Golden ratio |
Golden Section in music – found in the plural. music prod. the connection of important features of the construction of the whole or its parts with the so-called. golden ratio. The concept of Z. with. belongs to the field of geometry; Z. s. called the division of a segment into two parts, with Krom the whole is related to the larger part as the larger part is to the smaller (harmonic division, division in the extreme and average ratio). If the whole is denoted by the letter a, the larger part by the letter b, and the smaller part by the letter c, this ratio is expressed by the proportion a:b=b:c. In numerical terms, the ratio b:a is a continued fraction, approximately equal to 0,618034 …
During the Renaissance, it was established that Z. s. finds application in depicting. art-wah, especially in architecture. It was recognized that such a ratio of parts gives the impression of harmony, proportion, grace. Composers of the Netherlandish school (J. Obrecht) consciously used the Z. with. in their productions.
The first attempt to detect Z.’s manifestation with. in music made in ser. 19th century German scientist A. Zeising, who unjustifiably announced Z. s. universal, universal proportion, manifested both in art and in the natural world. Zeising found that close to Z. s. the ratio reveals a major triad (the interval of a fifth as a whole, a major third as a major part, a minor third as a minor part).
A more definite manifestation of the relations of Z. with. in music was discovered at the beginning. 20th century Russian researcher E. K. Rosenov in the field of music. forms. According to Rozenov, it already affects the period where melodic. the climax is usually located at a point close to the point Z. with. Quite often near a point Z. with. Turning points are also found in larger sections of music. forms (Z. s. manifests itself in the temporal ratio of parts, which, in the case of a change in tempo, does not coincide with the ratio of the number of measures) and even in whole one-part works. Although Rosenov’s analyzes are sometimes excessively detailed and not without stretches, in general, his observations about the manifestations of Z. s. in music were fruitful and enriched the idea of temporary muses. patterns.
Later Z. with. V. E. Ferman, L. A. Mazel, and others studied music in music. is a sign of sustainability, ext. completion of the melody. He showed that at the point Z. with. music period may be melodic. the apex not only of the entire period, but also of the second sentence, that this point may be the moment from which the second sentence develops differently from the first (these manifestations of the z. s. can be combined). On the scale of a sonata allegro and in three-part form, according to Mazel, the point Z. with. in the classic music usually falls at the beginning of the reprise (end of development), in the music of romantic composers it is located in the reprise, closer to the coda. Mazel introduced the concept of Z. with. in the course of music analysis. works; Gradually, it firmly entered the everyday life of owls. musicology.
References: Rozenov E.K., On the application of the law of “golden division” to music, “Izvestiya SPb. Society for Musical Meetings, 1904, no. June – July – August, p. 1-19; Timerding G. E., The Golden Section, trans. from German, P., 1924; Mazel L., Experience in the study of the golden section in musical constructions in the light of a general analysis of forms, Musical Education, 1930, No 2.
