The notion of bounded \(p\)-variation was introduced by \textit{N. Wiener} in 1924 [see Mass. J. Math. 3, 72--94 (1924; JFM 50.0203.01)]. \textit{D. Waterman} [Stud. Math. 44, 107--117 (1972; Zbl 0207.06901)] and \textit{Z. A. Chanturiya} [Dokl. Akad. Nauk SSSR 214, 63--66 (1974; Zbl 0295.26008)] have made important contributions concerning the concept mentioned above. In the present note, the authors define a certain type of variation as an important generalization of the concept of bounded variation. Namely: let \(f\) be a function defined on \((-\infty,\infty)\) with period 1, let \(\Delta:\cdots t_{-1}