5/4: Difference between revisions
added fourth complement |
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| Monzo = -2 0 1 | | Monzo = -2 0 1 | ||
| Cents = 386.31371 | | Cents = 386.31371 | ||
| Name = classic major third | | Name = classic/just major third | ||
| Color name = y3, yo 3rd | | Color name = y3, yo 3rd | ||
| FJS name = M3<sup>5</sup> | | FJS name = M3<sup>5</sup> | ||
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}} | }} | ||
In [[5-limit]] [[ | In [[5-limit]] [[just intonation]], '''5/4''' is the [[frequency ratio]] between the 5th and 4th harmonics. It has been called the '''just major third''' or '''classic major third''' 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 here 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 == | ||
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 (↓). | 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 (↓). | ||
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== See also == | == See also == | ||
* [[8/5]] – its [[octave complement]] | * [[8/5]] – its [[octave complement]] | ||
* [[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 plus one [[octave]] sounds even more [[consonant]] | ||
* [[Gallery of | * [[Gallery of just intervals]] | ||
* [[Wikipedia:Major third | * [[List of superparticular intervals]] | ||
* [[Wikipedia: Major third]] | |||
* [[:File:5-4.mp3]] – sound sample that illustrates 5/4 as the interval between sung overtones | * [[:File:5-4.mp3]] – sound sample that illustrates 5/4 as the interval between sung overtones | ||