ENGLISH SUMMARY

Valeria Tsenova

NUMBER MYSTERIES IN THE MUSIC OF SOFIA GUBAIDULINA

The book is a monographic research based on the materials from the collection of Sofia Gubaidulina at the Paul Sacher Foundation (Basle, Switzerland). This collection includes some remarkable sketches for the works from the 1990s. The most valuable for researchers are working materials to Gubaidulina's compositional techniques: formal plans, timbral schemes, and numbers. Many pages of the drafts are filled with formulas and calculations that refer to the temporal proportions of the form on different levels. Gubaidulina's interest in both the numerical aspect of composition and in numerical symbolism has been known for a long time, but only the drafts at the Basle archive give us concrete evidence of this fact.

Gubaidulina values two important elements in the compositional process: the constructive principle and its symbolic meaning. In her works from the beginning of the 1980's, she consciously uses numerical structures with sacral-mystical meanings. The composer uses different types of numerical structures. The deepest stratum of her aesthetics is the most valuable. Hidden from the eyes, it lies at the very foundation of the musical composition and is organised as a complicated system of numerical ratios.

In various interviews Gubaidulina has commented on the basis of the compositional techniques in the sonic space of contemporary music. She is convinced that rhythm is the most important foundation. However, Gubaidulina understands rhythm not only in the general sense as a series of durations. From 1984, she began working on the rhythm of the form, which means a special temporal structure of the work produced by the proportionality between sections of its form. Surely, this problem is not new and in all times has been of special interest for any creation of music. But in the twentieth century the rhythm of the form became an important aspect of contemporary compositional technique that is brilliantly demonstrated by Gubaidulina, who creates individual numerical plots in almost every work. The expression numerical plot was found in Gubaidulina's sketches and for our purposes can be used as a special term for the compositional technique that means the proportional calculation of the whole form.

The proportions of the Fibonacci series are the foundation for a majority of Gubaidulina's works from the middle of the 1980s (Perception, Im Anfang war der Rhythmus, Stimmen...Verstummen, Quasi hoketus). In her works one can also find other sequences, derived from the Fibonacci principle, for example the Lucas and Evangelists' series.

For Gubaidulina, as an organic, natural phenomenon, the Fibonacci series has an important semantic meaning. These numbers break away from a mechanical regularity, approach the ideal golden section and give the form an ability to breathe. Fibonacci numbers were frequently used in works by such composers as Debussy, Bartók, Stockhausen, Nono, but it is difficult to find such a diverse treatment as in Gubaidulina's music.

At first Gubaidulina was attracted by the logical beauty of the Fibonacci numbers; they exerted a fascinating and in some sense mystical influence on her. It was only later that this numerical series became the constructive basis of her works. She found various ways of using it. In Jetzt immer Schnee [Now always snow], for example, one can find a complicated rhythmical structure underlying the entire five-movement cycle, and in the Fourth Quartet the purely musical proportions are accompanied by light projection.

Such a pervasive treatment of rhythm can be found in a piece with the poetic title ...Heute früh, kurz vor dem Aufwachen..., written for 7 Japanese Koto, in Meditation über den Choral von J. S. Bach "Vor deinen Thron tret ich hiermit", and in many other works from the 1990s.

Gubaidulina has consistently spoken with great enthusiasm about the beauty of numbers. The following words are a prime example: "I am inspired by this working method: 'the dance of the numbers' and pure intuition. Music is developing in two opposite directions: according to the numerical plot and by intuition. And when these two approaches intersect the unanticipated outcome is beautiful." (From the conversation with the composer, 7 February 2000).

According to the Ancient Greeks number is the foundation of everything. It seems that numerical stratum of Gubaidulina's works should be understood in the sense of this Pythagorean concept. Perhaps it is not without significance, that the Greek also demonstrated their theory of number with the help of music.