Symmetrical frets |

symmetrical frets – frets, the scales of which are based on the equal division of the octave. Like other frets, S. l. are built on the basis of a certain center. element (abbreviated as CE). However, unlike, for example, from major or minor, S. l. are formed not on the basis of a major or minor triad, but on the basis of consonance (or central relations) resulting from the division of 12 semitones into 2, 3, 4 or 6 equal parts. Hence 4 possibilities – 12: 6, 12: 4, 12: 3, 12: 2 and, accordingly, 4 main. type S. l. They are named according to their CE (just as a major is named after its CE – major triad): I – whole-tone (CE 12: 6 = whole-tone six-tone); II – reduced, or low-frequency (CE 12: 4 = smart seventh chord); III – increased, or greater terts (CE 12: 3 = increased triad); IV – tritone (or double mode, the term of B. L. Yavorsky) (CE 12: 2 = tritone). Depending on specific. structures of the scale III and IV types of frets are subdivided into several. subtypes. Theoretically possible division 12:12 gives one more type of S. l. (V) – limiting, but devoid of property. structural and therefore standing apart. Pivot table S. l .:

Theoretical S.’s explanation of l. receive in line with the aesthetic. traditions of the theory of proportions, which puts them in a natural connection with other types of modal systems – the modes of the major-minor system and the Middle Ages. frets. The explanation common to all is that each type of mode, depending on its CE, corresponds to one of the numerical progressions known since antiquity – arithmetic, harmonic and geometric. The numerical series formed by them, which give the CE of each of these systems, are given in terms of the coefficients of the numbers. fluctuations.

Application examples S. l. in the music liter-re (the numbers indicate the numbers of S. l. in the musical example):

1. M. I. Glinka. “Ruslan and Lyudmila”, scale of Chernomor. 2. N. A. Rimsky-Korsakov. “Sadko”, 2nd painting. 3. N. A. Rimsky-Korsakov. “Golden Cockerel”, cock crow (number 76, bars 5-10). 4. N. A. Rimsky-Korsakov. “Snow Maiden”, Leshy’s theme (numbers 56-58). 5. A. N. Cherepnin. Study for piano. op. 56 no 4. 6. I. P. Stravinsky. “Firebird” (numbers 22-29). 7. I. F. Stravinsky. “Parsley”, the theme of Petrushka (see in Art. Polyaccord). 8. S. V. Protopopov. “Crow and Cancer” for voice with piano. 9. O. Messiaen. “20 views…”, No 5 (see article Polymodality). 10. A. K. Lyadoi. “From the Apocalypse” (number 7). 11. O. Messiaen. L’Ascension for organ, 4th movement. 12. A. Webern. Variations for fp. op. 27, 4th part (see in Art. Dodecaphony).

See also articles Tritone mode, Increased mode, Reduced mode, Whole-tone mode.

S. l. – one of the types of modality (modality) along with pentatonic, diatonic, decomp. kind of complicated frets. S. l. branched off from the common European systems of major and minor (the preforms of s. l. are transposing sequences, equal-tert cycles of tonalities, figuration, and anharmonicity of equal-interval consonances). The first samples of S. l. are random in nature (the earliest, before 1722, in the sarabande of the 3rd English suite of J. S. Bach, bars 17-19: des2 (ces2)-bl-as1-g1-f1-e1-d1-cis1. Use of C L. as a special expressive means began in the 19th century (increased mode and whole-tone scale in the bass Sanctus of the mass Es-dur by Schubert, 1828; increased mode and whole-tone scale in the bass in the opera God and Bayadere by Auber, 1830 , in 1835 post in St. Petersburg under the title La Bayadère in Love; also by Chopin). musical language, and connected with an interest in what is alien to this language.) A. N. Verstovsky, M. I. Glinka, A. S. Dargomyzhsky, N. A. Rimsky-Korsakov, P. I. Tchaikovsky, A. K. Lyadov, V. I. Rebikov, A. N. Skryabin, I. F. Stravinsky, A. N. Cherepnin, and also S. S. Prokofiev, N. Ya. Myaskovsky, D. D. Shostakovich, S. V. Protopopov, M. I.Verikovsky, S. E. Feinberg, A. N. Alexandrov and others. composers to S. l. F. Liszt, R. Wagner, K. Debussy, B. Bartok addressed; especially widely and in detail S. l. developed by O. Messiaen. In the music S.’s theory of l. were originally described as special alien modes (for example, in G. Kapellen, 1908, “Chinese whole-tone music” was demonstrated on samples composed by the author as “extreme exoticism”). In Russian theoretical musicology the first description of S. l. (under the name “circular” modulating sequences, “circles” of major and minor thirds) belongs to Rimsky-Korsakov (1884-85); the first theoretical S.’s explanation of l. was proposed by B. L. Yavorsky at the beginning. 20th century From abroad. theorists the theory of S. l. developed primarily by Messiaen (“Modes of Limited Transposition”, 1944) and E. Lendvai (“System of Axes”, on the example of Bartok’s music, 1957).

References: Rimsky-Korsakov N.A., Practical textbook of harmony, St. Petersburg, 1886, the same, Poln. coll. soch., vol. IV, M., 1960; Yavorsky B. L., The structure of musical speech, parts 1-3, (M., 1908); Kastalsky A.D., Features of the folk-Russian musical system, M. – Pg., 1923, 1961; A. M., A. Cherepnin (notography), “Contemporary Music”, 1925, No 11; Protopopov S. V., Elements of the structure of musical speech, parts 1-2, M., 1930; Tyutmanov I. A., Some features of the modal-harmonic style of HA Rimsky-Korsakov, in the book: Scientific and methodological notes of the Saratov state. conservatory, vol. 1-4, Saratov, 1957-61; Budrin B., Some questions of Rimsky-Korsakov’s harmonic language in operas in the first half of the 90s, Proceedings of the Department of Music Theory of the Moscow Conservatory, vol. 1, 1960; Sposobin I. V., Lectures on the course of harmony, M., 1969; Kholopov Yu. N., Symmetric modes in the theoretical systems of Yavorsky and Messiaen, in the book: Music and Modernity, vol. 7, M., 1971; Mazel L. A., Problems of classical harmony, M., 1972; Tsukkerman V.A., Some questions of harmony, in his book: Musical-theoretical essays and etudes, vol. 2, M., 1975; Capellen G., Ein neuer exotischer Musikstil, Stuttg., 11; his, Fortschrittliche Harmonie- und Melodielehre, Lpz., 1906; Busoni F., Entwurf einer neuen Дsthetik der Tonkunst, Triest, 1908 (Russian translation: Busoni F., Sketch of a new aesthetics of musical art, St. Petersburg, 1907); Schönberg A., Harmonielehre.W., 1912; Setacio1911i G., Note ed appunti al Trattato d’armonia di C. de Sanctis…, Mil. – NY, (1); Weig1923 B., Harmonielehre, Bd 1-1, Mainz, 2; Hbba A., Neue Harmonielehre…, Lpz., 1925; Messiaen O., Technique de mon langage musical, v. 1927-1, P., (2); Lendvai E., Einführung in die Formenund Harmoniewelt Bartoks, in: Byla Bartuk. Weg und Werk, Bdpst, 1944; Reich W., Alexander Tcsherepnin, Bonn, (1957).

Yu. H. Kholopov