Abstract: The subject of the research in the article is the work of the American composer John Milton Cage (1912-1992), who is considered one of the most famous and influential avant-garde musicians of the twentieth century. The composer's ideas about sound, the "open form of music", "random operations", "extended" musical instruments and many others were developed in the complex technical, discursive, institutional, cultural and political conditions of life in the United States, constantly changing in the course of his long and productive career.
The article analyzes the "artistic and theoretical" legacy of composer John Cage in a philosophical and aesthetic way and shows how his work problematized artistic inventions in music, blurring the boundaries between artistic expressive forms, and his legacy became not only interdisciplinary, but also transdisciplinary, as a result of which the composer's musical experiments were reflected in the work of such American artists like Bill Childs, Fritz Reiner, David Tudor, Christian Wolf, Morton Feldman, Earl Brown, La Monte Young, Pauline Oliveros, Cornelius Cardew, etc. The scientific novelty of the article is that the author attempts to comprehend the creative path of the composer as one of the radical innovators in music, whose musical innovations during the 50s, 60s of the twentieth century led to paradigmatic changes in all areas of American art. Cage fundamentally rebuilt the ideas of what music was and what music could be, eventually becoming one of the most influential avant-garde composers of his time, largely predetermined the trends of the movement of American musical culture of the twentieth century. Cage's experimental innovation, the composer's ability to capture the spirit of the times and the anticipation of many creative ideas related to the nature of sound, made his works an integral part of world culture, an important milestone in the modern development of music

Abstract: The subject of this research is the philosophical grounds that predetermined the discovery of proof of the existence of incommensurate or irrational magnitudes in the philosophy of Pythagoreans at the time when the very notion of irrationality was an anathema for those suggesting that the numbers were the rational entities underlying the Universe. Therefore, it became possible to express both, physical and cultural-aesthetic consistencies, by the similar to each other mathematical rows and geometrical proportions that predetermines the calculation methods for harmonic structures, uninterrupted proportions and limiting values – the first premise to the structure of ancient teaching on formation. Based on the interdisciplinary analysis and comparative method of research, the article analyzes the history of discovery of the phenomenon of incommensurability and irrationality. A conclusion is made that back in Pythagoras’ times, this discovery led to the need for substantial transformation of the entire fabric of elementary geometry in anticipation of structuring the general theory of proportions, causing the first in history crisis of ancient philosophy and mathematics. The author also substantiates and traces the discovered by Pythagoreans correlation between the irrational proportions and irrational mathematical constant of “golden ratio” that underlies the architectural proportions in the history of culture, as well as reflected in various regularities and spheres of human existence – science, culture, architecture, and art. Among the main conclusion is also the author’s hypothesis that universality of the irrationality of magnitudes of “golden ration” and their prevalence in the diverse natural and cultural regularities up to the present encourages the pursuance of meanings, which would unite them into a certain common theory that generalizes and expresses the structure of global constants.

Abstract: The article is devoted to the creative work of one of the most influential and contradictory figures in the history of music, American experimental composer of the XXth century, musical theorist, writer, artist, pioneer of aleatoric (accidental) electro-acoustic music and unusual use of musical instroments and the founder of electronic music that is based on accident and uncertainty as the essential and shape-generating element, John Milton Cage (5 September 1912- 12 August 1992). One of the first instrumental actions using aleatory music and noises of nature was his composition 'Water Music' that was created in 1952 for two 'prepared' pianos with the radio, water containers, card pile, stick, and a stop watch and used the sound of water as the main element of composition. It was one of the compositions that made John Cage popular around the world. Through denying deeply established composition principles, Cage rethought and essentially predetermined the experimental practice of music, thus changing the course of modern music and forming a new concept of the after-war art of the XXth century. The author of the present article views the composer's experimental creativity as one of the most radical attempts in the history of music aimed at extending the borders of music and applying new materials for composing and playing music. In the course of the research the author has used the philosophical aesthetic research method. The research methodology is based on the interdisplinary definition of such concepts as the uncertainy principle, choas theory, stochastic (probable) procedures, 'accidental operations', etc. The given article is one of the first one to provide an in-depth research of one of the most unique experimental compositions of Cage 'Water Music' and cover the theoretical gap in Russian academic literature on musical art concerning the composer's versatile creativity and personality. The author of the research makes a thesis that Cage created his own creative method that is based on the principle of managed accident, unity of life, nature and art, invention of new materials and instruments for creating and performing music. Along with other numerous theoretical and instrumental innovations that led the composer to the radical extension of the sound space and, in fact, changed the subject of the music in general. 

Abstract: The present publication is a translated article published in Vienna. Its form corresponds with the original publication, copyright rules and the author’s will. However, taking into account the peculiarities of our journal, we have to put footnotes inside the text in parentheses. We’ve kept author’s references to publications. We’ve also kept fonts and text style of the original edition.
Karlheinz Essl (born 1960 in Vienna) is an Austrian composer, performer, improvisator and “sound artist”. At the University of Vienna, he studied musicology; in 1989 he defended doctoral dissertation. In 1992–1993 Essl worked for the IRCAM commission in Paris. In 1994 he became a music supervisor of a collection in Klosterneuburg (Vienna). Between 1995 – 2006, he taught algorithmic music at the studio of promising music and media technologies named after an Austrian composer and organist Anton Bruckner in the The Anton Bruckner Private University for Music, Drama and Dance in Linz (Austria). Since 2007 he has been a professor of composition in electroacoustic and experimental music at the University of Music and Performing Arts Vienna. Essl’s work with computers with a focus on algorithmic compositions and music reproduction has had formative influence on his compositional thinking. Essl also works in the field of electronic music, real-time interactive compositions and sound installations. Since the early 1990s he has created various software environments for real-time compositions, which he uses in his live music performances and together with artists from other spheres – choreographers, dancers, artists and poets. In 1998 Essl started designing a computer electronic instrument M @ ZE 2. He uses it as an improvisator in live performances.
The publication, which realizes the interdisciplinary method of studying modern electronic music technologies, also contains the results of Essl’s work, who studies and creates electronic and interactive music, composes various music compositions and real-time sound installations. Music works of the composer form from the collisions of ordered, abstract models and original tonal expressive structures. The scientific novelty of the study consists in the fact that the translation of the article fills one of the gaps in Russian scientific literature about the studies of philosophy and aesthetics of music, devoted to the problem of historic development of electroacoustic music as, according to K. Essl, forming, generating and far-reaching musical potential. The paper also contains a detailed description of the composer’s research work with a focus on algorithmic compositions and generative music. 

Abstract: The present publication is a translated article published in Vienna. Its form corresponds with the original publication, copyright rules and the author’s will. However, taking into account the peculiarities of our journal, we have to put footnotes inside the text in parentheses. We’ve kept author’s references to publications. We’ve also kept fonts and text style of the original edition.
Karlheinz Essl (born 1960 in Vienna) is an Austrian composer, performer, improvisator and “sound artist”. At the University of Vienna, he studied musicology; in 1989 he defended doctoral dissertation. In 1992–1993 Essl worked for the IRCAM commission in Paris. In 1994 he became a music supervisor of a collection in Klosterneuburg (Vienna). Between 1995 – 2006, he taught algorithmic music at the studio of promising music and media technologies named after an Austrian composer and organist Anton Bruckner in the The Anton Bruckner Private University for Music, Drama and Dance in Linz (Austria). Since 2007 he has been a professor of composition in electroacoustic and experimental music at the University of Music and Performing Arts Vienna. Essl’s work with computers with a focus on algorithmic compositions and music reproduction has had formative influence on his compositional thinking. Essl also works in the field of electronic music, real-time interactive compositions and sound installations. Since the early 1990s he has created various software environments for real-time compositions, which he uses in his live music performances and together with artists from other spheres – choreographers, dancers, artists and poets. In 1998 Essl started designing a computer electronic instrument M @ ZE 2. He uses it as an improvisator in live performances.
The publication, which realizes the interdisciplinary method of studying modern electronic music technologies, also contains the results of Essl’s work, who studies and creates electronic and interactive music, composes various music compositions and real-time sound installations. Music works of the composer form from the collisions of ordered, abstract models and original tonal expressive structures. The scientific novelty of the study consists in the fact that the translation of the article fills one of the gaps in Russian scientific literature about the studies of philosophy and aesthetics of music, devoted to the problem of historic development of electroacoustic music as, according to K. Essl, forming, generating and far-reaching musical potential. The paper also contains a detailed description of the composer’s research work with a focus on algorithmic compositions and generative music. 

Abstract: The subject of research is the work of a renowned American composer, music theorist, artist and a pioneer of aleatory (chance music) in electroacoustic music John Milton Cage (05.09.1912 - 12.08.1992), author of the famous "prepared piano" and the piece  4'33'', the comosition of 'music silence'. Conceived by the composer in 1947-1948, the piece became for Cage the epitome of his idea that any sounds may represent and constitute music. The composer developed the idea of expanding the space of the academic performance of concerts by the use of natural sounds as elements of the music that changed not only the notion of music but also the concept of the musical material. Music critics evaluated John Cage as one of the most influential American composers of the twentieth century and one of the leading figures of the post-war avant-garde. In his research Lipov has used the philosophical - aesthetic method for studying the diverse creative work of the composer that formed the basis for the evaluation of the piece 4'33'' as a model of the music of silence and examples of the and music of noise and aleatoric music because it forms random sounds of the environment. The author examines the experimental work of the composer as one of the most radical attempts in the history of music to transform the musical text, to extend the boundaries of the art of music and the use of new sound materials for composing music. The main contribution of the author's research is that the research fills in theoretical gaps in Russian academic literature on the art of music and aesthetics of music in relation to the creative work and personality of the composer. 

Abstract: The subject of research is the work of a renowned American composer, music theorist, artist and a pioneer of aleatory (chance music) in electroacoustic music John Milton Cage (05.09.1912 - 12.08.1992), author of the famous "prepared piano" and the piece  4'33'', the comosition of 'music silence'. Conceived by the composer in 1947-1948, the piece became for Cage the epitome of his idea that any sounds may represent and constitute music. The composer developed the idea of expanding the space of the academic performance of concerts by the use of natural sounds as elements of the music that changed not only the notion of music but also the concept of the musical material. Music critics evaluated John Cage as one of the most influential American composers of the twentieth century and one of the leading figures of the post-war avant-garde. In his research Lipov has used the philosophical - aesthetic method for studying the diverse creative work of the composer that formed the basis for the evaluation of the piece 4'33'' as a model of the music of silence and examples of the and music of noise and aleatoric music because it forms random sounds of the environment . The author examines the experimental work of the composer as one of the most radical attempts in the history of music to transform the musical text, to extend the boundaries of the art of music and the use of new sound materials for composing music. The main contribution of the author's research is that the research fills in theoretical gaps in Russian academic literature on the art of music and aesthetics of music in relation to the creative work and personality of the composer. Moreover, this article is the first most comprehensive theoretical and aesthetic research devoted to the main musical composition of John Cage 4'33", the piece that fills an important niche in the history of music between the usual musical production and the sounds of nature. Cage's music consists of imitations of natural sounds and human voices which helps Cage to complete a brilliant musical process and overcome the cultural distance that has developed in classical music. 

Abstract: The translation of the scientific article is devoted to research of life and research activity of the Jesuit Afanasius Kirkher (1602 – 1680) - the German scientist –polymath, the inventor, "the scientist with world reputation", to the universal genius in the history of science: in cultural areas, divinity and different "innovative" activity which hasn't equal on completeness and universality of scientific knowledge. Kirkher was at the same time the inventor, the composer, the geographer, the geologist, the Egyptologist, the historian, the traveler, the philosopher, the owner of one of the first public museums, the physicist, the mathematician, the astronomer, the archeologist and the author more than 40 large published works. Article represents first and the fullest scientific translation from German in Russia of the published scientific research devoted to the scientist - to the theologian from the quarterly magazine "Borderline Researches in the field of Science" which is the edition of institute with the similar name of theologians and psychologists of area of SouthernTyrol in Austria (Innsbruck) [1] devoted to research of the interdisciplinary areas designated in terms of the Russian science as paranormal areas of consciousness and mentality. The translation meets a lack in the history of science of multilateral research activity of the outstanding scientist as Kirkher as Newton, Boyle, Leibniz and Descartes' contemporary, didn't take the lawful place in the history of scientific knowledge for the reason that owing to the ability of anticipation in due time as the Jesuit and the theologian he tried to combine some provisions of the Bible and secular, scientific gnoseology in a uniform view of the world. With considerable delay the scientific world recognized an unilaterality only traditionally - the scientific point of view on a peace arrangement and began to give more and more attention in the history of science to that scientists who aspired to the most complete idea of space and earthly world order.