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Okay, make a note of your desired perspective settings. Now go to project mode (using View->Planning Mode or cmd-1, not by pressing the Projects button in the toolbar!) and select the desired projects for your perspective. Having done so, use View->Context Mode or cmd-2 to switch to the context mode view and apply the desired perspective settings. Save as a new perspective.

The Projects and Contexts toolbar buttons actually open perspectives named (wait for it) Projects and Contexts, so if you click them in the process of setting up a perspective, you may not get quite what you want :-)