5/4 - Revision history

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

2025-11-03T13:15:18Z

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

← Older revision		Revision as of 13:15, 3 November 2025
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	== Approximations by edos ==		== Approximations by edos ==
	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 5/4.		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 5/4.
	{{~~Interval_Edo_Approximation~~ \| interval = 5/4\| max_edo=200}}		{{Interval edo approximation\|interval = 5/4\| max_edo=200}}

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

Pailiaq: /* Approximations by edos */

2025-11-03T07:13:15Z

Approximations by edos

← Older revision		Revision as of 07:13, 3 November 2025
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	== Approximations by edos ==		== Approximations by edos ==
	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 5/4. .		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 5/4.

	{{Interval_Edo_Approximation \| interval = 5/4\| max_edo=200}}		{{Interval_Edo_Approximation \| interval = 5/4\| max_edo=200}}

Pailiaq: /* Approximations by edos */

2025-11-03T07:12:57Z

Approximations by edos

@@ Line 18: / Line 18: @@
 == Approximations by edos ==
-Following [[edo]]s (up to 200, and also 643) contain good approximations<ref>error magnitude below 7, both, absolute (in ¢) and relative (in r¢)</ref> of the interval 5/4. Errors are given by magnitude, the arrows in the table show if the edo representation is sharp (&uarr;) or flat (&darr;).
+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 5/4. .
-{| class="wikitable sortable right-1 center-2 right-3 right-4 center-5"
+ {{Interval_Edo_Approximation | interval = 5/4| max_edo=200}}
 == See also ==

FloraC: Simplify

2025-04-16T13:37:16Z

Simplify

← Older revision		Revision as of 13:37, 16 April 2025
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	{{Wikipedia\|Major third}}		{{Wikipedia\|Major third}}

	In [[5-limit]] [[just intonation]], '''5/4''' is the [[frequency ratio]] between the 5th and 4th [[harmonic]]s. It has been called the '''just major third''', '''classic(al) major third''', or '''ptolemaic major third'''<ref>For reference, see [[5-limit]].</ref> to distinguish it from other intervals in that neighborhood. Measuring about 386.3 [[cent\|¢]], it is about 13.~~7 ¢~~ away from [[12edo]]'s major third of ~~400 ¢~~. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for [[5-limit]] harmony. It is distinguished from the [[Pythagorean]] major third of [[81/64]] by the syntonic comma of [[81/80]], which measures about 21.~~5 ¢~~. 81/64 and 5/4 are both just intonation "major thirds", 81/64 having a more active and discordant quality, 5/4 sounding more "restful"~~. It is a [[schisma]] sharp of 8192/6561, another 3-limit interval in the major third range often called a diminished fourth~~.		In [[5-limit]] [[just intonation]], '''5/4''' is the [[frequency ratio]] between the 5th and 4th [[harmonic]]s. It has been called the '''just major third''', '''classic(al) major third''', or '''ptolemaic major third'''<ref>For reference, see [[5-limit]].</ref> to distinguish it from other intervals in that neighborhood. Measuring about 386.3 [[cent\|¢]], it is about 13.7{{c}} away from [[12edo]]'s major third of 400{{c}}. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for [[5-limit]] harmony. It is distinguished from the [[Pythagorean]] major third of [[81/64]] by the syntonic comma of [[81/80]], which measures about 21.5{{c}}, and from the Pythagorean diminished fourth of [[8192/6561]] by the [[schisma]], which measures about 1.95{{c}}. 81/64 and 5/4 are both just intonation "major thirds", 81/64 having a more active and discordant quality, 5/4 sounding more "restful".

	In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated in [[:File: 5-4.mp3]] melodically in singing into a resonant [[udderbot]] (from the fundamental up to 5 and then noodling between 5 and 4).		In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated in [[:File: 5-4.mp3]] melodically in singing into a resonant [[udderbot]] (from the fundamental up to 5 and then noodling between 5 and 4).

VectorGraphics at 08:44, 16 April 2025

2025-04-16T08:44:29Z

← Older revision		Revision as of 08:44, 16 April 2025
Line 13:		Line 13:
	{{Wikipedia\|Major third}}		{{Wikipedia\|Major third}}

	In [[5-limit]] [[just intonation]], '''5/4''' is the [[frequency ratio]] between the 5th and 4th [[harmonic]]s. It has been called the '''just major third''', '''classic(al) major third''', or '''ptolemaic major third'''<ref>For reference, see [[5-limit]].</ref> to distinguish it from other intervals in that neighborhood. Measuring about 386.3 [[cent\|¢]], it is about 13.7 ¢ away from [[12edo]]'s major third of 400 ¢. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for [[5-limit]] harmony. It is distinguished from the [[Pythagorean]] major third of [[81/64]] by the syntonic comma of [[81/80]], which measures about 21.5 ¢. 81/64 and 5/4 are both just intonation "major thirds", 81/64 having a more active and discordant quality, 5/4 sounding more "restful".		In [[5-limit]] [[just intonation]], '''5/4''' is the [[frequency ratio]] between the 5th and 4th [[harmonic]]s. It has been called the '''just major third''', '''classic(al) major third''', or '''ptolemaic major third'''<ref>For reference, see [[5-limit]].</ref> to distinguish it from other intervals in that neighborhood. Measuring about 386.3 [[cent\|¢]], it is about 13.7 ¢ away from [[12edo]]'s major third of 400 ¢. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for [[5-limit]] harmony. It is distinguished from the [[Pythagorean]] major third of [[81/64]] by the syntonic comma of [[81/80]], which measures about 21.5 ¢. 81/64 and 5/4 are both just intonation "major thirds", 81/64 having a more active and discordant quality, 5/4 sounding more "restful". It is a [[schisma]] sharp of 8192/6561, another 3-limit interval in the major third range often called a diminished fourth.

	In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated in [[:File: 5-4.mp3]] melodically in singing into a resonant [[udderbot]] (from the fundamental up to 5 and then noodling between 5 and 4).		In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated in [[:File: 5-4.mp3]] melodically in singing into a resonant [[udderbot]] (from the fundamental up to 5 and then noodling between 5 and 4).

AraMax: Added a new language

2024-12-26T22:02:27Z

Added a new language

← Older revision		Revision as of 22:02, 26 December 2024
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	\| es =		\| es =
	\| ja =		\| ja =
			\| ro = 5/4 (ro)
	}}		}}
	{{Infobox Interval		{{Infobox Interval

BudjarnLambeth: /* See also */ link

2024-10-26T23:55:13Z

Fitzgerald Lee: /* See also */Who typed this? Could you please improve your grammar?

2024-10-16T13:40:55Z

See also: Who typed this? Could you please improve your grammar?

← Older revision		Revision as of 13:40, 16 October 2024
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	* [[6/5]] – its [[fifth complement]]		* [[6/5]] – its [[fifth complement]]
	* [[16/15]] – its [[fourth complement]]		* [[16/15]] – its [[fourth complement]]
	* [[5/2]] – the interval ~~plus~~ one [[octave]] sounds even more [[consonant]]		* [[5/2]] – the interval up one [[octave]] which sounds even more [[consonant]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

FloraC: Move reference to 5-limit page

2023-08-15T10:26:42Z

Move reference to 5-limit page

← Older revision		Revision as of 10:26, 15 August 2023
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	{{Wikipedia\|Major third}}		{{Wikipedia\|Major third}}

	In [[5-limit]] [[just intonation]], '''5/4''' is the [[frequency ratio]] between the 5th and 4th [[harmonic]]s. It has been called the '''just major third'''~~<ref>[https://marsbat.space/pdfs/HEJI2_legend+series.pdf ''The Helmholtz-Ellis JI Pitch Notation (HEJI)''] by [[Marc Sabat]] and [[Thomas Nicholson]] from Plainsound Music Edition</ref>~~, '''classic(al) major third'''~~<ref>[https://dkeenan.com/Music/IntervalNaming.htm ''A note on the naming of musical intervals''] by [[Dave Keenan]]</ref>~~, or '''ptolemaic major third'''<ref>[~~https://marsbat.space/pdfs/JI.pdf ''Fundamental Principles of Just Intonation and Microtonal Composition''~~] ~~by Thomas Nicholson and Marc Sabat —"'Ptolemaic' refers to intervals combining only the primes 2, 3, and 5~~."</ref> to distinguish it from other intervals in that neighborhood. Measuring about 386.3 [[cent\|¢]], it is about 13.7 ¢ away from [[12edo]]'s major third of 400 ¢. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for [[5-limit]] harmony. It is distinguished from the [[Pythagorean]] major third of [[81/64]] by the syntonic comma of [[81/80]], which measures about 21.5 ¢. 81/64 and 5/4 are both just intonation "major thirds", 81/64 having a more active and discordant quality, 5/4 sounding more "restful".		In [[5-limit]] [[just intonation]], '''5/4''' is the [[frequency ratio]] between the 5th and 4th [[harmonic]]s. It has been called the '''just major third''', '''classic(al) major third''', or '''ptolemaic major third'''<ref>For reference, see [[5-limit]].</ref> to distinguish it from other intervals in that neighborhood. Measuring about 386.3 [[cent\|¢]], it is about 13.7 ¢ away from [[12edo]]'s major third of 400 ¢. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for [[5-limit]] harmony. It is distinguished from the [[Pythagorean]] major third of [[81/64]] by the syntonic comma of [[81/80]], which measures about 21.5 ¢. 81/64 and 5/4 are both just intonation "major thirds", 81/64 having a more active and discordant quality, 5/4 sounding more "restful".

	In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated in [[:File: 5-4.mp3]] melodically in singing into a resonant [[udderbot]] (from the fundamental up to 5 and then noodling between 5 and 4).		In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated in [[:File: 5-4.mp3]] melodically in singing into a resonant [[udderbot]] (from the fundamental up to 5 and then noodling between 5 and 4).

FloraC: I suppose that file is the udderbot demo(?)

2023-08-15T09:14:02Z

I suppose that file is the udderbot demo(?)

← Older revision		Revision as of 09:14, 15 August 2023
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	In [[5-limit]] [[just intonation]], '''5/4''' is the [[frequency ratio]] between the 5th and 4th [[harmonic]]s. It has been called the '''just major third'''<ref>[https://marsbat.space/pdfs/HEJI2_legend+series.pdf ''The Helmholtz-Ellis JI Pitch Notation (HEJI)''] by [[Marc Sabat]] and [[Thomas Nicholson]] from Plainsound Music Edition</ref>, '''classic(al) major third'''<ref>[https://dkeenan.com/Music/IntervalNaming.htm ''A note on the naming of musical intervals''] by [[Dave Keenan]]</ref>, or '''ptolemaic major third'''<ref>[https://marsbat.space/pdfs/JI.pdf ''Fundamental Principles of Just Intonation and Microtonal Composition''] by Thomas Nicholson and Marc Sabat —"'Ptolemaic' refers to intervals combining only the primes 2, 3, and 5."</ref> to distinguish it from other intervals in that neighborhood. Measuring about 386.3 [[cent\|¢]], it is about 13.7 ¢ away from [[12edo]]'s major third of 400 ¢. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for [[5-limit]] harmony. It is distinguished from the [[Pythagorean]] major third of [[81/64]] by the syntonic comma of [[81/80]], which measures about 21.5 ¢. 81/64 and 5/4 are both just intonation "major thirds", 81/64 having a more active and discordant quality, 5/4 sounding more "restful".		In [[5-limit]] [[just intonation]], '''5/4''' is the [[frequency ratio]] between the 5th and 4th [[harmonic]]s. It has been called the '''just major third'''<ref>[https://marsbat.space/pdfs/HEJI2_legend+series.pdf ''The Helmholtz-Ellis JI Pitch Notation (HEJI)''] by [[Marc Sabat]] and [[Thomas Nicholson]] from Plainsound Music Edition</ref>, '''classic(al) major third'''<ref>[https://dkeenan.com/Music/IntervalNaming.htm ''A note on the naming of musical intervals''] by [[Dave Keenan]]</ref>, or '''ptolemaic major third'''<ref>[https://marsbat.space/pdfs/JI.pdf ''Fundamental Principles of Just Intonation and Microtonal Composition''] by Thomas Nicholson and Marc Sabat —"'Ptolemaic' refers to intervals combining only the primes 2, 3, and 5."</ref> to distinguish it from other intervals in that neighborhood. Measuring about 386.3 [[cent\|¢]], it is about 13.7 ¢ away from [[12edo]]'s major third of 400 ¢. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for [[5-limit]] harmony. It is distinguished from the [[Pythagorean]] major third of [[81/64]] by the syntonic comma of [[81/80]], which measures about 21.5 ¢. 81/64 and 5/4 are both just intonation "major thirds", 81/64 having a more active and discordant quality, 5/4 sounding more "restful".

	In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated ~~here~~ melodically in singing into a resonant [[udderbot]] (from the fundamental up to 5 and then noodling between 5 and 4).		In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated in [[:File: 5-4.mp3]] melodically in singing into a resonant [[udderbot]] (from the fundamental up to 5 and then noodling between 5 and 4).

	== Approximations by edos ==		== Approximations by edos ==
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[:File:5-4.mp3]] – sound sample that illustrates 5/4 as the interval between sung overtones

	== Notes ==		== Notes ==

← Older revision		Revision as of 23:55, 26 October 2024
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	* [[16/15]] – its [[fourth complement]]		* [[16/15]] – its [[fourth complement]]
	* [[5/2]] – the interval up one [[octave]] which sounds even more [[consonant]]		* [[5/2]] – the interval up one [[octave]] which sounds even more [[consonant]]
			* [[Ed5/4]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]