I found this little trick from one of the videos, which I logged on to and watched at Logic Studio Training. If you use the tape delay plug in, if you set the frequency response from 20 to 20k, turn the dry mix down to zero and the wet mix up to full, as long as you turn the smooth parameter down to zero, set the feedback to zero, and keep the depth and rate of the modulation at zero, as well keep the flutter and flutter intensity at zero, you can mimic the sound of analog tape compression and warmth pretty good. There is an arrow head, which is at the very bottom of the plug in below the freeze button. If you click the arrow, it will even allow you to tweak the distortion level.
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Trick in Logic Pro for Analog Tape Compression and Warmth
2011-01-13 by Brian