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Put a pillow into the bass drum as a way to help with the overtones and tuning of the drum. While its possible to achieve a good punch without it, most folks (at least other band members and recording engineers) prefer to have a solid "thud" sound with a slight over ring. Whether you choose to use a pillow or not, the tuning procedure is still the same.
Start by tightening the lugs until they are all finger tight. You will notice wrinkles in the head around the edges. Choose any tuning lug and tighten it 1/2 turn. Then, go directly across the head and do the same with that lug. Continue in this fashion around the drum until the wrinkles are gone and you hear a tone when you tap on the head. Once you begin fine-tuning, you will want to turn the lug no more than 1/4 turn. When tuned properly, you should hear the same pitch when you tap on the head in front of each lug. (Approximately 1" in from the rim.) Different shells sound different depending on how high or low they are tuned, so experiment with the tuning.
Because there are so many different types of materials used to construct snare drums, including wood, steel, copper and brass, the snare can be tuned to an amazing number of tones and textures. Again, experiment with different tunings to find the tone that works for you.
I prefer a very tight, fat snare sound. To achieve this I start with the bottom snare head. Using the same technique as the bass drum, make sure the tension is even as you go around the head. I like to have the bottom head as tight as possible, which gives the snare a tight snap when I hit it. Use your own judgment.
The top head I tend to keep quite a bit looser, in order to "fatten" the snare sound. If you still have too much over ring, a small piece of duct tape will help to alleviate this. Place it approximately 1" from the rim of the snare, directly across from you (this will keep you from hitting that spot with your sticks).
Even tension on the top and bottom heads is critical for good tom tone. You may want to take each drum off the mount to tune the bottom head (using the same technique as above). Find a pitch that sounds good to your ear, and try to tune the drum to that pitch.
Again, there is no right or wrong tuning for your kit, as long as it sounds good to you. It will take a while to tune your kit, so don't get discouraged. The best advice I can give you is to use small increments when you begin to fine-tune the drums. 1/4 turns are usually more than enough.
One last tip. Placing the drum flat on a carpeted surface can also help when you are just learning to tune the drum. This dampens the other head, letting you hear just the head you are tuning.