Quoting song lyrics in your writing requires permission, especially if your purpose is not scholarship or criticism (and even then, permission may be needed). This blog post answers many questions about quoting song lyrics, but it does not give legal advice.
In general, the copyright term for notated music is the same as for text, but you need to be aware of what the copyright actually covers. Some music scores, such as operas, have a single copyright for the entire work, but others, such as pop song collections, have a copyright on each song. Knowing the size of the copyrighted unit is crucial in determining whether fair use applies to your situation.
For collaborative works (for example, a song with music and lyrics by two different people), the "life of the author plus 70 years" copyright term is determined by the date that the last collaborator dies. So if the composer died in 1950 but the lyricist lived until 1980, the song is still under copyright.
To request permission to use copyrighted music, look for the publisher's name in the copyright statement, or search the ACE database to identify the rights holder.
Every audio recording has two copyrights, one for the content itself and one for the recording of it. But while a song published in 1920 is no longer protected by copyright, a recording of it made in 2020 still is. All audio recordings published after February 15, 1972 have a copyright term of life-plus-70-years. For recordings published before February 15, 1972, the Classics Protection and Access Act established a formula for determining when they enter the public domain. Basically, the copyright expires 95 years after the first publication of the recording, plus an additional period based on when the sound recording was first published:
Like other copyrighted materials, audio recordings are subject to fair use and/or educational exemptions under certain circumstances. For guidance in these areas, click the fair use tab at the top of this page.
The Music Publishers Association offers Copyright Resources
The U.S. Copyright Office has a web page called What Musicians Should Know about Copyright
The Music Library Association's Copyright for Music Librarians web page addresses copyright questions involving audio and video recordings, music scores, arrangements, sampling, course reserves, and more.
The Copyright Alliance's Music Copyright Cases Musicians Should Know discusses some of the most significant cases from 1908 to the present.
The Music Copyright Infringement Resource, from the George Washington University School of Law and Columbia Law School, offers facts about music copyright infringement cases from the mid-19th century forward.
If you want to avoid having to figure out copyright all together, there are many websites that offer music with Creative Commons licenses, some of which give you the legal right to use it in videos and other projects. Here are a few of them: