There are a variety of synonyms for the phrase "copy down," each with their own unique connotations and contexts. One common synonym is "transcribe," which emphasizes the act of accurately reproducing written or spoken words. "Jot down" suggests a quicker, more informal process of recording notes or ideas, while "scribe" implies a more formal or historical context. "Record" is a broader term that can refer to any type of information, whether written or spoken. "Note" and "memorize" both emphasize the process of retaining information, while "write down" is a straightforward, practical synonym that can be used in any context. Ultimately, the choice of synonym depends on the specific purpose and tone of the writing or conversation at hand.