Temperament |

from lat. temperatio – correct ratio, proportionality

Alignment of the interval relationships between the steps of the pitch system in music. order. T. characteristic of subsequent stages in the development of each of the muses. systems: to replace the “natural” systems (for example, Pythagorean, pure, i.e. e. based on intervals from the natural scale), artificial, tempered scales come – uneven and uniform T. (12-, 24-, 36-, 48-, 53-speed, etc.). The need for T. arises in connection with the requirements of the muses. hearing, with the development of sound-altitude music. systems, means of music. expressiveness, with the advent of new forms and genres and, ultimately, with the development of music. tools. So, in Dr. Greece, in search of a more perfect tuning of the tetrachord, Aristoxenus proposed dividing a quart into 60 equal parts and for two b. seconds (a – g, g – f) select 24 shares, and for m. seconds (f – e) – 12; practically it is very close to modern. 12-speed uniform T. The most intensive searches in the area of ​​T. belong to the 16th-18th centuries. e. by the time of formation of homophonic-harmonic. warehouse, the development of large forms of music. production, the formation of a complete major-minor system of keys. In the previously used Pythagorean and pure tunings (cf. Stroy) there were small height differences between enharmonic. sounds (cf. Enharmonism), did not match each other in height, for example, the sounds his and c, dis and es. These differences are important to express. performance of music, but they hampered the development of the tonal and harmonic. systems; it was necessary either to design instruments with several dozen keys per octave, or to abandon transitions to distant keys. First, uneven T. musicians tried to keep the value of b. the thirds are the same as in the pure tuning (Temperament A. Shlyka, P. Arona, midtone T. and etc.); for this, the magnitude of some fifths changed slightly. However, dep. fifths sounded very out of tune (i.e., Mr. wolf fifths). In other cases, eg. in midtone T., b. the third of a pure tuning was divided into two whole tones of the same size. It also made it impossible to use all the keys. A. Werkmeister and I. Neidhardt (con. 17 – beg. 18 centuries) abandoned b. thirds of a pure order and began to divide the Pythagorean comma between decomp. fifths. Thus, they practically came close to the 12-speed uniform T. In the 12-step equal-tempered tuning, all pure fifths are reduced in comparison with the fifth from the natural scale by 1/12 of the Pythagorean comma (about 2 cents, or 1/100 of a whole tone); the system became closed, the octave was divided into 12 equal semitones, all intervals of the same name became the same in size. In this system, you can use all the keys and chords of the most decomp. structures, without violating the established norms for the perception of intervals and without complicating the design of instruments with a fixed pitch of sounds (such as organ, clavier, harp). One of the first very accurate calculations of the 12-speed T. produced by M. Mersenne (17th century); the table of movement along the circle of fifths with a return to the starting point was placed in his “Music Grammar” by N. Diletsky (1677). The first bright experience of art. the use of the tempered system was carried out by I. C. Bach (The Well-Tempered Clavier, ch. 1, 1722). 12-speed T. remains the best solution to the system problem. This T. created the conditions for the further intensive development of the modal harmonic. systems in the 19th and 20th centuries. When singing and playing instruments with non-fixed pitch, musicians use the so-called. Mr. zone system, in relation to Krom tempered system is a special case. In turn, T. also affects the zone structure, determining the average values ​​of the step zones. Developed by N. A. Garbuzov theoretician. the concept of the zonal nature of pitch hearing (see. Zone) made it possible to identify psychophysiological. the basis of the 12-speed T. At the same time, she convinced that this system cannot be ideal. For the sake of overcoming intonation. disadvantages of 12-speed T. tunings were developed with a greater number of tempered steps per octave. The most interesting of them is the variant of the system with 53 steps in an octave, proposed by N. Mercator (18th century), Sh. Tanaka and R. Bosanquet (19th century); it allows you to quite accurately reproduce the intervals of the Pythagorean, clean and 12-step equal temperament tunings. Yet none of these systems received a practical.

In the 20th century experiments to create diff. options T. continue. In Czechoslovakia in the 20s A. Khaba developed 1/4-tone, 1/3-tone, 1/6-tone and 1/12-tone systems. In the Sov. Union at the same time, A. M. Avraamov and G. M. Rimsky-Korsakov conducted experiments with a quarter-tone tone system; A. S. Ogolevets proposed 17- and 29-step T. (1941), P. P. Baranovsky and E. E. Yutsevich – 21-step (1956), E. A. Murzin – 72-step system T. 1960).

References: Khaba A., Harmonic basis of the quarter-tone system, “To new shores”, 1923, No 3, Shtein R., Quarter-tone music, ibid., Rimsky-Korsakov G. M., Substantiation of the quarter-tone musical system, in: De musisa. Vremnik discharge of history and theory of music, vol. 1, L., 1925; Ogolevets A. S., Fundamentals of the harmonic language, M., 1941; his, Introduction to modern musical thinking, M., 1946; Garbuzov N. A., Intrazonal intonation hearing and methods of its development, M. – L, 1951; Musical Acoustics, ed. H. A. Garbuzova, M., 1954; Baranovsky P. P., Yutsevich E. E., Pitch analysis of the free melodic system, K., 1956; Sherman N. S., Formation of a uniform temperament system, M., 1964; Pereverzev N. K., Problems of musical intonation, M., 1966; Riemann H., Katechismus der Akustik, Lpz., 1891, 1921

Yu. N. Rags