View source for 5/4

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| de = Naturterz
| en = 5/4
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| ro = 5/4 (ro)
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{{Infobox Interval
| Name = just major third, classic(al) major third, ptolemaic major third
| Color name = y3, yo 3rd
| Sound = jid_5_4_pluck_adu_dr220.mp3
}}
{{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{{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).

== 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.
{{Interval edo approximation|interval = 5/4| max_edo=200}}

== See also ==
* [[8/5]] – its [[octave complement]]
* [[6/5]] – its [[fifth complement]]
* [[16/15]] – its [[fourth complement]]
* [[5/2]] – the interval up one [[octave]] which sounds even more [[consonant]]
* [[Ed5/4]]
* [[Gallery of just intervals]]
* [[List of superparticular intervals]]

== Notes ==
<references/>

[[Category:Third]]
[[Category:Major third]]