deletions | additions       diff --git a/The_closer_two_tones_are__.tex b/The_closer_two_tones_are__.tex  index 0c282eb..738028d 100644  --- a/The_closer_two_tones_are__.tex  +++ b/The_closer_two_tones_are__.tex 
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If a human being detects frequency differences by the presence of beating, then, roughly speaking, a beat of a duration greater than twice the duration of the tone sounding cannot be detected by a human being. Each bar in the samples was sounded for about 2 seconds, which puts an upper limit on a human listeners capacity to detect frequency differences. The duration of beating for two nearby frequencies can be determined by the following equation  \begin{equation}  beat beat\  duration \  = \  1 \  / |(f0 - \ |(f0\ -\  f1)| \end{equation}