A method of recording a musical text using numbers (see Musical writing).
The possibility of using C. s. due to the value in the sound structure of numerical proportions, the ordering of elements, the similarity between musical-functional and numerical ratios. In some cases, C. s. turns out to be more expedient than other systems of music. signs. According to C. s. pitch, meter and rhythm can be indicated, sometimes other parameters of music.
Most widely C. with. used to designate pitch, primarily intervals (1 – prima, 2 – second, etc.). S. I. Taneev proposed a new C. s. intervals, in which the numbers indicate the number of seconds in the interval (prima – 0, second – 1, third – 2, etc.); this made it possible to construct a mathematically exact theory of polyphonic. connections (see Movable counterpoint). Roman (sometimes also Arabic) numerals are used in the step system of the doctrine of harmony to designate chords by indicating the steps that are their prima (for example, I, V, nVI, in III, etc.), which allows you to write chords in any tonality, regardless of the specific height of the prima; Arabic (sometimes also Roman) numerals in the step and function systems denote the sounds of a given chord (for example,
– dominant seventh chord with an elevated fifth). The designation of the steps of the octave (do, re, etc.) is Arabic. figures received a certain distribution in Russian. school practice choir. singing (according to the digital system of E. Sheve; see Solmization): steps in the average singing. octave (1st octave for treble and alto, small – for bass and tenor) – 1, 2, 3, 4, 5, 6, 7 (pause – 0), in a higher octave – with a dot on top (
etc.), in the lower octave – with a dot below (
etc.); elevated steps –
, lowered –
. The numbers correspond to sounds of any key, for example. in F major:
(A figure with one dot on the right is equal to a half note, with two dots is equal to a half with a dot, and with three dots is a whole note.)
C. s. used in tablature, general bass, in the practice of learning to play on some bunks. instruments (domra, balalaika, two-row chromatic harmonica). When learning to play the strings. instruments use a series of parallel lines, the number of which corresponds to the number of strings of the instrument; numbers are written on these lines corresponding to the serial numbers of the frets on the fingerboard. Lines are numbered from top to bottom. Such a recording is a kind of digital tablature. In the notes for the harmonica, numbers are often put down, indicating the ordinal number of the key corresponding to this note.
C. s. ubiquitous to designate metrorhythmic. ratios – from the mensural signs of the 14th-15th centuries. (by F. de Vitry in the treatise “Ars nova” when describing modus perfectus u modus imperfectus) up to modern. metric signs. In theory, classical metrics X. Riemann Ts. used to denote metric. clock functions:
(where, for example, 4 is a function of a small conclusion, a half-cadence; 8 is a function of a full conclusion; 7 is a function of a light measure, intensively gravitating towards the next, most difficult one). In electronic music, with the help of numbers, the basics can be recorded. music parameters – frequency, dynamics, duration of sounds. In the practice of serial music, numbers can be used, for example, to convert pitch relationships into rhythmic ones (see Seriality), for permutation. Diff. C. s. are used to count other related phenomena, for example, for fingering.
References: Albrecht K.K., Guide to choral singing according to the Sheve digital method with the application of 70 Russian songs and 41 three-part choirs, mainly for folk schools, M., 1867, 1885; Taneev S.I., Mobile counterpoint of strict writing, Leipzig, (1909), M., 1959; Galin R., Exposition d’une nouvelle méthode pour l’enseignement de la musique, P., 1818, id., under the title: Méthode du Meloplaste, P., 1824; Chevé E., Méthode élémentaire de musique vocale, P., 1844, 1854; his own, Méthode Galin-Chevé-Paris, Méthode élémentaire d’harmonie, P., 1846; Kohoutek C., Novodobé skladebné teorie zbpadoevropské hudby, Praha, 1962, under the title: Novodobé skladebné smery v hudbe, Praha, 1965 (Russian translation – Kohoutek Ts., Technique of Composition in Music of the 1976th Century, M., XNUMX).
Yu. N. Kholopov