The Gemara in Eiruvin 104a quotes a dispute regarding whether one may make music on Shabbos: Rav Menashe is stringent and forbids any production of sound, while Rava is relatively lenient and only forbids music. The Beis Yosef (OC 338:1) quotes the Rif and Rambam, who pasken like Rava, and he infers from the Rosh that he holds likewise. He therefore paskens in Shulchan Aruch (Ibid.) that only music making is forbidden, and the Mishnah Berurah (ad. loc.) emphasizes that this is true even with one's hands and no instrument.
The Rambam the Shulchan Aruch quotes (Shabbos 23:4) explains that the prohibition is because of Tikkun, that the instrument might break, and he might come to fix it.
It sounds like the Rambam is saying that it is d'Rabbanan as a gezeirah on the melachah d'Oraisa of fixing. We have a rule that you cannot make a gezeirah to protect another gezeirah (Beitzah 3a et. al.). The only rationale I can think of would be to prohibit banging on the table or clapping would be as a gezeirah for instruments. As the Mishnah Berurah is explaining the Shulchan Aruch, who, in turn, is basing himself off of the Rambam, the Mishnah Berurah would seem to have a gezeirah l'gezeirah issue.
Are we forced to say kulah chadah gezeirah hee (it was all established at the same time as one decree), or is there a separate reason for clapping that avoids this issue?