… “Then he decided to achieve an emancipated musical discourse through re-examination of all parameters of music” (taken from Wikipedia)
“Carter brought together the most disparate worlds without seeking synthesis! This is what I find so fantastic. He did not seek to synthesize Schönberg’s expressivity and Stravinsky’s rhythmic energy or neoclassicism, but created both worlds together, so to speak. He let himself and his music be influenced by both worlds at once and lived in both worlds at once.”
“The fact that he dealt with such differing worlds at the same time is perhaps the reason for, to put it negatively, an unnecessary complexity #1 of his music from the 1950’s to the 1970’s”.
#1 The unnecessary complexity is only on its first, input layer, and when we look at it in the hidden layers, it creates the potential for occurance of the beauty of rhythm_melody – a new structure/distribution, that has nothing to do with either rhythm or melody as isolated properties. And which smoothly extends the melody to rhythm and back in spite of the heterogeneous components of its manifold, similarly as the spacetime dimensionality is smoothly extended in mathematical analysis.
“He always sought unity without compromise or synthesis.”
“He never gave up the idea of contrapuntal thinking”
“For me personally, Elliott Carter is also one of the most important composers of the 20th and 21st centuries because he represents substance. He is living proof of uncompromising, complex music, and is for this reason at first glance inaccessible. When one delves into the music and sees its development, it becomes more accessible. I believe this is Carter’s great lesson: to always concentrate uncompromisingly on the musical substance, and not to try to incorporate popular elements like so many composers today. I don’t want to name any names, but there is too much so-called “contemporary” music that gives not very curious interpreters the opportunity to claim that they are also interested in contemporary music. This is in fact simply a populistic attitude, and the “contemporary” aspect is usually limited to the fact that the composer still lives and may even be young”.
 Elliott Carter and his use of metric and temporal modulaton in his Eight Pieces for Four Timpani : an
examination into the application of click tracks during the preparation and performance of these works
 The sense of opening
 Harmony Book
Along with Carter i believe he has smoothly extended serialism into rhythm_melody (my heuristic invention) as the inhomogeneous/relativistic smallest part of the musical texture. And that is the new music theory, which distributes/integrates harmony and counterpoint, rhythm and melody into an independent manifold, a structure-forming identity, unalterable by any distortion.