First of all, if you are recording a performance (i.e., not using pre-existing audio) then you need the permission of the copyright holder of the written music, i.e., the composer, lyricist, arranger and/or publisher; not the performers.
You have not given any jurisdiction but if you are publishing on the internet then you must comply with the copyright laws of each and every nation that has access to the internet i.e.: all 196 of them. However, 168 of them are covered by the Berne Convention and the others include places like Burma, Somalia and Afghanistan where prosecuting you is unlikely to be a high priority.
You don't nominate your jurisdiction so here is a fact sheet for Australia; other Berne convention signatories will be similar.
If you have sheet music then the names of the copyright holders will be written on it; you can approach them directly or through the relevant industry body in your country.