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For a positive integer \(k,\) let \( [k] = {1,2,…,k}\), let \(P([k])\) denote the power set of the set \([k]\) and let \(P*([k]) = P([k]) – {\emptyset}\). For each integer \(t\) with \(1 \le t < k\), let \(P_t([k])\) denote the set of \(t\)-element subsets of \(P([k])\). For an edge coloring \(c : E(G)\to P_t ([k])\) of a graph \(G\), where adjacent edges may be colored the same, \(c' : V(G) \to P*([k])\) is the vertex coloring in which \(c' (v)\) is the union of the color sets of the edges incident with \(v\). If \(c'\) is a proper vertex coloring of \(G\), then \(c\) is a majestic \(t\)-tone k-coloring of \(G\) For a fixed positive integer \(t\), the minimum positive integer \(k\) for which a graph \(G\) has a majestic t-tone k-coloring is the majestic t-tone index \(maj_t (G)\) of \(G\). It is known that if \(G\) is a connected bipartite graph or order at least 3, then \(maj_t(G) = t + 1\) or \(maj_t (G) = t + 2\) for each positive integer t. It is shown that (i) if \(G\) is a 2-connected bipartite graph of arbitrarily large order \(n\) whose longest cycles have length \(l\) where where \(n-5 \leq l \leq n\) and \(t\geq 2\) is an integer, then \(maj_t(G)=t+1\) and (ii) there is a 2-connected bipartite graph F of arbitrarily large order n whose longest cycles have length n-6 and \(maj_2(F)=4\). Furthermore, it is shown for integers \(k,t \ge 2\) that there exists a k-connected bipartite graph \(G\) such that \(maj_t(G) =t+2\). Other results and open questions are also presented.