Can I make an audio recording of printed copyrighted music arrangements?

Yes, you can do so legally--"ONLY" if you have the approved, expressed, and written consent of the original composers of the copyright music. When such music work is filed with the Copyright District Office, normally in Washington, DC, the form that they must submit, along with the original copies of music and any music sheets, contains the names of the original composers of said music for which they hold all rights. In this document, they are given a list to check and write the names of each creator of that work. If producing this recording of you performing each piece is for your own entertainment, then such steps to protect yourself will not be necessary. However, if and when you plan on distributing your recordings, making it available for downloading, or even given it to family members, will become a serious legal issue that no one is able to afford if you leave it in the hands of court appointed jurors. The fines associated with illegal downloading and piracy ranges anywhere from $3,500, at the least, to the full extent of the Constitutional Law of $150,000 max.