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Dear Ms. Baxter,
Thank you for sharing your question with the History Hub.
My understanding is that a “special muster” is one that falls outside of the regular cycle and that it could stem from any number of occurrences like a battle, a troop relocation, an order from a commanding officer, etc. Regarding the specific special muster you referred to, you might find this discussion helpful. It seems that many units experienced special musters on April 10, 1863.
For further information, we recommend that you contact the Textual Reference Branch at the National Archives in Washington, DC (Archives I). Their email address is firstname.lastname@example.org.
Thank you, again, for posting your question, and good luck with your ongoing search!