I know the shofar is not to be blown on rosh hashana except when performing it for a mitzva, but is a shofer permitted to be blown when it is not shabbos or a chag for recreational (not mitzva or mitzva preparation) purposes?
Assuming the Shofar was not previously blown for a mitzvah:
Yes, as explicitly written in Psalms 150:3, where the shofar is listed among other musical instruments:
הַלְלוּהוּ, בְּתֵקַע שׁוֹפָר; הַלְלוּהוּ, בְּנֵבֶל וְכִנּוֹר.
(See also Ps 81:4, 98:6)
In addition, the Gemara (Rosh haShana 33b) includes a discussion about whether one fulfills his mitzvah obligation if he blew "to make musical sounds" on Rosh haShana, implying that one is allowed to use a shofar to make music.
Finally, there are many cases in Tanach where a shofar was blown for non-mitzvah purposes, (mostly involving wars and coronations; Shoftim 3:27, 2 Samuel 2:28, 1 Kings 1:34, 2 Kings 9:13, Amos 3:6, among others), and the Gemara (Shabbat 35b) mentions that a Shofar is blown on Friday to tell people to prepare for Shabbat.
If the cantor used his voice to sing Kol Nidre, is it permissible for him to sing in the shower? What is different is the kavanah. On Rosh Hashanah, both the sounder and the hearer must have the intention of fulfilling the mitzvah. The rest is just blowing in the wind.
Unless its to practice it would be degrading to the mitzva.
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