Herb, here is where I'll have to disagree with you about not being concerned about room modes (nodes and anti-nodes are part of the story).

With a 4' x 4' enclosed pace, you absolutely will have to contend with the standing wave / room mode frequencies because you will 'light up' these with more than just holding notes at the fundamental frequencies. It's a fairly small 'room', and because of the small dimensions, that puts the modes into regions that will get excited by both tonal and non-tonal instruments. And because two dimensions are the same, the modal behavior becomes much more intense and prevalent. Peter hasn't said what the height of the closet will be, but that plays a part here as well.

The first modes dealing with the 4' dimensions are at 141 Hz, and the next multiples are at 282 Hz, right around middle C. The acoustic treatment will not be deep enough to easily manage these room modes.

The small 'box' that this closet is, is an entirely different kind of space than your monitoring room. Yes, you can try to filter out these peaks that will end up in the recording, but if you can avoid them it's best to do so up front. Some judicious planning can work wonders to eliminate the problems ahead of time.

The other big difference here is that your monitoring/mixing space has lots of large objects which break up the acoustic space and make it much more difficult for standing waves/modes to be present.

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