Discrete string simulating a musical gamma

The discrete string with fixed endpoints carrying a finite number of beads is determined by masses of beads and distances between them. The string possesses a set of simple eigenfrequencies corresponding to harmonic eigenmodes. In the paper the following problem is treated: to find a discrete string carrying seven beads such that its eigenfrequencies coincide with the freqiencies of the notes of the first octave of the musical gamma. The problem is solved in two steps. First, the spectral inverse problem is considered, that is, recovering the string by its spectrum and a set of constants related to the normalized eigenmodes. A procedure of solving this problem is described. One of the main results of the paper is a necessary and sufficient conditions for solvability of the spectral inverse problem. The second step is numerical realization of the procedure.