I am wondering if you would be able to share with me some of the shitot and discussions of rishonim and achronim on Beitza 36b regarding the Mishna that says that clapping and dancing is forbidden on Shabbat.
Rabbi Ari Enkin, Ramat Beit Shemesh, Israel
The Shulhan Aruch (OC 339:3) codifies this Mishnah, making only one caveat: that if it is done in unusual manner it is permitted (Rambam).
Tosfos (Beitzah 30a) says that, since it is now rare to find someone who can repair musical instruments, the Gezeirah on clapping and dancing is no longer in effect. This is in line with the opinion of Tosfos in other places that certain Gezeiros no longer exist because the reason for the Gezeirah no longer exists (see Tosfos, Beitzah 6a, ha'Idna). The REMA (339:3), in explaining an existing Minhag to be lenient regarding clapping and dancing, brings the opinion of Tosfos.
Rav Moshe Feinstein (OC II, 100) says that, whereas we can offer a straightforward explanation of the opinion of Tosfos in regards to other Gezeiros, here it is very difficult to understand their position. For example, in regards to the Gezeirah on Giluy (drinking water that has been left uncovered) we can say that the Gezeirah was not on the water itself but rather on the Chashash (suspicion) that the water was poisoned by a snake. That is, their Gezeirah was to elevate the remote possibility that it was poisoned, to a real possibility, and therefore automatically the water becomes forbidden because of Piku'ach Nefesh. Therefore once the possibility became exceedingly remote, as it is today, it was no longer included in the Gezeirah. The same logic can be used for the Gezeirah of Mayim Acharonim where the concern was Melach Sedomis.
But in our case the Gezeirah seems to be on the actual clapping and dancing and therefore the Gezeirah remains in effect even if the reason does not exist anymore (similar to Chazal's decree that a Kesem is only Asur if it is larger than a Gris. This remains true today even though Kinim are almost nonexistent). See Rav Feinstein's Teshuvah for an interesting explanation of Tosfos.
Eliya Raba says that the opinion of Tosfos cannot be relied on for anything other than clapping and dancing, but not for actually playing instruments on Shabbos.
The Maharshal says that b'Makom Mitzvah we can rely on the opinion of Tosfos Lechatchilah (see Mishnah Berurah to OC 339, note 10 and Sha'ar ha'Tzion note 7).
This is not a Psak Halachah