Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aω of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr(Aω) = 1/d. tr(Aρ). It is proved that the set of all C*-algebras of sections of locally trivial C*-algebra bundles over S2 with fibres Aω has a group structure, denoted by πs1(Aut(Aω)), which is isomorphic to Z. if d > 1 and {0} if d > 1. Let Bcd be a cd-homogeneous C*-algebra over S2 × T2 of which no non-trivial matrix algebra can be factored out. The spherical noncommutative torus Scdρ is defined by twisting C*(T2 × Zm-2) in Bcd C*(Zm-2) by a totally skew multiplier ρ on T2 × Zm-2. It is shown that Scdρ Mp∞ is isomorphic to C(S2) C*(T2 × Zm-2,ρ) Mcd(C) Mp∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p.