Steal This Music by 
Pop Song Piracy by Using an existing recording of music (performed by someone else, such as a well-known singer or pianist) as background music in a video you plan to publish online on YouTube or elsewhere with public access typically requires two licenses: a synchronization license from the publisher of the sheet music, and then a master license from the recording company that released the performance. For the synchronization license, you can search the ASCAP database, the BMI, database, or the SESAC database for the publisher contact information. Alternately, you may wish to do a web search. For the master license, you can do a web search for the recording company of the specific recording artist. Feel free to reach out to refdesk@muhlenberg.edu if you need assistance in tracking down any of this information.
There are two main streams of royalties that we will discuss here. One stream of royalties goes to the original songwriter (or her publisher who would then distribute a percentage of the royalties to her). We'll call this the composition/song royalty. The other stream of royalties goes to the performer (or the recording company who then distributes a percentage of the royalties to him). We'll call this the sound recording royalty.
I. The composition/song royalty
This royalty is typically collected anytime the song is performed or reproduced. Let's start first with performances, that can be live, radio, or digital (streamed online). The online streaming is further divided into two types: interactive streams (Spotify and Pandora Premium, which allow users to select specific songs), and non-interactive (Pandora, radio, which don't allow users to select specific songs). Most of the performance royalties are managed by huge "blanket" public rights organizations, or PROs--ASCAP, BMI, or SESAC. These organizations funnel royalties between the users (radio stations, and the like) and the songwriters/publishers.
In addition, a reproduction royalty (collected as part of "mechanical" licenses) is collected and distributed by Mechanical Licensing Collective (MLC), a governmentally appointed agency. Only on-demand, interactive streaming services like Spotify and Pandora Premium pay this mechanical license; Pandora and radio stations, that are non-interactive, need not pay for a mechanical license. This is because no reproduction is said to have taken place in a non-interactive environment.
Mechanical royalties are also collected from recording companies and performance artists who want to cover a song. Also, anyone video-recording a musical performance for public distribution on YouTube or elsewhere pays what is called a synchronization license.
II. The sound recording royalty
This royalty goes to the musical performing artist or more likely the recording company with whom the artist is in contract. This royalty is not collected from terrestrial (non-digital) radio, but is collected from any digital streams--radio, Sirius, Pandora, Spotify. Non-interactives like Pandora pay through Sound Exchange. Interactives like Spotify and Pandora Premium negotiate directly with the recording companies.
Unlike the physical classroom, where live and recorded music can be performed without restriction, the online environment necessitates that a copy of the music be made, unless the music is already available commercially or otherwise in the streaming format. When a copy is made of music that is still under copyright, then the user must either get permission from the copyright owner, or rely on either of two exceptions to copyright: fair use or the TEACH Act. The TEACH Act is probably the first place to turn, since non-dramatic musical works can be performed in their entirety in a password-restricted online teaching environment under this portion of the copyright code, without needing to ask permission of the copyright owner.
Dramatic music (music from plays or opera) is more restrictive. Here the TEACH Act uses the phrase "reasonable and limited portions." So a portion of the work can be performed, but perhaps not its entirety. One could rely on fair use here, but more likely it is prudent to obtain access through a commercial platform like Naxos or otherwise seek permission from the copyright owner.
As for music scores, they can be displayed online, per the TEACH Act, in an amount that would be comparable to that shown during an in-person single class session.
If you have written a musical composition, you may want to register copyright with the United States Copyright Office. This will enable you to sue in a court of law should the need arise in order to protect your creative work. In addition, you should also register with a performance rights organization (PRO) such as ASCAP or BMI to secure royalties from public performances of your work.
Alternatively, you can let a music publisher (AKA music publishing administrator) do all the registration and promotion work for you, for a percentage of your profits/royalties. One of the best-known publishing administrators is TuneCore. The music publisher you select may or may not ask you to transfer the copyright to them.
Any live public performances (beyond the classroom) of copyrighted music require a license. While there is an exception when there is no compensation of any kind for performers or organizers, it is generally safer to obtain a license. Fortunately, three major performance rights organizations (PROs)--ASCAP, BMI, and SESAC-- hold the licenses to a vast majority of musical works under copyright. Muhlenberg College pays fees annually to have "blanket" licenses with these organizations and so can be considered covered in its live musical performances. These blanket licenses cover only the live performance, not any recording of the performance.
To make an audio recording (without video), and distribute copies of the recording online or in physical format, free or for fee, a mechanical license is needed. The mechanical license can best be obtained by contacting the publisher of the song. To obtain publisher contact information, search the ASCAP database, the BMI, database, or the SESAC database. Alternately, you may wish to do a web search for the publisher of the song.
A synchronization license is required for live musical recordings that are video-recorded with the intention of distributing on the web via the College website, YouTube or other platform. A synchronization license is obtained directly from the song publisher. You can do a web search, or search the ASCAP database, the BMI, database, or the SESAC database for publisher contact information.
I. The MMA first of all has changed the way mechanical royalties get collected and paid to songwriters/publishers, from interactive digital streams and any musical recordings (covers) of a song. Now all mechanical royalties will be collected and paid by a new governmental organization called the Mechanical Licensing Cooperative (MLC). As of January 1, 2021, songwriters and music publishers must register with The MLC using its online claiming portal to receive royalty payments under the new blanket license.
II. Title II of the MMA brings pre-1972 sound recordings (formerly unprotected at the federal level) partially into the federal copyright system and provides federal remedies for unauthorized use of sound recordings fixed before February 15, 1972. This means that royalties will now be collected for digital streams of pre-1972 sound recordings.
From the Music Library Association: "Operas, ballets, and musical theater works are dramatic works; in music business jargon the right to perform them is referred to as a "grand" right. Permission to perform any dramatic work must be obtained directly from the copyright owner or its licensee, which is often the publisher that sells or rents the performance materials. [Footnote: American musical theater works are, in most cases, handled differently. The publishers who print the music (individual songs, selections, or piano-vocal scores) usually do not have the right to license performances. The right to license amateur, professional, and LORT (League of Resident Theatres) productions is usually assigned by the authors to an agency such as the Rodgers and Hammerstein Theater Library, Music Theater International, Tams-Whitmark, Samual French, etc.]"