In the sphere of musical research, the intersection of two seemingly very different subject areas-music and mathematics is in essence related to one of the trends of music-attributing the theory of music to science, to the sphere of mathematica. It is regarded the longest-lasting interdisciplinary dialogue. The implication of numerical proportions and number sequences in the music composition of different epochs is closely related to this sphere. A significant role in creating music was attributed to the so-called infinite Fibonacci sequence. Perhaps the most important feature of the Fibonacci numbers, which attracted the attention of thinkers and creators of different epochs, is the fact that by means of the ratio between them it is possible to come maximally close to the Golden Ratio formula, which expresses the laws of nature. On a practical plane, often the climax, the most important part of any composition, matches the point of the Golden Ratio; groups of notes, rhythm, choice of tone pitches, a grouping of measures, time signature, as well as proportions between a musical composition's parts may be regulated according to Fibonacci principles. The article presents three analytical cases-Chopin's piano prelude, Bourgeois' composition for organ, and Reich's minimalistic piece, attempting to render music composition structure to the logic of Fibonacci numbers.