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My plan is to super chunk the back two corners, but with them both being short I am concerned this won’t be enough bass trapping.
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In a room your size I would say NO. Your going to need to cover A LOT more corners to get the low end under control.
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I currently put my first axial mode at around 42 hz (though this was calculated on the room being a rectangle shape, as I don’t know how to factor in the odd shaped roof).
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Mode calculators are to give you a general idea, which they are never 100% right and actually used for planning a build (most of the time). To really know the problem areas you would need to test of the room. See the following FREE program.
Room EQ Wizard Home Page Quote:
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More bass traps of the same spec covering the side/front walls?
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Covering more corners is the ticket.

Also you need Thick absorption on the back wall, to help with nulls and peaks coming from that area.
Tune traps are great, but for larger rooms. You have problems though out the frequency range, so broad band will work much better for you.