https://en.xen.wiki/index.php?action=history&feed=atom&title=VarianceVariance - Revision history2026-07-27T20:18:49ZRevision history for this page on the wikiMediaWiki 1.43.6https://en.xen.wiki/index.php?title=Variance&diff=82785&oldid=prevCmloegcmluin: categories2021-12-29T04:45:17Z<p>categories</p>
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</table>Cmloegcmluinhttps://en.xen.wiki/index.php?title=Variance&diff=82782&oldid=prevCmloegcmluin: extract from EA page2021-12-29T04:43:51Z<p>extract from EA page</p>
<p><b>New page</b></p><div>'''Variance''' is a property of [[Wikipedia:Vector_(mathematics_and_physics)|vectors]] which indicates how their entries ''vary'' with respect to the system's units: [[Wikipedia:Covector|covectors]] vary in the same direction as the units, hence the co- prefix meaning "with", while (contra)vectors vary in the opposite direction to the units, hence the contra- prefix meaning "against".<ref>This notion of variance is not to be confused with the unrelated notion of variance in statistics.</ref><br />
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In other words, let's say we ''divide'' octaves (our units) into 1200 parts to get cents, so that they're now 1/1200th the size they used to be. If we wanted our system to represent the same information, then, we have a couple options for recalibrating with respect to the new units. <br />
# We could choose to change our vectors. If we choose this, we must ''multiply'' the numbers in each of our vectors by 1200. <br />
# We could choose to change our covectors. If we choose this, we must ''divide'' the numbers in each of our covectors by 1200. <br />
So we say that the vectors vary in the opposite direction to the units, but the covectors vary in the same direction as the units. In other words the vectors are "contravariant" with the units and the covectors are "covariant" with the units.<ref>Interestingly, [[RTT|regular temperament theoreticians]] are more similar to physicists than mathematicians in a certain respect: we have units of measurement associated with our vectors, such as octaves or cents.</ref><br />
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==Footnotes==<br />
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