Originally Posted by
gearhead82
I built my first wheel last week. ......
Is it normal for the tire pressure to have a noticeable effect on the spoke tension?......
Yes, the tire's air pressure compresses the rim. The amount of compression depends on the rim and tire width and the tire pressure, but it can be significant. Standard guidelines for spoke tension factor this effect in, and you would have no reason to notice.
I suspect that your wheels were inadequately tensioned, especially the left side rear, so the pressure related compression created the slack you're feeling.