic/just minor third
	\| Color name = g3, gu 3rd		\| Color name = g3, gu 3rd
	~~\| FJS name = m3<sub>5</sub>~~
	\| Sound = jid_6_5_pluck_adu_dr220.mp3		\| Sound = jid_6_5_pluck_adu_dr220.mp3
	}}		}}
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	* [[:File:Ji-6-5-csound-foscil-220hz.mp3]] – another sound example		* [[:File:Ji-6-5-csound-foscil-220hz.mp3]] – another sound example

	~~[[Category:5-limit]]~~
	[[Category:Third]]		[[Category:Third]]
	[[Category:Minor third]]		[[Category:Minor third]]
	~~[[Category:Superparticular]]~~
	[[Category:Over-5]]		[[Category:Over-5]]