What would a drummer to make the sound of a drum give a note of lower pitch?

It depends largely on how it is tuned. A large drum will generally produce a lower sound, but this is because they are usually tuned to produce that pitch because smaller drum heads do not have enough surface area to create that low a pitch without becoming floppy. Likewise, a large drum head such as a floor tom can produce a higher pitch, but not as high as a very small drum like a piccolo snare.