Rhythmical Aspects

Ligeti was one of few composers to be aware of Joseph Schillinger's works. Schillinger (1895-1943)[5] was a composer, music theorist and composition teacher. He endlessly followed the idea of merging sciences and music.

Combining music and mathematics is a long-term dream of many musicians. From Aristotle to Jean-Philippe Rameau and to Iannis Xenakis, scientifically oriented musicians have sought (and some of them actually found) interesting ways of dealing with musical matters by using their scientific backgrounds.

Schillinger was a very versatile musician. He had some mathematical background and was very found of Jazz music. It is said that the created the first Band in his native Ukraine.

As a technology oriented composer he worked closely with Leon Theremin (1896-1993) and composed music for the Thereminovox. He himself invented some interesting musical instruments, with the Rhythmicon (1932) among them which can be considered as the first rhythm-machine.

Schillinger settled and worked in the U.S.A. where he was teacher at the Columbia Teachers College and was also giving private lessons, often by mail.

Among his well-known students were George Gershwin, Glenn Miller, Robert Emmett Dolan, Carmine Coppola, Vic Mizzy, Leith Stevens, John Barry and many others.

He has been very influential to music composers working in the motion picture industry in the early forties.

From his rational way of dealing with music theory and composition emerged a Schillinger System of Musical Composition[6]. His mailed private lessons were compiled and edited by Lyle Dowling and Arnold Shaw in a monumental book which is published with that title.

His other important work, to which he was referring to ``as his most important book'' is The Mathematical Basis of the Arts[7].

The book has many insights on the process of artistic creation, the history of music and arts.

Few sample citations will enlighten this very important music thinker's approach by doing so it will also help to set Ligeti's attitude and some of his compositional techniques.

Joseph Schillinger wrote in his The Mathematical Basis of the Arts[7]

The history of art may thereupon be described in the following form:
32#32

[...]

It is time to admit that aesthetic theories have failed in the analysis as well as synthesis of art.

[...]

The cult of craftsmanship transforms into formalism and scholasticism.

Despite his outstanding contributions Schillinger is curiously unknown in music theory circles. Among those contributions are: a very systematic and complete theory of voice-leading by using simple circular permutation techniques and modulo arithmetic, an interesting theory of pitch scales and symmetrical divisions of one or more octaves^3.5, interesting investigations on the semantics of the music, enlightening opinions on orchestration and instrumentation...

However his most important contributions are probably in the field of the musical rhythm.