The harmonic and melodic connection numbers involving the mutual inclusions among the generic groups of notes arbitrarily emitted

The present paper is aimed to provide specific details and new results related to the music network described in the previous study by the author. While the first paper served as an introduction and extensive analysis of the model in all its potential applications, the present study is aimed at providing supplementary data to quantitatively support the previous one. The music concepts described in the present paper concern the evaluation of all the potential mutual inclusions and connections among chords, scales, and more in general any generic group of notes arbitrarily played by each musician. These concepts characterize the specific algorithm purposely developed and implemented in an interactive software application tool that can be employed for performing the melodic and harmonic analyses of any kind of tune. Geometric music graphs that take into account these groups are automatically designed by the software in order to trace the harmonic and melodic zones touched by each music composition. These geometric graphs are constituted by the connections (that can also represent mutual inclusions) among the generic groups of notes. The primary focus of the present paper is on the quantitative results and data characterizing the inner structure related to these graphs.