Mathematical creation of melodies

The guess of the mathematical basis of melodies for several centuries. In any case, the statements about the “algebra in music” were made repeatedly, although there were no more specific statements, apparently, excluding the mathematical analysis of the phenomena of consonance and dissonance and their role in the construction of the musical system [1]. As for the mathematical foundations of the melodies themselves, I do not know any work in this direction, and judging by the new attempts regularly appearing in the press, there were no such work algorithm at all related to mathematics.
In 2009-2016 I published three editions of the brochure of "The Secret of Harmony" (SG) with an explanation of the mathematical principle of the formation of melodies [2] and two books ("Melodies gained in a dream" and "romances" [3.4]) containing about a hundred songs and romances from Melodias created by mathematically, which were actually an experimental verification and confirmation of the stated in the SG. In each subsequent publication of SG, the analysis of the issue under discussion was improved. However, as I was convinced, musicians and composers still need a more intelligible description of the process of creating melodies, detailing and explaining it that I am trying to implement in this book. Although it is difficult to achieve a combination of visualization with the severity of the presentation, I hope that I managed to do this in it.
Here I partially repeat in a brief form what was already in the SG, so as not to force the reader to previously get acquainted with the SG, as well as affect a number of issues that were not discussed earlier