Let A be a finite dimensional algebra (associative, with an identity) over an arbitrary field k, and let D b(A) denote the derived category of bounded complexes of finitely generated right A-modules (in the sense of \textit{J. I. Verdier} [Lect. Notes Math. 569, 262-311 (1977; Zbl 0407.18008)]). Following \textit{D. Happel} and \textit{C. M. Ringel} [Trans. Am. Math. Soc. 274, 399-443 (1982; Zbl 0503.16024)], we shall call a (finitely generated) module \(T_ A\) a tilting module if \(Ext\) \(1_ A(T,T)=0\), \(Ext\) \(2_ A(T\),-)\(=0\), and the number of non-isomorphic indecomposable summands of T is equal to the rank of the Grothendieck group \(K_ 0(A)\) of A. Let now H be a hereditary (finite dimensional) algebra. An algebra A is called piecewise hereditary of type H if D b(A)\(\overset \sim \rightarrow D\) b(H), as triangulated categories, and it is called iterated tilted of type H (in the sense of the reviewer and \textit{D. Happel} [Commun. Algebra 9, 2101- 2125 (1981; Zbl 0481.16009)] if there exist a sequence of algebras \(A=A_ 0,A_ 1,...,A_ m=H\) and a sequence \(T\) \(i_{A_ i}\), \(0\leq i