The context is comparing the loudness changes in two sounds.
An eighth note at quarter equals 120 is 0.25 seconds long
So is it talking about four eighth notes beamed together, or is it something to do with intervals?
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You’re not parsing your sentence right. You should understand “An eighth note at [quarter equals 120] is 0.25 seconds long.”
“A quarter = 120” is a tempo indication meaning “you should play 120 quarters per minute”, i.e. a quarter last half a second. An eighth note thus lasts half that, that is 1/4 second.