Music prohibited

Igros Moshe, (OC I #166) Question What is the prohibition of listening to music because of the destruction of the Temple? Answer It seems from the gemora (Gitten 7) that there is no distinction between instrumental music and voice. Rashi says the prohibition is at a feast. This is also the view of Tosfos as well as the Mishna in Sotah(48). There is also the view of the Yerushalmi that music causes excessive joy. And Tosfos says this is even when there is no banquet if it is done on a regular basis which produces the same effect as a banquet The Rambam prohibits instrumental music in all circumstances even without a banquet while singing is only prohibited with wine. It is not clear the source of the distinction between instrumental music and singing as this seems inconsistent with the gemora in Gitten. . In conclusion that singing is only prohibited at a banquet for someone who does it regularly and this is the view of almost all Rishonim other than the Rambam. The Rambam seems to be inconsistent between his Teshuvos and Mishna Torah. Work songs seem permitted because a person is habituated to them. Nevertheless a bal Nefesh should be strict like the Rambam in his teshuvos. Instrumental music is prohibited in all circumstances as stated in the Rambam and Shulchan Aruch. It seems it is only permitted not at a banquet for someone who doesn’t do it regularly even though it is only a Rabbinic prohibition. It seems from Tosfos and Remah that if this is for a mitzva it is permitted even if not at a wedding. However a banquet done for the sake of charity I am uncertain if it is permitted as a mitzva purpose because the meal and the Simcha are not actually a mitzva but merely are done to gather people to make donations. But perhaps they are to be considered mitzvos since they honor those who are doing the mitzva of charity. Therefore it is best to be strict if possible but not to protest against those who are lenient. Concerning listening to music on a radio – If it is vocal than it is permitted while instrumental musicx is prohibited. During Sefirah instrumental music should be prohibited even to those who are normally lenient. 

Igros Moshe, (OC III #87) Question: Are music lessons permitted during Sefira? Answer If the lessons are for parnassah it is permitted even during Sefirah since for him it is not for joy. However if it is for pleasure it is prohibited during Sefira according to the custom.  The Rambam (Tanis 5:14) rules that it is prohibited the entire year. This is also the view of Shulchan Aruch (OC. 560:3). It is appropriate to be strict like the Rambam and Shulchan. Even the Remah cites a view that music is permitted if not at a banquet and for one who is not habituated. Therefore one should not protest those that are lenient This is also applicable to listening to instrumental music. However during Sefirah it is prohibited according to everyone. 

Rambam (Tanis 5:14) Similarly, they ordained that one should not play melodies with any sort of musical instrument. It is forbidden to celebrate with such instruments or to listen to them being played [as an expression of mourning] for the destruction. Even songs [without musical accompaniment] that are recited over wine are forbidden, as [Isaiah 24:9] states: "Do not drink wine with song." It has, however, become accepted custom among the entire Jewish people to recite words of praise, songs of thanksgiving, and the like to God over wine.

Shulchan Aruch (OC 560:3) Similarly they decreed not to play music with instruments, and musical devices, and all things that make music to rejoice with them.  There are those who say, the prohibition is specifically for those whom they regularly play them, like for kings who stand and rest to instruments or in the house of a feast. (Tur) It is forbidden to make them heard because of the destruction, and even song by mouth over wine is forbidden, as it says: "In song one may not drink wine" (Isiah 24:9). And all of Israel is already accustomed to saying words of praise or songs of thanks and remembering the goodnes of the holy one blessed be he over wine.  Similarly for the need of a Mitzvah, like for house of a Groom and Bride, all this is permitted. (Tosefot, Smug, and Hagehot Maymoni)