I'm lucky in that I have a wonderful herb garden and a food dehydrator. I have noticed in the past that some herbs do not retain their crispness or taste in humid weather over time, plus some store-bought spices (like onion powder or garlic powder) clump together, humidity or not! Several of the medications that I take come with those little packets of silica gel. When I'm finished with that medication, I save those packets and put them in with my herbs and spices to help keep them fresh and dry.
Another bonus for these little packets: my husband uses them in his tool box drawers to keep the rust away!
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For years, I have kept small containers easily at hand in my spice cupboard, away from heat and light. But I have also kept larger amounts in a shelf in my freezer, which will keep them fresh for years.
Most fresh herbs are just like rooting plants, they need water. And if you want to you can take a 2 liter bottle cut in half and turn the bottle neck down into the bottom of the bottom half to make it look like a funnel in the bottle.
To freshen your pepper add a few peppercorns to the pepper shaker!