5/4: Difference between revisions
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| ro = 5/4 (ro) | |||
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{{Infobox Interval | {{Infobox Interval | ||
| Name = just major third, classic(al) major third, ptolemaic major third | |||
| Name = classic | |||
| Color name = y3, yo 3rd | | Color name = y3, yo 3rd | ||
| Sound = jid_5_4_pluck_adu_dr220.mp3 | | Sound = jid_5_4_pluck_adu_dr220.mp3 | ||
}} | }} | ||
{{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''' or ''' | 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 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 | == Approximations by edos == | ||
Following [[ | 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 (↑) 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]] | ||
! 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 | ! class="unsortable" | Equally acceptable multiples <ref>Super-edos up to 200 within the same error tolerance</ref> | ||
|- | |- | ||
| [[25edo|25]] || 8\25 || 2.3137 || 4.8202 || ↓ || | | [[25edo|25]] || 8\25 || 2.3137 || 4.8202 || ↓ || | ||
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| [[643edo|643]] || 207\643 || 0.0004 || 0.0235 || ↑ || | | [[643edo|643]] || 207\643 || 0.0004 || 0.0235 || ↑ || | ||
|} | |} | ||
== See also == | == See also == | ||
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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 | * [[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]] | ||
== Notes == | |||
<references/> | |||
[[Category:Third]] | [[Category:Third]] | ||
[[Category:Major third]] | [[Category:Major third]] | ||