Abstract: The subject of the study is aleatoric forms (including indeterminacy in the process of musical thought writing and development) which, in spite of individual author's development, are based on traditional principles of organization, such as repetition, variation, presentation of thematism and its development, main body and development, sonata form, etc. The object of the study are the works by composers of the twentieth century that are based on the aleatoric principle and at the same time inherit the tradition of classical-romantic forms. Mobile aleatoric forms, as a rule, have a clear material disposition (sequence of themes, sections, fragments or episodes), and the order of presentation of thought through them does not change considerably despite the uncertainty of some parameters. The study is based on the method of analysis of modern musical forms developed by the “Kholopov” school of musicology, the work’s text analysis of which starts from the material and methods of its development end ends up with the principles of texture and development of musical thought in general. The main conclusions of the study are the following theses: mobility of the aleatoric form at the text level (not the order of its writing) represents the measure of mobility that is acceptable for composition on the basis of traditional principles of organization. Thus such incongruous categories as aleatoric music and traditional forms can also be combined: composers of the twentieth century turned to classical forms as stability of the works’ structure allowed them to preserve traditional forms even in a mobile text.

Abstract: The subject of this research is the artistic and aesthetic principles of the American avant-gardist John Cage, based on the religious and philosophical principles and categories of Zen Buddhism applied in his musical compositions. Such principles as unintentionality, incident, indeterminism, inconstancy and variability, unity, simultaneous plurality, intefusion of art and life, have formed under the influence of the four noble truths of Buddhism, categories of inaction, Nothingness, emptiness, and also the essential foundations of Zen Buddhism, including the representations about the world (human and nature), spiritual practice, etc. All of the aforementioned principles will find application in the specific writing techniques, genres, forms and types of musical and creative activity of Cage. The scientific novelty of this research lies in the first attempt within Russian musicology to connect the religious and philosophical principles and categories of Zen Buddhism with the artistic and aesthetic principles of Cage, draw analogies between them, provide a concrete explanation to what they represent and how they affect the composer’s musical works.

Abstract: The subject of this research is so-called open form of Luciano Berio – one of the innovators of European avant-garde. He composed music in mobile forms that were changing in material and structure. The object of this research is the oeuvres of Luciano Berio in the open form of diversified genres. Berio applied the aleatoric technique of composing, as well as wrote a number of articles dedicate to the open form. He desired to materialize in music the philosophical-aesthetic principles of J. Joyce and U. Eco. The article reviews the concept of Berio's open musical form and few of his works, in which it found its reflection. Methodology of the research implies the aesthetic and theoretical analysis of the ideas and concepts of Berio, expressed by him in the article about open form, as well as music-theoretical analysis of composer’s oeuvres with application of the new terms. The scientific novelty consists in first Russian-language analysis of open form concept in the works of Luciano Berio, its specific materialization in music compositions, identification of the key features of the open form, examination of the score and its sound realization that demonstrates the mobility of composition at the level of text and structure, tracing the practical implementation of aleatoric technique of composing alongside its impact upon morphogenesis. The article also provides a translation from English into the Russian language of Berio’s article dedicated to the open form.

Abstract: The subject of this research is John Cage's methods of composition used by him in the 1940th years: melodic or rhythmic ostinato, counterpoint technique and rhythm pattern technique. He has found in these, initially traditional methods of composition, something new and has anticipated what will appear in music later, in particular, ways of the repetitive technique used by minimalists. Special attention is paid to such Cage's works as Metamorophisis and Amores Cycles as well as Credo in Us that present the composer's typical style. The research method used by the author to analyze Cage's composition technique involves analysis of the sound material, its features, and principles of organisation of small and major structural units and form in general. The novelty of the research is that Cage's techniques (ostinato, counterpoint, rhythm pattern technique, etc.) are studied in detail on the example of musical pieces for the first time in Russian academic literature, and the early period of works by Cage, who is better known as an experimenter and avant-gardist, is also researched for the first time in Russian literature. At the same time there is a discovered individual approach in using of these methods of the composition which are characterizing composer style of Cage.

Abstract: The object of this research is the compositional methods of Belgian composer Henri Pousseur, who pursued the aleatoric principle in music. Over the period of 1960’s – 1970’s, such principle was extensively applied by the composers of North America and Europe. Americans from J. Cage's circle referred to the unlimited aleatoric music, including improvisation of the graphic and verbal scores, while their European colleagues preferred the limited aleatoric music. Pousseur also turned to the limited aleatoric composition in performing process, which substantiated the diverse degree of the fluidity of form – from mobile, when the score remains unchanged, but its spate parameters vary, to the modular, in which the order of parts is unpredicted, and thus, the process of evolution of the musical thought. The author gives attention to the most notable oeuvres of H. Pousseur in aleatoric writing technique, as well as how the compositions are executed and formed. The plays by Pousseur are subject to analysis from the multiple perspectives: sound material, its properties, structure, dramaturgical process, which allows formulating an integral concept of a composition. The scientific novelty consists in the fact that the aleatoric writing technique of H. Pousseur is being explored in the Russian language for the first time on the example of specific compositions, considering the author’s commentaries that have also been translated from French. Special contribution of the author into the national musicology consists in studying the individual "method of windows" of Pousseur, which prior to that was barely mentioned in the literature, as well as the analysis of forming of such opuses as "Characters I" and "Mobile".

Abstract: Object of research is the aleatory form in 20th century music organized by means of numbers and numerical rows which are mainly specially composed by authors of works. Using numbers and rows as constructive determinants, composers solve a problem of forming of works with the mobile musical text and structure. Special attention is paid to concrete works and their internal organization, making a mobile form united. The main conclusion of the research is the fact that the aleatory principle influencing forming demanded application of additional musical and extra musical resources of form organisation, and the numerical method was one of the most effective. The novelty of a research consists in descovery the organizing numbers and rows hidden in the musical text and not mentioned earlier by neither composers, nor researchers, externally itself, sometimes, not showing in any way.

Abstract: One of the most popular method used in music of the second half of the 20th - beginning of the 21st centuries is the aleatory technique when music is composed by using random interaction. Form making is one of the main problems that arise when the aleatory technique is being used. Moving and uncertain, aleatory form required certain rigidity and determinancy at minor and major levels. In such compositions, form making function is performed through pitch or rhythmic organisation, dramaturgical patterns or other constructive forces or factors that influence the form and give it a single structure. Noteworthy that the aleatory composition technique is often combined with the principle of organising numbers that is widely used by many authors. Aleatory forms managed by organising numbers are typical for Cage, Stockhausen or Gubaydullina. These composers used all kinds of number sequences and groups that are viewed by the author of the present article. 

Abstract: One of the most popular method used in music of the second half of the 20th - beginning of the 21st centuries is the aleatory technique when music is composed by using random interaction. Form making is one of the main problems that arise when the aleatory technique is being used. Moving and uncertain, aleatory form required certain rigidity and determinancy at minor and major levels. In such compositions, form making function is performed through pitch or rhythmic organisation, dramaturgical patterns or other constructive forces or factors that influence the form and give it a single structure. Noteworthy that the aleatory composition technique is often combined with the principle of organising numbers that is widely used by many authors. Aleatory forms managed by organising numbers are typical for Cage, Stockhausen or Gubaydullina. These composers used all kinds of number sequences and groups that are viewed by the author of the present article.