First, in practice, it's highly unlikely you would be sued over such a potential infringement. This also means that court cases directly on point don't really exist, but I think the Canadian Copyright Act and existing case law points to private performances not being copyright infringement, and are thus legal. In the American case, I believe it's the same, with their statute being even clearer.
In Canadian copyright law, copyright is defined in section 3(1) of the Copyright Act:
For the purposes of this Act, copyright, in relation to a work, means the sole right to produce or reproduce the work or any substantial part thereof in any material form whatever, to perform the work or any substantial part thereof in public or, if the work is unpublished, to publish the work or any substantial part thereof, and includes the sole right [to ... list of specfic rights] and to authorize any such acts.
It's clear from the outset that public performance does indeed require permission. The list of specific rights that I've omitted here for brevity don't reveal any infringed right. That leaves the question of whether an unrecorded (unfixed in legal jargon) private performance constitutes a reproduction. My opinion is no, since why else would section 3(1) need to have a separate clause for performance if performance was already covered within the scope of reproduction? Additionally, it would seem likely that Parliament would have specifically protected private performance if it so chose, given that they already felt the need to specifically protect public performance.
The Supreme Court is likely in agreement. In Théberge v. Galerie d'Art du Petit Champlain inc., 2002 SCC 34 at paragraph 42, they wrote in what appears to be dicta (replacing their underlining with bold):
The historical scope of the notion of “reproduction” under the Copyright Act should be kept in mind. As one would expect from the very word “copyright”, “reproduction” is usually defined as the act of producing additional or new copies of the work in any material form. [...]
Therefore, I conclude that unfixed private performances are not within the scope of Canadian copyright protection.
I'm less familiar with American copyright law, but the statute appears even clearer than the Canadian one in this respect. Instead of reproduction, the American act uses copies which in s. 101 is defined to mean material object, so definitely not a performance. The rights granted by American copyright law are listed in s. 106, and I don't see any infringed right. Subsection 4 notably covers public performance, but not private performance. Therefore, unfixed private performances are also not within the scope of American copyright protection.
Finally, I'll note that I don't believe the dividing line between private & public is well-defined in either Canada or the US and would have to be hashed out in future case law.