It is well known that R. Moshe (Igros Moshe O.C. 1:166) held that it was forbidden to listen to any musical instruments unless it is within the context of a real seudas mitzvah (he is mesupak whether a fundraising dinner for a tzedaka would even qualify since the seudah is not a mitzvah, the raising money is). As R. Moshe himself points out this pesak is somewhat radical since it directly contradicts a Rama (560:3). The Shulchan Aruch forbids: 1. to play or listen to musical instruments for simcha. 2. vocals even without instruments cannot be sung while drinking wine (the bach is machmir that all singing is assur unless it is a work song for the purpose of team building to accomplish a job like we see at the end of Sotah). The source for the Shulchan Aruch is the Rambam. However, the Rama qualifies the first din in regard to musical instruments, that it is only forbidden if it is routine, but not if it is only once in a while. We generally rely on the Rama to permit attending occasional concerts and the like.
Rav Moshe points out that this entire distinction between instrumental music and vocals, made by the Rambam, seems to contradict our gemara in gittin 7a which implies that we had a hava amina to assur only instruments, but concludes that even vocals are assur. Rashi limits the issur to singing while drinking and Tosafos suggest being machmir even without drinking based on the Yerushalmi to sing routinely even without drinking. From both Rashi and Tosafos we have no indication that there would be any issur (even with instruments) so long as it was without drinking and not routine. But, the R. Moshe explains that the Rambam learned the gemara differently. The gemara means to say that had we would have limited the pasuk of "b'shir lo yishtu yayin" to instruments, but once we have another pasuk implying that instruments are always assur, we use the pasuk of "b'shir lo yishtu yayin" to assur even vocal singing over wine. Being that from Rashi we only see the issur of vocal singing while drinking since that was the topic of the question, but it is possible that rashi would agree to the Rambam that instruments are always assur (unless it is a mitzvah), we must assume that all agree to the Rambam and assur musical instruments even once in a while. The limitation of the Rama to one who does it routinely is only for vocal singing, but instruments are always assur (this is clearly not the opinion of the Rama himself since he places his comment limiting the issur to cases of routine on the discussion of instrumental music). Rav Moshe's approach undermines the proof of the Bach to assur vocal singing from the gemara in sotah that assurs the sone fo the weavers, because in those situations it was a routine, but if it is not routine then vocals are permitted. But instruments are never permitted unless it is a mitzvah (he even considers radio and tapes of musical instruments to be assur - apparently he would of also signed the ban against lipa's "big event"!).
In conclusion, the gemara which assurs the singing of the weavers (gardiyim) in sotah, seems to either prove like the bach that singing is always assur even without wine, or like r. moshe that the distinction between routine and just once in a while applies to vocals without music. But if we are going to assume that the Bach is wrong because vocals are only assur with wine, and R. Moshe is wrong because the heter for non-routine music is even by instruments and not just by vocals; then why would the vocal singing of the gardiyim be assur?
[this is one of the reasons that i never sing, the other is that i can't carry a tune]