5/4: Difference between revisions

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{| ~~class~~=~~"wikitable"~~

{{interwiki

|-

| de = Naturterz

| ~~[[File:5_4_glyph.png~~|~~alt~~=5 4 ~~glyph.png~~|~~113x123px~~|~~5 4 glyph.png]]~~

| en = 5/4

|-

| es =

~~| JI Glyph for 5/4~~

| ja =

|}

| ro = 5/4 (ro)

}}

{{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

}}

'''5/4'''

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".

~~{{Monzo|~~ -~~2 0 1 }}~~

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).

~~386~~.~~31371 cents~~

== 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.

[[~~File:jid_5_4_pluck_adu_dr220.mp3~~]] ~~<br~~/> [[~~:File:jid_5_4_pluck_adu_dr220.mp3|jid_5_4_pluck_adu_dr220.mp3~~]]

== 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]]

~~In [[Just Intonation]], '''5~~/4''' is the frequency ratio between the 5th and 4th harmonics. 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".

== Notes ==

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 [http://udderbot.wikispaces.com/home udderbot] (from the fundamental up to 5 and then noodling between 5 and 4).

[[Category:Third]]

[[Category:Major third]]

~~[[File:5-4.mp3]] <br/> [[:File:5-4.mp3|5-4.mp3]]~~

~~5/4 converted to cents (¢): 1200 * log (5/4) / log (2) = 386.314...~~

~~5/4 the interval, like all ''intervals'', refers to a ''relation'' between two pitches. It has been called the ''just major third'' to distinguish it from the other intervals in that neighborhood.~~

~~:'' See also [[Gallery of Just Intervals]]''~~

[[Category:~~5-limit~~]]

[[Category:~~just_interval]]~~

~~[[Category:major_third]]~~

~~[[Category:ratio]]~~

~~[[Category:superparticular]]~~

~~~~

~~[[de:Naturterz~~]]

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-{| class="wikitable"
+{{interwiki
-|-
+| de = Naturterz
-| [[File:5_4_glyph.png|alt=5 4 glyph.png|113x123px|5 4 glyph.png]]
+| en = 5/4
-|-
+| es =
-| JI Glyph for 5/4
+| ja =
-|}
+| ro = 5/4 (ro)
+}}
+{{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}}
-'''5/4'''
+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".
-{{Monzo| -2 0 1 }}
+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).
-.31371 cents
+== 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}}
-[[File:jid_5_4_pluck_adu_dr220.mp3]] <br/> [[:File:jid_5_4_pluck_adu_dr220.mp3|jid_5_4_pluck_adu_dr220.mp3]]
+== 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]]
-In [[Just Intonation]], '''5/4''' is the frequency ratio between the 5th and 4th harmonics. 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".
+== Notes ==
+<references/>
-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 [http://udderbot.wikispaces.com/home udderbot] (from the fundamental up to 5 and then noodling between 5 and 4).
+[[Category:Third]]
+[[Category:Major third]]
-[[File:5-4.mp3]] <br/> [[:File:5-4.mp3|5-4.mp3]]
-/4 converted to cents (¢): 1200 * log (5/4) / log (2) = 386.314...
-/4 the interval, like all ''intervals'', refers to a ''relation'' between two pitches. It has been called the ''just major third'' to distinguish it from the other intervals in that neighborhood.
-:'' See also [[Gallery of Just Intervals]]''
-[[Category:5-limit]]
-[[Category:just_interval]]
-[[Category:major_third]]
-[[Category:ratio]]
-[[Category:superparticular]]
-<!-- interwiki -->
-[[de:Naturterz]]