Ah, these are special dusters, not in the slightest acquainted with polish and the like! They serve several purposes, especially in combination with different pairs of sticks. Firstly, they alter the resonance of a drum.
The NSO is blessed with a magnificent set of four copper-bowl, pedal timpani made by Ludwig, a world-class manufacturer based in America. Such is their quality that, when each drum is struck, the note sounds for a long time - sometimes too long. Covering part of the drum head with a duster reduces the resonance. This is particularly useful when adjusting to different acoustics and also when short notes need to be played in quick succession, with no time to deaden the drum with the fingers.
Secondly, dusters can be used to create different effects; the muffled drums Berlioz requests in "The March to the Scaffold" are very different from the firepower required at the end of Shostakovich Symphony 5, for example. Look out for muted timpani in the third movement of Mahler ... more.
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